tag:blogger.com,1999:blog-66455838429722044432024-03-27T16:53:01.207-07:00The Education ScientistAnonymoushttp://www.blogger.com/profile/11351479269650780356noreply@blogger.comBlogger19125tag:blogger.com,1999:blog-6645583842972204443.post-74565992438395462532015-09-15T07:00:00.000-07:002015-09-15T07:00:00.592-07:00Learning the Times Tables? Here's How to Do It - Without Tears!<span style="font-family: Arial, Helvetica, sans-serif;">The multiplication facts (or “times tables”). </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">They’re important. Kids who don’t know them will struggle later in math.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">But many kids resist learning these facts, complaining that they are boring and pointless. And many parents dread them, having had similar experiences as students themselves (and maybe having forgotten their math facts by the time their kids are learning them).</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Let’s look at how we can apply a bit of insight from learning science to make the times tables easier to learn and remember.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">What’s the problem?</span></h2>
<span style="font-family: Arial, Helvetica, sans-serif;">The multiplication facts are usually presented in a table like the one below (the familiar “times table”). We’ll focus on the facts from 1x1 through 10x10 here.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQsEyWDuB0eTukJsOZTjfBn4kCdojjCCzxPUZpb6NECZemXmFGQfUu_SeZt5dYZtFoXlpX-3JY7Rz-4qprphe9zlHDhvZLVOMHjs4CMEvcSzTKmyqSp_l8OtV8SA3ur4ID3eslaRAsWXVD/s1600/Image01.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQsEyWDuB0eTukJsOZTjfBn4kCdojjCCzxPUZpb6NECZemXmFGQfUu_SeZt5dYZtFoXlpX-3JY7Rz-4qprphe9zlHDhvZLVOMHjs4CMEvcSzTKmyqSp_l8OtV8SA3ur4ID3eslaRAsWXVD/s400/Image01.gif" width="512" /></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">The most common strategy for learning the facts is “brute force memorization” – which means using a combination of worksheets, drills, flashcards and the like to badger the brain into remembering this information through sheer repetition – that is, repeating the same problems over and over again. </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">If the brain were like the hard drive on your computer, this might be fine. In fact, we can enter the table of numbers above into a spreadsheet and save it to our computer’s hard disk on the first try – no problem at all.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">But we know from brain research that your brain is <i>nothing like</i> the hard drive on your computer. In fact, brute force memorization alone is probably one of the <i>worst possible ways</i> for a human being to learn something. Brute force memorization can be unpleasant - no wonder kids resist it! – and it’s ineffective. Even if you manage to hammer the information in there, it’s more likely than not to leak away pretty quickly.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">There is a better way</span></h2>
<span style="font-family: Arial, Helvetica, sans-serif;">The brain isn’t set up to store large numbers of isolated facts rapidly (like a hard drive). Instead, it’s set up to identify and encode <i>meaningful patterns</i>. </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">What kinds of patterns? Well, visual relationships and symmetry are two good examples. Let’s take a look.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">How is the times table constructed?</span></h2>
<span style="font-family: Arial, Helvetica, sans-serif;">Have you ever thought about where the times table comes from? To understand that, first think about what a multiplication represents. </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">If we take a multiplication like 8x4, we are saying we want to copy one number (the multiplicand) a certain number of times (the multiplier). There’s no hard and fast rule about which order the multiplier and multiplicand are written. For our purposes, consider the first number (8) to be the multiplicand (the number being copied) and the second number (4) to be the multiplier (the number of copies). So in this case “eight times four” means “copy the number eight, four times.” (Note that the word “multi-ply” is derived from the words for “many layers” – you can see why in the diagram below).</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiq5toG5-h6xklX7g-Vg3CoVEqwpGwmnIX5GXOypIk32PptYJLqXCDpIM_5I3FjPxa7rmnYP-4WWqTjczzb5MKZGQhs8ge7pZx6KdieaARJAcMYr4cGh2qPhQigmrf2QTYx7bomkg-MqQJb/s1600/Image02.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiq5toG5-h6xklX7g-Vg3CoVEqwpGwmnIX5GXOypIk32PptYJLqXCDpIM_5I3FjPxa7rmnYP-4WWqTjczzb5MKZGQhs8ge7pZx6KdieaARJAcMYr4cGh2qPhQigmrf2QTYx7bomkg-MqQJb/s400/Image02.gif" width="512" /></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">How do we get from the four eights to the result of the multiplication (which is 32)? Easy – just count out the number of squares in the whole rectangle like so…</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOYcaFaGufRHy5-3KYLFbwMr4KtJv-g3gIrXsyeTVRQyq3pdd3opqlUlR_VxkBpKqDWIVzfDbhpo4UmDATakmho1sETr5U7xci1d0sh6PMcT7xmMMoNtMj-BJz4eAyClIDwUCB0j5gsfEJ/s1600/Image03.gif" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOYcaFaGufRHy5-3KYLFbwMr4KtJv-g3gIrXsyeTVRQyq3pdd3opqlUlR_VxkBpKqDWIVzfDbhpo4UmDATakmho1sETr5U7xci1d0sh6PMcT7xmMMoNtMj-BJz4eAyClIDwUCB0j5gsfEJ/s640/Image03.gif" width="512" /></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">The familiar times table is made up of all the rectangles representing all the multiplications from 1x1 to 10x10 laid one on top of the other, so that only the very last square of each one - containing the final count of squares in that rectangle - peeks through. If you look at the cell for the multiplication of interest, you can see that it is at the top, right corner of a rectangle that represents the multiplication of interest (and covers that number of squares).</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbzlJ1BDwIGRXQuMAehyphenhyphenQm5weX-VI35e9xfRe4sF9uyzBnUIkcQlgExhuFMZ-Qfenosj415d1jyJxd5a0051ofpAFOf5ZQ80dh6XzjhreJgz-W230UmlWkBoHpNv623BU83ePrPrM0C9-N/s1600/Image04.gif" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="334" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbzlJ1BDwIGRXQuMAehyphenhyphenQm5weX-VI35e9xfRe4sF9uyzBnUIkcQlgExhuFMZ-Qfenosj415d1jyJxd5a0051ofpAFOf5ZQ80dh6XzjhreJgz-W230UmlWkBoHpNv623BU83ePrPrM0C9-N/s640/Image04.gif" width="640" /></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">This visual relationship between the individual multiplication problems and the structure of the whole table can help students understand and remember the facts, because they can start to picture the problems visually in their mind’s eye. Also, if they forget one of the facts, then this conceptual understanding gives them a way to reconstruct it from known facts nearby. </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">How can symmetry help students learn the facts?</span></h2>
<span style="font-family: Arial, Helvetica, sans-serif;">Consider the multiplication 8x4=32. This means, “copying eight squares four times gives you thirty-two squares.” Notice that 4x8=32 means something different, namely “copying four squares eight times gives you thirty-two squares.” The picture below shows the two visually. </span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiAdato6MRTa_ZNAZbiSbBImzxwXHE4UzFPT_L-hP3L19-cT1R2wJXucE5gfZBX3P4rMAZTTjNWw997LQBmjothoXIay4gWnva5nSJWqqmzX9W08_6ddbn6xJ6Mn63g9nmj5-kumkVphSP/s1600/Image05.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="256" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiAdato6MRTa_ZNAZbiSbBImzxwXHE4UzFPT_L-hP3L19-cT1R2wJXucE5gfZBX3P4rMAZTTjNWw997LQBmjothoXIay4gWnva5nSJWqqmzX9W08_6ddbn6xJ6Mn63g9nmj5-kumkVphSP/s400/Image05.gif" width="400" /></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">The rectangles represented by the two multiplications are different shapes, but they give the same result in the end (32 squares). This works for any two numbers you multiply – changing the order changes the rectangle’s shape but doesn’t change the quantity that results. This is called the <i>commutative property</i> of multiplication. </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Now let’s apply this insight back to our times table. Look at the table below. It’s the same as the one above, but color-coded to highlight the symmetry associated with the commutative property. Notice that if you folded the table on its diagonal, the numbers in the two halves would overlap perfectly.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjW8eBmnB3U7pP7kefcG0MX6VZtAGA-CHecqU4pZF3sj2qjaQ0yw1bT7Nj9w6SxR_JnXuYFtrOpH2V5FFiHbJw4Nbz8eqt4eyhZ1QYj8FcoP6JBDq7lviZfTh9f05_z0uyepnm8lkY3ZVev/s1600/Image06.gif" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="390" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjW8eBmnB3U7pP7kefcG0MX6VZtAGA-CHecqU4pZF3sj2qjaQ0yw1bT7Nj9w6SxR_JnXuYFtrOpH2V5FFiHbJw4Nbz8eqt4eyhZ1QYj8FcoP6JBDq7lviZfTh9f05_z0uyepnm8lkY3ZVev/s640/Image06.gif" width="640" /></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">For students, this is great news – it means instead of memorizing all 100 facts, they can learn 55 facts (45 facts in one of the triangles plus the ten facts along the diagonal that are perfect squares like 1x1 or 4x4 – on the diagonal the multiplicand and multiplier are the same and so they have no mirror image). Learning this one relationship cuts the number of facts almost in half instantly. </span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJl3WsVabIyw2FuvIswThUUXISl4yyiaA_5PGkkQ0lt-YrfE2DErpFXSLkfAzxHPpFZCfIli0oPNQm2PMfS-PIBRBoebjbbQab4aVIA05vg-lB1LZho9l19lUGx4JMNU1nZSovMdirQ9vf/s1600/Image07.gif" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="392" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJl3WsVabIyw2FuvIswThUUXISl4yyiaA_5PGkkQ0lt-YrfE2DErpFXSLkfAzxHPpFZCfIli0oPNQm2PMfS-PIBRBoebjbbQab4aVIA05vg-lB1LZho9l19lUGx4JMNU1nZSovMdirQ9vf/s640/Image07.gif" width="640" /></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Multiplying by 1: Mono-plying</span></h2>
<span style="font-family: Arial, Helvetica, sans-serif;">We can cut the number of facts down further by looking at specific groups of facts. Multiplying by one, for example, is not really multiplying at all – it’s mono-plying (if multi-ply means “many layers” then mono-ply means “one layer”). </span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaI48EmMWCQA80yH3HvAgrztUaIM8dEnnvTc2p3vm_YcD9zqqG5obkER10N7gSSW-kfXdzysGF19BoIDJK8kwI4GS20YgD5F-E774uBty6TORz989EEAUdMmazIacZ2q07V4RxePHA8KBH/s1600/Image08.gif" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="194" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaI48EmMWCQA80yH3HvAgrztUaIM8dEnnvTc2p3vm_YcD9zqqG5obkER10N7gSSW-kfXdzysGF19BoIDJK8kwI4GS20YgD5F-E774uBty6TORz989EEAUdMmazIacZ2q07V4RxePHA8KBH/s640/Image08.gif" width="640" /></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Remembering the mono-plying rule (multiplying any number by 1 gives you back that same number) takes care of another ten facts, leaving us with just 45 facts to learn.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgg7OLMZlkClPPAIUrM8Or8_RIaUyY9kqHXN0YvB71K3226lrOHIsOIZX2NeK9ZyHAkUGea14vTwELfXqhLi76Z5heRrQ_-xVJ5XBuRXJTt44JB5IH41_uiWfPFR3DJDPieqkxDRbZ3uCyf/s1600/Image09.gif" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="390" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgg7OLMZlkClPPAIUrM8Or8_RIaUyY9kqHXN0YvB71K3226lrOHIsOIZX2NeK9ZyHAkUGea14vTwELfXqhLi76Z5heRrQ_-xVJ5XBuRXJTt44JB5IH41_uiWfPFR3DJDPieqkxDRbZ3uCyf/s640/Image09.gif" width="640" /></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Multiplying by 10</span></h2>
<span style="font-family: Arial, Helvetica, sans-serif;">Multiplying tens is easy, too. It’s just like multiplying by one except you append a zero to the result.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">2x1 = 2 and 2x10 = 20 = “twenty” (derived from the words “twin tens”)</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">3x1 = 3 and 3x10 = 30 = “thirty” (derived from the words “three tens”)</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">4x1 = 4 and 4x10 = 40 = “forty” (derived from the words “four tens”)</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">and so on…</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">To see why, look at the picture.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGFfRij8DuD4XguIWnBDusKscD0IrJP56ejQj_yzsigaH9KcybUG-8nC-Jv1vI_NSqvztNo-2fj71oaHVEtIJPAQD11wWF4y7411B4ZVlNuw5a3IcI3XIDtVsCxW0kM02R4nTuc23Cjijy/s1600/Image10.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="192" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGFfRij8DuD4XguIWnBDusKscD0IrJP56ejQj_yzsigaH9KcybUG-8nC-Jv1vI_NSqvztNo-2fj71oaHVEtIJPAQD11wWF4y7411B4ZVlNuw5a3IcI3XIDtVsCxW0kM02R4nTuc23Cjijy/s400/Image10.gif" width="400" /></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Adding the rule for multiplying tens takes care of another nine facts, leaving just 36 to learn. </span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqRbUkrUmD-NVFYr8zaszor5Q0OZta4tZTcBCpk2OSu9-JtiJHMHAcWoFmfLYlPCBXpXBa6mhjnoZwKdHI5khsqT-tRRWTPJ9IKsP33P7BQ9wE0q6IVIe-RZyd5ywhNoNIVZJeek1XFrS-/s1600/Image11.gif" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="368" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqRbUkrUmD-NVFYr8zaszor5Q0OZta4tZTcBCpk2OSu9-JtiJHMHAcWoFmfLYlPCBXpXBa6mhjnoZwKdHI5khsqT-tRRWTPJ9IKsP33P7BQ9wE0q6IVIe-RZyd5ywhNoNIVZJeek1XFrS-/s640/Image11.gif" width="640" /></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">If 36 multiplication facts still seems like a lot, consider that there are 26 letters in the English alphabet plus ten digits that have names (zero, one, two, etc.), which is also 36 facts. Your child memorized those, and you can use the same kinds of techniques for the remaining 36 times table facts. Just keep in mind that helping a child to understand where the facts come from along with patterns like the visual relationships between rectangles and the symmetry that comes from the commutative property will make learning the facts (and other things later, like long multiplication, division, and algebra) much easier. The knowledge will also stick better and last longer.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Summary</span></h2>
<span style="font-family: Arial, Helvetica, sans-serif;">To summarize, we started with 100 multiplication facts to learn, from 1x1 through 10x10. </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">First we introduced a few key concepts:</span><br />
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<li><span style="font-family: Arial, Helvetica, sans-serif;"><u>What is multiplication?</u> It’s copying one number a specified number of times (as in “eight times four” and “times table”) and counting up the quantity that results</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><u>Where does the times table come from?</u> From stacking all the multiplication rectangles on top of one another, letting just the last square of each with the total quantity for that rectangle show through</span></li>
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<span style="font-family: Arial, Helvetica, sans-serif;">Then we introduced a few key rules:</span><br />
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<li><span style="font-family: Arial, Helvetica, sans-serif;"><u>Commutative Property</u>: It doesn’t matter which order you multiply two numbers – it means something different but you still get the same result (Example: 8x4 = 4x8 = 32)</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><u>Multiplying by one (or mono-plying)</u>: When you multiply any number by one, you just get that number back</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><u>Multiplying tens</u>: Just like multiplying by one, except you append a zero to the result (Example: 1x4 = 4 and 10x4 = 40). Remember: the name “forty” is just a short form of “four tens”</span></li>
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<span style="font-family: Arial, Helvetica, sans-serif;">With these few rules we cut down the number of facts to a manageable 36. Not only does this reduce the memorization load by about two-thirds, but the conceptual understanding will make the remaining facts easier for students to learn and remember.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Additional resources</span></h2>
<span style="font-family: Arial, Helvetica, sans-serif;">This is a lot of information (who knew there was so much to know about the lowly times tables?).</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Some teachers, tutors, and parents can make use of it in the form it’s presented here in the blog post. To make it easier for everyone else, I’ve packaged this information up into some free videos and a couple of inexpensive apps for iPhone and iPad - each priced less than a <a href="http://www.staples.com/Oxford-3-x-5-Unruled-White-Index-Cards-100-Pack/product_517524" target="_blank">pack of index cards</a>. (Note: If you are searching for one of the apps on an iPad, you'll need to change the default filter from "iPad" to "iPhone" apps to find them).</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Another great way to help kids learn is to insert yourself into the process – show them you’re interested and available to help if they need it. The same way you read books to your children when they were small, you can sit with them and work through some math mini-lessons at the table, in Minecraft, or using these apps.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>Video examples of using Minecraft to learn arithmetic:</b></span><br />
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<li><a href="http://theeducationscientist.blogspot.com/2013/08/teaching-math-with-minecraft-impromptu.html#.VFDIt_TF8QS" style="background-color: white; color: #6ea1bb; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 15.4px; line-height: 21.56px; text-decoration: none;"><span style="font-family: Arial, Helvetica, sans-serif;">Minecraft Math #1: Numbers - Even, Odd, Prime & Square Root</span></a></li>
<li><a href="http://theeducationscientist.blogspot.com/2014/01/teaching-math-with-minecraft-2.html#.VFDI6_TF8QQ" style="background-color: white; color: #6ea1bb; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 15.4px; line-height: 21.56px; text-decoration: none;"><span style="font-family: Arial, Helvetica, sans-serif;">Minecraft Math #2: Addition, Multiplication & Commutativity</span></a></li>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>Bognor’s curse – An Interactive Educational Mini-Adventure</b></span><br />
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<a href="https://itunes.apple.com/us/app/bognors-curse/id969509748?mt=8" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;" target="_blank"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijy7L_cng5POlLYlWtwpiFU2Vsk9eI-9f9fy53AgiPluC-Ub9Ql_c_2jPUOPPyo0D45EF0NJivYQQbBb-eEl1UsLab9vZ6_6nMmjY7uukCllh06BcLRqp_5rGFLjF7DS6C2LE3CF9UQGqY/s1600/Image12.gif" /></a></div>
<i style="font-family: Arial, Helvetica, sans-serif;">Something’s gone terribly wrong at the Ministry of Magic. The evil wizard Bognor has cast a terrible curse across the land and it’s up to you – a lowly apprentice – to defend your village and defeat his dark magic. To succeed, you’ll have to master some basic Arithmancy. Will you do it?</i><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><a href="http://bit.ly/1OaG08l" target="_blank">Watch the video</a></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><a href="http://bit.ly/BognorsCurseApp-iTunes" target="_blank">Experience the magic</a></span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>Multiplication Explained – Master the Times Tables with Understanding</b></span><br />
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<a href="https://itunes.apple.com/us/app/multiplication-explained-master/id855749165?mt=8" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;" target="_blank"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVnaZhCP5pdGOSNjaU11F5uNW_Jj8uouoOjh2HcEmUAV8NgzV-IyDzP3wo78qyoHvQBZeaaOgkUf6GJNqPQdx3IiYcF7hoxjag85UwqFN4-6o4v4au0fx89ZeB-kv5MpjPTo4adWt4cFIY/s320/Image13.gif" width="193" /></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><i>Multiplication Explained is more than a typical flashcard app. It is a complete mini-curriculum designed to promote both conceptual understanding and fact fluency at the same time. </i> </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><a href="http://bit.ly/1NzlIFB" target="_blank">Watch the Video</a></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><a href="https://itunes.apple.com/us/app/multiplication-explained-master/id855749165?mt=8" target="_blank">Get the App</a></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>Comment and share!</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">I always love to hear from parents, teachers, and students about ways I can make these resources more useful to help you learn and teach, and what other topics you would like to explore in the blog. </span>Anonymoushttp://www.blogger.com/profile/11351479269650780356noreply@blogger.com73tag:blogger.com,1999:blog-6645583842972204443.post-2664593405921024082015-08-17T08:00:00.000-07:002015-08-20T07:35:09.704-07:00Educational Assessment: A Huge Waste of Time and Money?<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNNyzP0uw7L0bQN0V9OqIljhzJk81sBH1tchERANtd4RB6bxLtGsZ5GCh0Ee72y6rv7uHfcwju_SDxkHdsQ0nj89rAAAVg31zD8Mk7QOMV_5lnmsKAtxMEJw0UsyUbB7-fEqIytSX1P8MR/s1600/Driving+Map+LA+to+NYC+512x.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: #444444; font-family: Arial, Helvetica, sans-serif;"><img border="0" height="167" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNNyzP0uw7L0bQN0V9OqIljhzJk81sBH1tchERANtd4RB6bxLtGsZ5GCh0Ee72y6rv7uHfcwju_SDxkHdsQ0nj89rAAAVg31zD8Mk7QOMV_5lnmsKAtxMEJw0UsyUbB7-fEqIytSX1P8MR/s320/Driving+Map+LA+to+NYC+512x.jpg" width="320" /></span></a></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif;"><b>An educational road trip</b></span></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif;">Imagine it’s 1980 - no World Wide Web, no cell phones, no GPS. Your child is learning to drive a car. They have to drive from Los Angeles to New York in time to attend an important event that could well influence the course of their future life. How would you help them do it? They’d need a long-range plan, of course – a map with a route marked out on it. But this plan alone wouldn’t get them there – they’d need to actively interpret the directions in the real world – identifying which of the many small streets is the right one to turn on, looking for signs and landmarks to know when to change lanes and prepare to exit the highway, constantly checking to make sure they didn’t take a wrong turn, and figuring out how to get back on track when they inevitably do. They must, in other words, constantly be <i>assessing</i> the situation – determining where they are on the map, where that puts them in relation to the route, and what to do at each moment to stay on track and on schedule.</span></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif;">This driving scenario is analogous to formal education. In this case, the <i>subject matter</i> (arithmetic, world history, etc.) is the <i>map</i>. The <i>curriculum</i> is the <i>route</i> marked out on the map. The <i>student</i> is the <i>driver</i>. The <i>assessment</i> is the process of tracking location and progress in relation to the route, destination, and schedule.</span></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;"><b>What’s missing from this picture?</b><o:p></o:p></span></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;">If you are a parent, this scenario might make you feel uneasy. Would you really be ok having your child learn to drive while also following a complex and unfamiliar route across thousands of miles over a number of days with important consequences riding on their timely arrival? (Analogously, would you expect that your child would buckle down and successfully learn to read books or master algebra on their own by June, given that they want to be a writer, carpenter, engineer, doctor, or architect when they grow up?) Probably not. If they had to make the trip by car and they had to do the driving, you’d probably want to send someone along with them – a <i>navigator and guide</i> who knows the route well, can coach them on how to drive safely and skillfully, and looks after their well-being during the trip - making sure they leave on time each morning, get plenty of sleep, and don’t get lost or sidetracked visiting roadside attractions along the way.<o:p></o:p></span></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;">In the educational analogy, the <i>navigator </i>is the educational guide. But not a classroom teacher – this navigator is a personal tutor working with one student.<o:p></o:p></span></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;">Imagine that we cannot afford to provide a navigator (personal tutor) for each driver, but that we can allocate one navigator for each fleet of twenty-five cars. These cars are all leaving from different starting cities, at different times, moving at different speeds, with drivers who have different levels of driving experience and skill, and different levels of familiarity with their route. Nonetheless, the fleet navigator is responsible for seeing that all drivers arrive in New York within the same hour.<o:p></o:p></span></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;">In the educational analogy, the <i>fleet navigator</i> is the <i>classroom teacher</i>. The cities the students start in are their prior knowledge of the subject matter (arithmetic, history, and so on), New York represents the destination – the set of learning objectives that the teacher is expected to help all students achieve by a specific calendar date (such as the end of the school year), and the diverse speeds and routes represent the fact that students come to any class with diverse levels of prior knowledge about the subject matter, different capabilities and limitations with respect to learning, different levels of interest in the topic, and so on. And yet the teacher is still expected to get them all to New York within the same hour.<o:p></o:p></span></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;"><b>What does any of this have to do with assessment?</b><o:p></o:p></span></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;">I frequently hear people make statements like this:<o:p></o:p></span></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;">“I feel that all this effort on assessment stuff is mostly a huge waste of time and money.”<o:p></o:p></span></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;">To borrow a line from the film <i><a href="https://en.wikipedia.org/wiki/The_Princess_Bride_(film)" target="_blank">The Princess Bride</a></i>:<o:p></o:p></span></div>
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<i><span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;">You keep using that word ["assessment"]. I do not think it means what you think it means. <o:p></o:p></span></i></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;">When people talk about assessment, they typically seem to be thinking of written tests, and may even have in mind one specific “high-stakes” test. And that is indeed one form of assessment. But assessment, in an educational context, simply means gathering data to figure out where a student is on the map, evaluating where that puts them in relation to the route and schedule, and answering specific questions such as what adjustments to make to keep them on track and on time. </span></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;">Assessment can be done with the eyes and ears as well as with a paper test or an electronic GPS-like dashboard. The personal navigator sitting in the car with the student-driver, for example, is constantly <i>assessing</i> the situation using her five senses – looking for road signs, watching what the driver is doing, feeling the acceleration and deceleration of the car, comparing the car’s location against the marked route, and so on. Believe it or not, that’s assessment. (More specifically, that’s <i>formative assessment</i>.) Another form of assessment is the determination of whether the trip was a success or failure overall – if the child arrives in New York in time for the event, the trip was a success and otherwise it was a failure. (This is an example of <i>summative assessment </i>– in this case, we might call this a “high risk” assessment because the outcome of the assessment correlates with big consequences, for better or worse<i>.</i>)<o:p></o:p></span></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;">The fleet navigator (classroom teacher) obviously can’t be in the car with any of the drivers – she has to manage all twenty-five cars for the duration of the trip. But this is 1980, remember – before GPS and cell phones. So the fleet navigator not only can’t see what every driver is doing inside their cars at any given moment, but she also has no way of tracking precisely where any student’s car is at any given time. She can’t do anything to help the drivers reach their destination without information about their location and progress – she would effectively be flying blind. Classroom teachers face a very similar challenge - they can't directly observe what's going on in students' heads, and they simply can't teach effectively without good information about where each student is and how they are progressing.<o:p></o:p></span></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;"><b>What might we do?</b></span></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;">One reasonable strategy would be to set up a series of checkpoints along the main routes. Drivers check in when they arrive at these checkpoints and that way the fleet navigator can update the map with their approximate locations. If someone fails to check in at the expected time, or if they check in from an alternate location because they cannot find the checkpoint, then the fleet navigator can investigate the problem and decide how to take corrective action to get them back on track.<o:p></o:p></span></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;">These checkpoints are analogous to formal educational assessments – including (but certainly not limited to) written tests. The location of a student’s car is analogous to their state of understanding of the subject matter – their progress in the class relative to the curriculum (route) and learning objectives (destination). The checkpoints (formal assessments or tests) help the fleet navigator (classroom teacher) to know much more precisely where each driver (student) is. Importantly, these checkpoints provide early warning – if we have to wait for the child to miss the event in New York (or fail to achieve the learning objectives by the end of the year) to find out if they were on track all along, by then <i>it’s way too late to do anything about it</i>.</span></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;">The effectiveness of a classroom teacher – like the effectiveness of our fleet navigator – depends critically on the availability of data about individual students. In addition to the informal assessments teachers are doing constantly using their eyes and ears, formal assessments (including tests) are the checkpoints that provide much of the detailed data about how students are progressing, whether they are on track, and what corrective actions the teacher needs to take.</span><br />
<span style="color: #444444; font-family: Arial, Helvetica, sans-serif;"><span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;"><br /></span><span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;"><b>But why can't teachers just give Friday quizzes and find out all they need to know?</b></span></span></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif;"><span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;"><br /></span><span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;">An assessment (quiz, exam, standardized test, etc.) is a measurement instrument - like a ruler, weight scale, or thermometer. Unlike a ruler, however, which measures things that one can actually see, an assessment is a <i>psychometric</i> ruler - it measures knowledge and skills and other intangible entities of the mind that we can't actually see and that are, in fact, much harder to define than an attribute like length or width. </span></span><br />
<span style="color: #444444; font-family: Arial, Helvetica, sans-serif;"><span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;"><br /></span><span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;">Let's ask roughly the same question but in a different domain: "Why do we need to provide engineers and medical doctors with rulers, weight scales, and thermometers to do their work? Why can't they just create their own to find out all they need to know to do their jobs?" There are a number of reasons. Consider calibration, for example. Back in the day people did make and use their own rulers and weights, and they came up with very different measures for the same thing - a major problem if you are paying by the ounce for something, or if you are building a bridge from two ends that should meet in the middle, or if a medical diagnosis depends on the value being measured (body temperature, for instance).</span></span><br />
<span style="color: #444444; font-family: Arial, Helvetica, sans-serif;"><span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;"><br /></span>That's not quite the same as the educational scenario, though. Since we can't see the invisible knowledge constructs we are trying to measure in education, we'd have to actually ask "Why can't engineers and medical doctors just create their own measurement instruments while blindfolded and wearing heavy gloves so they can neither see nor feel the thing they are trying to measure?"</span><br />
<span style="color: #444444; font-family: Arial, Helvetica, sans-serif;"><br />Imagine two math teachers in adjacent classrooms each make up their own 10-question math quiz for the same instructional unit. I've drawn a couple of homemade rulers below to illustrate what that might look like. Obviously, there are major problems with these measurement instruments. Let's consider just a few of the more glaring ones.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjllZutqIsDwOqOMMhLh6lQNzldM6SDcqu07cja9bB-_oXs2f_VgRokuhZ1N2pejvxb0Kt63GNYc-qTHyPMTG_6FnS4Jira9KcrDqx9z6iVgdjP-KE6NV6ZkrKLI8kitCZ11bRG3Ba4EI6i/s1600/HomemadeRuler2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: #444444; font-family: Arial, Helvetica, sans-serif;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjllZutqIsDwOqOMMhLh6lQNzldM6SDcqu07cja9bB-_oXs2f_VgRokuhZ1N2pejvxb0Kt63GNYc-qTHyPMTG_6FnS4Jira9KcrDqx9z6iVgdjP-KE6NV6ZkrKLI8kitCZ11bRG3Ba4EI6i/s320/HomemadeRuler2.png" width="314" /></span></a></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif;"><i>Problems with consistency of measurements</i></span></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif;">Looking at the first ruler, for example, the difference between a score of 1 and 2 is small compared to the difference between a score of 2 vs. 3. The evenness of the numbers masks underlying unevenness in student understanding, which can lead to invalid educational conclusions and actions.</span></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif;"><i>Problems with interpreting scores</i></span></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif;">The second ruler is measuring two different dimensions and adding them together. That would be like adding someone's height in feet to their hair length in inches and reporting the resulting number as a score. How are we to interpret such a score? As a common educational example: when we include printed word problems in our math quiz, a child who struggles with reading may be unable to complete any of them - not because they don't understand the math but because they can't fluently read the problems. Their score doesn't reflect their math competency - it's a combined math plus reading score. </span></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif;"><i>Problems with comparing performance across students</i></span></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif;">Now compare the two rulers. How are we to compare the performance of students across the two math classes? For example, imagine a student in each class scores a 4 on their version of the quiz. What can we say about the performance of the two students? They earned the same score - do they have the same math competency? Certainly not. If you look at the length marked by the 4's, then evidently the second student scored about twice as much as the first student. The numbers are not comparable, but they invite interpretation, evaluation, and decision-making as if they mean something specific and comparable. This is a very real problem that colleges face, for example, when looking at student transcripts. Looking at two applicants from different states, both having a high school GPA of 3.3, how are the admissions officers to compare them? They really can't. Love it or hate it, that's one reason the SAT is so widely used - unlike GPA, standardized tests like the SAT provide a common ruler for measuring student competency in specific domains like math and language so the scores can be compared in meaningful ways across students, classes, and schools.</span></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;"><b>So, is investment in educational assessments a huge waste of time and money?</b></span></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;">There is certainly room for healthy debate about whether any particular assessment is valid and fair, how assessments should be administered to students, and how the assessment data should be used. But is it really reasonable to ask whether we can do entirely without educational assessment in schools? Or whether we should really care about the quality and validity of assessment data? Only if it doesn’t really matter what students are learning or when they are actually learning it. But if that’s the case then we have to ask ourselves this: why do we bother sending our children to formal schools with highly trained teachers in the first place? If we really don’t care what they are learning or when, wouldn’t it be better to send them to day care or adventure camp five days each week instead?<o:p></o:p></span></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;">In fact, assessment is not a huge waste of time and money. But without high quality assessment in place to inform effective instruction, large parts of the rest of the educational system might well be.</span><br />
<span style="color: #444444; font-family: Arial, Helvetica, sans-serif;"><span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;"><br /></span><span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;"><b>Postscript: A peek at the future of educational assessment</b></span></span><br />
<span style="color: #444444; font-family: Arial, Helvetica, sans-serif;"><span style="color: #444444; font-family: Arial, Helvetica, sans-serif; mso-bidi-font-family: "Trebuchet MS"; mso-bidi-font-size: 22.0pt;"><b><br /></b></span>Now fast-forward from 1980. Imagine a world where teachers have the equivalent of GPS in the classroom - that is, continuous, detailed data on student learning plotted in relation to the curriculum goals, delivered in real-time, and actionable at a glance. Yet students never have to take tests. </span><br />
<span style="color: #444444; font-family: Arial, Helvetica, sans-serif;"><br />It may sound far-fetched, but it already exists. It's called "embedded assessment" and we've built such a system over at <a href="http://www.nativebrain.com/" target="_blank">Native Brain</a> to demonstrate conclusively that it's not only technically possible but that it can be made to work at scale in typical public school classrooms - <i>today</i>. (See the screenshot below.)</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhY7CKmR88HLiIaNbj6OK0dG3QMH4tmukFB650rvspTzQN9NVU02-4Wtd50-cIKP30bxe2PO0SnsAD_E2jHFu-WpRWwTzPq6unfunJBE45QqHkhrTW0yUzyi7DFyRQwNguEIZdATGDdBOy_/s1600/NB+Demo+dashboard+with+callout+v02.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: #444444; font-family: Arial, Helvetica, sans-serif;"><img border="0" height="296" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhY7CKmR88HLiIaNbj6OK0dG3QMH4tmukFB650rvspTzQN9NVU02-4Wtd50-cIKP30bxe2PO0SnsAD_E2jHFu-WpRWwTzPq6unfunJBE45QqHkhrTW0yUzyi7DFyRQwNguEIZdATGDdBOy_/s640/NB+Demo+dashboard+with+callout+v02.jpg" width="640" /></span></a></div>
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif;">As I've said before in this blog, we have the know-how right now to make mainstream public school education much, much better than it currently is. The same way that GPS suddenly transformed the way we drive, technology in the classroom can transform the way teachers teach and the way students learn. There is definitely a <i>way</i>. The question is, do we have the <i>will</i> to make it happen?</span><br />
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<span style="color: #444444; font-family: Arial, Helvetica, sans-serif;">(Note: As of the date of this posting the <a href="https://itunes.apple.com/us/app/native-numbers-complete-number/id570231808?mt=8" target="_blank">Native Numbers iPad math curriculum</a> and accompanying <a href="http://www.nativebrain.com/dashboard" target="_blank">GPS-like instructional dashboard</a> are currently available at no cost to parents and teachers.)</span><br />
<span style="color: #444444; font-family: Arial, Helvetica, sans-serif;"><br /></span><span style="color: #444444; font-family: Arial, Helvetica, sans-serif;">Check it out. Send us your thoughts. Share.</span></div>
Anonymoushttp://www.blogger.com/profile/11351479269650780356noreply@blogger.com26tag:blogger.com,1999:blog-6645583842972204443.post-66300550584162983272014-10-28T07:55:00.000-07:002014-10-29T04:02:17.510-07:00Minecraft Scientists Ep. #1: Fishin' In the Rain (STEM Education)<div class="separator" style="clear: both; display: none; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjR218hgmJcFHTeCyqqjz8xWcaRkLdHbZLOXHz77ylZgl52n8udYSfZD5O1EtVWjpvKaX5DQm6H5lCxwJbMSFMN3Jfa-6qXe7B1uLp1RQfIa3Dtgtdk9HLuQ5cIRm4_eUoN226ePJSDeuY/s1600/MCScienceEp1_Thumbnail_512x512.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjR218hgmJcFHTeCyqqjz8xWcaRkLdHbZLOXHz77ylZgl52n8udYSfZD5O1EtVWjpvKaX5DQm6H5lCxwJbMSFMN3Jfa-6qXe7B1uLp1RQfIa3Dtgtdk9HLuQ5cIRm4_eUoN226ePJSDeuY/s1600/MCScienceEp1_Thumbnail_512x512.png" height="320" width="320" /></a></div>
<span style="font-family: Arial, Helvetica, sans-serif;">Minecraft might be the ultimate tool for STEM education (Science, Technology, Engineering, and Mathematics). Check it out...</span><br />
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<object class="BLOGGER-youtube-video" classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0" data-thumbnail-src="https://i.ytimg.com/vi/tzRL9EA_jnI/0.jpg" height="266" width="320"><param name="movie" value="https://www.youtube.com/v/tzRL9EA_jnI?version=3&f=user_uploads&c=google-webdrive-0&app=youtube_gdata" /><param name="bgcolor" value="#FFFFFF" /><param name="allowFullScreen" value="true" /><embed width="480" height="399" src="https://www.youtube.com/v/tzRL9EA_jnI?version=3&f=user_uploads&c=google-webdrive-0&app=youtube_gdata" type="application/x-shockwave-flash" allowfullscreen="true"></embed></object></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><i>(Want to try the experiment yourself? Get instructions in the spreadsheet linked below.)</i></span><br />
<b><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b>
<b><span style="font-family: Arial, Helvetica, sans-serif;">What Is Science?</span></b><br />
<span style="font-family: Arial, Helvetica, sans-serif;">Science – experimental science in particular – is like a game of 20 questions we play with Mother Nature. We have a question like “Am I more likely to catch fish on rainy days than on clear days (or does it make a difference)?” Maybe no human being knows the answer, but Mother Nature does. </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Only she isn’t going to just tell us the answer straight up – she doesn’t speak English, after all. We have to be more clever in how we get the answers from her. </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>The Scientific Method</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">One thing we can do is make a guess (form a hypothesis), and then submit the guess to her (run an experiment). For example, for the question about when you are likely to catch more fish, we might run an experiment like this: go to the same exact fishing spot each day for 10 clear days and 10 rainy days, always arriving and leaving at the same time of day, always using the same rod and tackle, and always using the same bait. (We call this “controlling” for location, time of day, total fishing time, equipment, and bait, and we do it to make sure that it’s the weather and not some other factor like the particular bait we use that is causing any differences in how many fish we catch each day.)</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">The data we get from the experiment (the number of fish we catch on 10 clear days and 10 rainy days) is Mother Nature’s answer to one of our questions, and it might range from “yes” to “probably yes” to “maybe” to “probably no” to “no” to “no comment.” (Also: we usually have to analyze the raw data in some way to find out what her answer actually is.) Through playing this game of 20 questions with Mother Nature and pulling together all of the clues we get from our experiments we can get more precise and certain answers to our questions over time. </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>21st Century Science Education: Real Science in a Virtual World</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">The best (and most fun) way of really learning science is by doing real experiments like the 20-day fishing experiment described above. But real experiments like this one often require a lot of money and time, and so we can’t really do that for every kid. </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Or can we? The video shows an example of doing real science in the virtual world of Minecraft a lot faster and less expensively than we could in the real world - and without having to get wet! </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">File this under “things I wish they had when we were in school.” </span><br />
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<b><span style="font-family: Arial, Helvetica, sans-serif;">Science Can Surprise Us!</span></b><br />
<span style="font-family: Arial, Helvetica, sans-serif;">Swifty7777 and I have run the experiment once (collecting 20 Minecraft days’ worth of data between the two of us – less than an hour of real time) – and, as often happens in science, we were surprised by what we found. In fact, our results seem to contradict what the <a href="http://minecraft.gamepedia.com/Fishing" target="_blank">Minecraft wiki</a> says is true - they indicate you should catch about 20% more fish in the rain than on a clear day. (Watch the video for details on what we found.)</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Who is right – us or the Minecraft wiki?</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>Your Turn! Try the Experiment Yourself</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">You can help us figure it out: replicate our experiment (that means run it again the same way – just like real scientists do!) and see if you get the same results. </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span><span style="font-family: Arial, Helvetica, sans-serif;">Besides, if you really want to learn science, you have to do more than watch videos of other people doing it - you have to get in there and work through it yourself. We've provided an <a href="https://drive.google.com/open?id=0B8S8k6IaF_ugMUgyQTlSUHRYd0k&authuser=0" target="_blank">Excel spreadsheet for you to download here</a> that makes it easy for you to do that.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">If you email your filled out spreadsheet to <a href="mailto:info@i4kd.com">info@i4kd.com</a> with the subject line “Minecraft Fishing Experiment #1”, we’ll post your results so people can compare them to ours.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Happy fishing!</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Epic_MC_Player and Swifty7777</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">// The Minecraft Scientists</span><br />
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<b><span style="font-family: Arial, Helvetica, sans-serif;">Instructions for running the experiment yourself are <a href="https://drive.google.com/open?id=0B8S8k6IaF_ugMUgyQTlSUHRYd0k&authuser=0" target="_blank">here</a> (same as link above).</span></b><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>If you liked this "learning with Minecraft" video, you might also like these:</b></span><br />
<a href="http://theeducationscientist.blogspot.com/2013/08/teaching-math-with-minecraft-impromptu.html#.VFDIt_TF8QS"><span style="font-family: Arial, Helvetica, sans-serif;">Minecraft Math #1: Numbers - Even, Odd, Prime & Square Root</span></a><br />
<a href="http://theeducationscientist.blogspot.com/2014/01/teaching-math-with-minecraft-2.html#.VFDI6_TF8QQ"><span style="font-family: Arial, Helvetica, sans-serif;">Minecraft Math #2: Addition, Multiplication & Commutativity</span></a>Anonymoushttp://www.blogger.com/profile/11351479269650780356noreply@blogger.com159tag:blogger.com,1999:blog-6645583842972204443.post-90364403178905647622014-10-15T06:17:00.000-07:002014-10-16T06:30:21.702-07:00Common Core Math Standards Making You Crazy? Some Things to Consider<div class="separator" style="clear: both; display: none; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyIPVuXuPEqxQ51yrANwB3BnmKPeWC6Xv9CHjkFsESnndkIfP8wT1wxUspMNFQzGesaih9jIgvu7RCly2A8b3JsRPlnoY3rVgud1mAnVJkuPtjJiAzcR5aPlTCa0K1cHk09pTgeswNJej1/s1600/Common+Core+Subtraction+small.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyIPVuXuPEqxQ51yrANwB3BnmKPeWC6Xv9CHjkFsESnndkIfP8wT1wxUspMNFQzGesaih9jIgvu7RCly2A8b3JsRPlnoY3rVgud1mAnVJkuPtjJiAzcR5aPlTCa0K1cHk09pTgeswNJej1/s1600/Common+Core+Subtraction+small.png" /></a></div>
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<span style="font-size: large;"><b>Pop Quiz!</b></span></h2>
<i>(No Googling or peeking at other people's answers before responding, please - this is a closed-book quiz. Also: this will <u>not</u> go on your permanent record.)</i><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGyV_pkT0GBWTYj0LEVirkArIyzOAC7zGwNiUAAh0Uyt5lbHUk2F3MCQgWJgnaxBpGhWakHslnLCdfs52_RI2tJa7dJI7K3WnJY8OWjQSeAieH9iJeKBKFWPRRhD6KF5Uib9OzOkByHZ15/s1600/LongMultiplication.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGyV_pkT0GBWTYj0LEVirkArIyzOAC7zGwNiUAAh0Uyt5lbHUk2F3MCQgWJgnaxBpGhWakHslnLCdfs52_RI2tJa7dJI7K3WnJY8OWjQSeAieH9iJeKBKFWPRRhD6KF5Uib9OzOkByHZ15/s1600/LongMultiplication.png" height="320" width="230" /></a></div>
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With reference to the long multiplication problem above, please answer the following questions.<br />
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<span style="font-size: small;">Q1) What does the "4" that is circled mean?</span></h2>
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<b>Q2) What does that zero in the second row mean (the one that is circled)?</b><br />
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<iframe allowtransparency="true" frameborder="0" height="240" name="poll-widget-5198309740911121206" src="http://www.google.com/reviews/polls/display/-5198309740911121206/blogger_template/run_app?txtclr=%23333333&lnkclr=%23007cbb&chrtclr=%23007cbb&font=normal+normal+14px+Arial,+Tahoma,+Helvetica,+FreeSans,+sans-serif&hideq=true&purl=http://theeducationscientist.blogspot.com/" style="border: none; width: 100%;"></iframe></div>
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We'll come back to this later.<br />
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Common Core Math Standards: What's the Point?</span></h2>
Our topic today is the Common Core Math Standards. They seem to have some people in a tizzy.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyIPVuXuPEqxQ51yrANwB3BnmKPeWC6Xv9CHjkFsESnndkIfP8wT1wxUspMNFQzGesaih9jIgvu7RCly2A8b3JsRPlnoY3rVgud1mAnVJkuPtjJiAzcR5aPlTCa0K1cHk09pTgeswNJej1/s1600/Common+Core+Subtraction+small.png" title="Common Core Subtraction Problem: Counting Up Method"><img align="left" alt="Common Core Subtraction Problem: Counting Up Method" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyIPVuXuPEqxQ51yrANwB3BnmKPeWC6Xv9CHjkFsESnndkIfP8wT1wxUspMNFQzGesaih9jIgvu7RCly2A8b3JsRPlnoY3rVgud1mAnVJkuPtjJiAzcR5aPlTCa0K1cHk09pTgeswNJej1/s1600/Common+Core+Subtraction+small.png" width="320" /></a>The picture at left, for example, has been making the rounds on the internet. Evidently someone snapped this picture of their child's math homework because they were enraged by it, and lots of people are hopping on the bandwagon.<br />
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This is curious to me.<br />
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The intent here should be pretty clear - the point is to develop the child's <i>conceptual understanding</i> of subtraction. This happens in parallel to developing their fluency in the standard subtraction algorithm that we all learned as children (not shown on this page, but also covered in the Common Core standards). The standard subtraction algorithm is efficient for calculating, but doesn't support understanding.<br />
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Do We Really Need to Change the Way We Teach Math?</span></h2>
Why would we want to teach a child to understand the concepts behind the algorithms? Isn't that just a waste of time? We all did fine just learning the algorithms by rote, didn't we?<br />
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Well, no. It turns out <a href="http://www.nytimes.com/2013/10/08/us/us-adults-fare-poorly-in-a-study-of-skills.html?_r=0" target="_blank">adults in the U.S. aren't very good at math</a>.<br />
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Speaking of which - let's take a moment to reflect on the quiz above. How did you do on it? How quickly could you answer? Did you step away to search the internet for some clues or look at the poll results before submitting your own answers? (<i>Naughty monkey!</i>) How confident were you in your responses?<br />
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The simple fact is we are failing our kids in math education, and we have been for generations. Here are some more fun facts to illustrate the point:<br />
<ul>
<li>According to the <a href="http://www.nationsreportcard.gov/reading_math_2013/#/what-knowledge" target="_blank">National Assessment of Educational Progress</a>, only about two in five U.S. 4th graders are proficient in math. That drops to about one in three students by 8th grade.</li>
<li>According to the <a href="http://www.oecd.org/unitedstates/PISA-2012-results-US.pdf" target="_blank">Programme for International Student Assessment</a>, the U.S. ranks below the international average on tests of mathematics. This is despite the fact that <a href="http://www.cbsnews.com/news/us-education-spending-tops-global-list-study-shows/" target="_blank">the U.S. spends more</a> per pupil than other countries.</li>
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It's pretty clear we're doing something wrong. Solving big problems like this requires big changes.<br />
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<span style="font-size: large;">
How Can We Do Better?</span></h2>
If we look at some of the top performing countries, like Singapore, and ask what they are doing that we aren't, the most obvious difference is that they focus on conceptual understanding a whole lot more than we do, and they spend a lot less time teaching things by rote. They teach the kids several models and methods for thinking about numbers and operations on numbers, for example - methods like the "Counting Up" method represented in the picture above. It's not a secret. We have just stubbornly refused to do it (until recently, anyway, with the arrival of the Common Core math standards).<br />
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But Aren't We Just Complicating Things?</span></h2>
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Teaching concepts may take more time than memorizing a few recipes for calculating without understanding (at least initially), and some people seem to object to spending the extra time. </div>
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This is extremely short-sighted. There may be more time spent initially developing understanding, but that investment will pay dividends many times over across the student's time in school, from kindergarten through high school (and beyond). Understanding the concepts makes later learning far more efficient - and effective. By spending more time developing foundational understanding, we could actually get <i>better</i> outcomes while spending <i>less</i> time on the math curriculum <i>overall</i>. Not only that, but students who understand what's going on have a much better experience, are more engaged, and are more confident. All good.<br />
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Why Can't We Just Do What We've Always Done?</span></h2>
What does it look like when we fail to teach children conceptual understanding? The video below shows one example of a second grader working on some grade-level math problems.</div>
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<iframe allowfullscreen="" frameborder="0" height="360" src="//www.youtube.com/embed/okrKm6yu7y8?feature=player_detailpage" width="640"></iframe>
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Notice that she knows the numbers and she knows how to count - these are typically learned by rote. Her conceptual understanding is very weak, however, and as a result she has to go through a laborious process of counting up from zero to answer simple questions like "How much do I have if I add 10 to 35?" And then she gets the wrong answer. Repeatedly.<br />
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Time invested in developing authentic understanding is not a waste of time. Quite the contrary. The real waste is time spent teaching without developing understanding - which produces the kind of disjointed, brittle, and tentative knowledge shown in the video - which is ultimately quite useless and will likely fade away rapidly.<br />
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This is all too common. This could well be any of our children. The maddening thing is that there's every reason to believe this child - and virtually every child - is completely capable of understanding the concepts she would need to reason fluently about the questions being asked of her in this video. She's not failing at math. Our education system is failing her. The same way it has failed generations before her. In large part by teaching math by rote, without conceptual understanding. (Don't scapegoat the teachers, by the way - the root problems here are systemic.)<br />
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We could try to press ahead as some people are advocating and just teach this child the algorithms for long addition, multiplication, and division as we have always done. But with such a weak foundation of understanding, what would we really expect to achieve that way? Her performance on those would quickly come to look like her performance here - labored, uncertain, and error-prone. Eventually she could well stop using the algorithms for lack of confidence, or even forget them altogether.<br />
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This is the sort of large scale, systemic problem the Common Core Math Standards are meant to rectify. <br />
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Could the explanation in the textbook shown in the picture above be edited for clarity? Sure it could.<br />
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Is that evidence that the Common Core is a failure and should be trashed? Far from it. We've been doing math education wrong for a very long time. The Common Core Math Standards represent a big step in the right direction - in the direction of what Singapore and other top-performing countries do, in fact.<br />
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Some people seem to think the textbook image above is crazy. What's really crazy is recognizing that the status quo is not acceptable while repeating the same educational processes generation after generation and expecting a better result.<br />
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Come to think of it, wasn't that literally <a href="http://www.brainyquote.com/quotes/quotes/a/alberteins133991.html" target="_blank">Einstein's definition of insanity</a>?Anonymoushttp://www.blogger.com/profile/11351479269650780356noreply@blogger.com12tag:blogger.com,1999:blog-6645583842972204443.post-2807895336347799032014-07-28T07:49:00.002-07:002015-03-01T04:08:02.456-08:00Celebrating Howard Gardner's Extraordinary Mind, Life, and Work (with a free book download)<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgc-nKHZQwFiBPIFfim18nbf-cKLi4juuokmFibQGFnmtV0axrqHDK3S0DLlrK7d8pUf4YSdp_0z_xhmr5TqkA-UQ57UPpeWvPK2tazXuV2phhoFU0-vpi2eMVpmPn01NzpJvn2fnYSMOvq/s1600/Howard_gardner.jpg" imageanchor="1" style="float: left; margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgc-nKHZQwFiBPIFfim18nbf-cKLi4juuokmFibQGFnmtV0axrqHDK3S0DLlrK7d8pUf4YSdp_0z_xhmr5TqkA-UQ57UPpeWvPK2tazXuV2phhoFU0-vpi2eMVpmPn01NzpJvn2fnYSMOvq/s1600/Howard_gardner.jpg" /></a></div>
<i><span style="font-family: Arial, Helvetica, sans-serif;">Howard Gardner is the Hobbs Professor of Cognition and Education at the Harvard Graduate School of Education.</span></i><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>Howard Gardner</b> has been identified by <i>Foreign Policy</i> and <i>Prospect</i> magazines as one of the <a href="http://www.foreignpolicy.com/articles/2008/05/14/top_100_public_intellectuals" target="_blank">100 most important public intellectuals</a> in the world today. His work has fundamentally changed the way many people (and institutions) think about intelligence (with his theory of Multiple Intelligences), creativity, and education (to name just a few of the areas he has touched).</span><br />
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<b><span style="font-family: Arial, Helvetica, sans-serif;">Happy Birthday, Howard!</span></b></h3>
<span style="font-family: Arial, Helvetica, sans-serif;">Howard turned 70 last year. To celebrate, his wife (Ellen Winner) and one of his former students (Mindy Kornhaber) hosted a Festschrift in his honor. (A Festschrift – derived from the German for ‘celebration writing’ – is a collection of writings published in honor of a scholar.) They invited Howard’s teachers, peers, colleagues, and former students to contribute essays inspired by his work and his relationships with them. One hundred and sixteen of Howard’s close colleagues contributed to the two-volume work, entitled <i>Mind, Work, and Life: A Festschrift on the Occasion of Howard Gardner’s 70th Birthday</i>. Each contribution includes a personal note from the contributor and a personal response from Howard. Running 605 pages in length, this is quite a remarkable work, providing a unique and intimate portrait of this extraordinary man and his profound influence on some of the people who have worked most closely with him.</span><br />
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<b><i><span style="font-family: Arial, Helvetica, sans-serif;">Mind, Life, and Work: A Festschrift on the Occasion of Howard Gardner's 70th Birthday</span></i></b></h3>
<span style="font-family: Arial, Helvetica, sans-serif;">The complete two-volume Festschrift is available for free download as a <a href="http://howardgardner01.files.wordpress.com/2012/06/festschrift-_-volumes-1-2-_-final.pdf" target="_blank">PDF here</a>, or if you prefer physical books you can buy it at cost from Amazon <a href="http://www.amazon.com/Mind-Work-Life-Festschrift-Occasion/dp/1499381700/ref=pd_bxgy_b_text_y" target="_blank">here</a>. Other options, including kindle versions of the two volumes, are listed <a href="http://howardgardner.com/2014/05/27/mind-work-and-life/" target="_blank">here</a>.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">My contribution (starting on p. 223) is entitled, <i>There’s More Than One Way to Bridge a Gap: On the Promise of Computational Neuroscience for Education</i>. I wrote it as a doctoral student in Education, soon after I took my first class with Howard. At the time, I was just beginning to wrestle in earnest with the question: “How can scientific insights about the brain and mind help us make education better?” As reflected in this essay, Howard’s teaching was instrumental in helping me frame the key issues in a new and more productive way, which I have continued to build on to this day. If you are interested in the relationship between the brain and mind, or in how we might go about leveraging insights about the biology of learning to improve educational practice, you might find it interesting. I look forward to reading your comments on that or anything else in the book.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Enjoy!</span><br />
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Anonymoushttp://www.blogger.com/profile/11351479269650780356noreply@blogger.com16tag:blogger.com,1999:blog-6645583842972204443.post-42105643756845750072014-05-08T08:41:00.001-07:002014-05-09T08:24:11.242-07:00Teacher Appreciation Week: A Personal Tribute to TeachersIt’s easy to see and criticize the flaws in our education system here in the U.S. – especially our public education system. And teachers are the face of public education – which means they often take the brunt of the criticism and discontent from all quarters, even for issues completely beyond their control.<br />
<br />
Teacher Appreciation Week is a time to pause and reflect on the good and important work that teachers do – and to openly express our gratitude to these people who have dedicated their lives to helping our children (and us, when we were children ourselves) become happy and productive members of society.<br />
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I am a product of public education. I can only imagine what my life would have been like if I had been born into a society without it. And I can only imagine what my school experience – and my life – would have been like without the benefit of the extraordinary courage, kindness, and skillful teaching exhibited by many individual teachers I had the good fortune to meet along the way.<br />
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Carole Rosen-Kaplan, for example, was my 11th grade English teacher. She became a dear friend. Sadly, she passed away recently. Carole’s sons asked me to provide some comments for her memorial service. I realize now – too late – that although we talked a couple of times a year, I never told her how much I appreciated her as a teacher, or what a profound impact her teaching had on my life. I regret that.<br />
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I’m trying to make up for it a bit by “paying it forward.”
Teaching is extraordinarily hard work. Often it’s thankless. Sharing the comments below is my way of saying to all of you, teachers:<br />
Thank you.<br />
I appreciate what you do.<br />
The work you do influences and transforms your students’ lives in ways you (and they) will probably never know.<br />
<br />
***<br />
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I met Carole when I was a high school junior. Her English Composition class wasn’t the English elective I wanted that year, but it was the only one that fit my schedule.<br />
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In retrospect, the class was so thoughtfully crafted and compelling that even today (decades later) I could probably write down most of the syllabus from memory.<br />
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I wrote my first short story for that class. It was about an archaeologist who stumbles upon a powerful relic in Egypt and uses it to travel back in time but ends up trapped. Carole (Mrs. Rosen-Kaplan to me then) asked me if I plagiarized it. I thought “Wow, that must be a pretty good story.” I don’t think it was her intent in that moment, but that honest exchange started me thinking that if I could accidentally make an English Composition teacher believe I had stolen a published story then maybe I could be a real writer who actually published stories. (Inspiration takes many forms.)<br />
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I wrote several chapters of a novel that year (which she read and commented on in her own time), and later became president of the school’s Creative Writing Club - my first formal leadership role. One of my short stories won a prize in a writing competition. I later wrote a short story for my college essay. It worked! (I got in.) AND a love poem for a woman. It also worked! (She’s my wife.)<br />
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It turns out that English Composition is<i> crazy powerful stuff</i>.<br />
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That year I argued against nuclear stockpiling in a mock trial of the global superpowers and wrote passionately about the Vietnam war, the Holocaust, and human slavery.<br />
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The class *involved* writing but it wasn’t *about* writing. It was about love and hate, good and evil, right and wrong, politics and power.<br />
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As I reflect back on the class now, though, I realize that what is remarkable to me about Carole’s teaching is that we didn’t simply *read* other people’s thoughts on these themes or even write about them in the abstract. When writing for Carole we had to choose sides - we had to “try on” different points of view and in the end commit to one. On the theme of War: <i>will you, as the author of this essay, choose to glorify or vilify it?</i><br />
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More importantly - on the subject of war: <i>will you, as the author of your <u>own life</u>, choose to glorify or vilify it?</i><br />
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But helping us find our voice was only one of Carole’s objectives. Her other objective was to impress upon us our responsibility to use it.<br />
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Perhaps the most poignant statement of individual responsibility I have ever read is captured in these lines by Martin Niemöller (assigned in Carole's class) about the Nazi purges:<br />
<blockquote class="tr_bq">
<i>First they came for the Socialists, and I did not speak out – Because I was not a Socialist. </i><br />
<i>Then they came for the Trade Unionists, and I did not speak out – Because I was not a Trade Unionist. </i><br />
<i>Then they came for the Jews, and I did not speak out – Because I was not a Jew. </i><br />
<i>Then they came for me – and there was no one left to speak for me. </i></blockquote>
I have recalled this passage to mind many times over the decades. It reminds me of my right - and my responsibility - to use my voice. More importantly, it reminds me that sometimes doing the right thing is deeply uncomfortable all around - and that courage does not mean the absence of fear but rather doing the right thing in the face of fear. Speaking up and speaking out is not the responsibility of a chosen few - it is the right and responsibility of every human being.<br />
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Carole’s class was called “English Composition” but the full title should have been something like <i>English Composition: How to Find Your Voice and Raise Hell Through Writing</i>.<br />
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I think Carole saw promise in me as her 11th grade English Composition student and was disappointed that in the end she didn’t inspire me to pursue a creative writing career.<br />
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But here is what I would say to her in response to that…<br />
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Carole,<br />
Thanks in part to you I know who I am and who I aspire to become. I know what I stand for. I stand for what is right, what is true, what is just, and what is good. I stand for people - especially the people who can’t stand for themselves, like children. I stand for the right of every human being to discover their own voice and have the opportunity to be heard. I stand for the importance of helping people discover who they are, who they want to become, what they are deeply passionate about, and how to become the authors of their own lives.<br />
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No, you didn’t inspire me to become a creative writer.<br />
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You inspired me to become an Educator. Like you.<br />
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All my love,<br />
-Mike Connell<br />
April 26, 2014Anonymoushttp://www.blogger.com/profile/11351479269650780356noreply@blogger.com20tag:blogger.com,1999:blog-6645583842972204443.post-3012812591361820292014-05-03T07:47:00.002-07:002014-05-03T07:47:55.587-07:00Mind the Quicksand: A Word of Warning to EdTech Investors<div class="separator" style="clear: both; text-align: left;">
<a href="http://upload.wikimedia.org/wikipedia/commons/2/2f/Computer_Space-Early_arcade_games_machines.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div>
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<a href="http://upload.wikimedia.org/wikipedia/commons/2/2f/Computer_Space-Early_arcade_games_machines.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a><span style="font-family: Arial, Helvetica, sans-serif;">I read about a new EdTech startup this morning in TechCrunch. It's called </span><i style="font-family: Arial, Helvetica, sans-serif;">Galxyz</i><span style="font-family: Arial, Helvetica, sans-serif;">. I started writing a comment on the article page itself, but then it got really long and kind of "meta." So I thought it might make an interesting blog post.</span></div>
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<a href="http://upload.wikimedia.org/wikipedia/commons/2/2f/Computer_Space-Early_arcade_games_machines.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://upload.wikimedia.org/wikipedia/commons/2/2f/Computer_Space-Early_arcade_games_machines.jpg" height="240" width="320" /></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Here's the <a href="http://techcrunch.com/2014/04/29/osman-rashid-announces-galxyz/" rel="nofollow" target="_blank">description of the company</a> from TechCrunch:</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><i>Galxyz (it’s pronounced “galaxies”, and it’s a nightmare to spell) is building a science-focused game for tablets and smartphones. And the company really is just focused on one game — Rashid [the founder] described it as “an intergalactic science adventure,” one that kids could potentially play for years, battling a villain called King Dullard across the galaxies. As they do so, they’re also learning about science at their own pace.</i></span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">You can check out their epic </span><a href="http://vimeo.com/93230380" rel="nofollow" style="font-family: Arial, Helvetica, sans-serif;" target="_blank">promo video here</a><span style="font-family: Arial, Helvetica, sans-serif;"> (I would embed it, but that might violate copyright).</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Sounds interesting enough. Although an antagonist called "King Dullard" is a little on-the-nose, if you know what I mean.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">What's the new angle on education, I wondered?<br /><br /><i>Apparently the idea came to Rashid as he saw his own children playing educational games, which he found lacking in several ways. He said they weren’t engaging enough, the content wasn’t deep enough, or they required the parents to get involved in order for the kids to advance. That second point is why he’s focusing on a single title — so that kids can just keep playing rather than running out of material after a few weeks.</i></span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>Wow - it seems so obvious once he points it out. I wonder why this hasn't occurred to anyone before? </b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span><span style="font-family: Arial, Helvetica, sans-serif;">Anyone who follows this blog knows that I believe it is entirely possible to make education orders of magnitude better. And that I applaud any authentic effort to try.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">But from where I stand, this has "Titanic" written all over it. </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">I am confident that producing truly effective education at scale is harder than any business or engineering challenge the good people at Galxyz have ever faced. </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">This isn't about them, though. I wish them well. For purposes of this blog post, they represent just the latest in an endless parade of investor-backed EdTech entrepreneurs who seem to have almost exactly the same creation story. I'm not upset about it. I'm more intrigued.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">One aspect of education that fascinates me is that to outsiders it always looks so *simple*.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">As simple as running across that wet, sandy patch of ground in the jungle to get to a fabulous treasure twenty feet away. But wait...it's hard to believe no one has run over there and taken that treasure before...hmmm...don't you wonder why? (Hint: <i>That's not sand</i>.)</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span><span style="font-family: Arial, Helvetica, sans-serif;">What follows is my prediction for this venture. </span><br />
<a href="http://upload.wikimedia.org/wikipedia/commons/2/2f/Computer_Space-Early_arcade_games_machines.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">To be clear, this is not what I wish for them. I want truly better education more than just about anything, and I'm indifferent as to whether it comes from a for-profit or non-profit venture, as long as we get it. And it's so close I can almost taste it. </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">The prediction is based on a pattern that I see play out over and over and over and over <i>and over</i> again (that's right - five 'overs'). </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">It looks like this...</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>Day 1</b>: Outlook bright, mattress so overflowing with cash I can't climb onto it so am sleeping on the couch, burn rate 7, feeling great, gonna make history and be a hero by fixing education because I'm...</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">(<i>Choose all that apply</i>)</span><br />
<ul>
<li><span style="font-family: Arial, Helvetica, sans-serif;">A product of an education system, and therefore I know how to educate...more better...than anyone</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">More funner than anyone in education today</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">In possession of more revolutionary technology than those other people</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">More smarter</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">Mo' richer</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">A bit confused about the difference between money, intelligence, and expertise</span></li>
</ul>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>Day 30</b>: Epic teaser promo video produced, first prototype created and friends (who are also employees, or hoping to be) are saying it's definitely the next big thing - time to pick up the pace of hiring animators, writers, and engineers! Mattress so overstuffed with clams that I rolled off it last night. (Ouch.) Outlook blazing, increasing burn rate to 9.0.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>Day 180</b>: A bunch more concepts storyboarded and prototyped, things seem to be moving right along. Still, things are getting a bit confusing. We discovered that narratives are inherently linear and learning appears to be inherently nonlinear, so that's creating some "design challenges" (so-called). Can the kids go through the same narrative ten times if that's what they need in order to understand the concept? But wait - even if they will tolerate that, isn't one definition of insanity "doing the same thing over and over while expecting a different result"? Should we have multiple narratives for each concept? Wow - that would be expensive. Let's stick with the one narrative. Should we at least present each concept in multiple different ways to help kids understand it? But will all those choices confuse them? And what other ways are there to present the concepts within a single narrative? This is taking longer than we thought - better hire more animators and engineers! Mattress slightly overstuffed with cabbage. Burn rate goes to 11. Outlook bright.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Day 240</b>: Somehow a couple of teachers got wind of what we were doing and we invited them in for a demo. They were really harshing on our mellow. They think the whimsical five minute cut scenes between short sets of learning activities are too long - complaining about how that's going to "steal learning time" or something. But don't they understand that's what makes learning fun?! (And how many simoleons we have invested in those videos?!) They also wanted to know what kinds of student performance data we are going to provide. We showed them the awesome score meter and the leaderboards but they didn't seem to get it. That's why we didn't want to bring any teachers up in here - we just knew they wouldn't understand our Vision. Mattress still stuffed with ample Benjamins. Burn rate holding steady at 11.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Day 330</b>: Brought some kids in to play test for the first time. They thought the narrative was kind of hokey and felt tacked on to the learning activities. Lenny's kid called it "chocolate covered broccoli." That's why I didn't want to bring students up in here - we just knew they wouldn't understand our Vision. The writers and animators are getting a little up in arms because people keep changing requirements and trying to mess with their narrative. I sympathize with them - the narrative is the hard and expensive part, so shouldn't we revise the science material to fit it instead of the other way around? Running a bit behind schedule. Mattress feeling a bit lumpy. Better pull back on contractors to conserve cash. Burn rate reduced to 8.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">You can imagine where it goes from here - the way of <a href="http://en.wikipedia.org/wiki/38_Studios" target="_blank">38 Studios</a> or a quick exit that amounts to a soft crash landing. Like I said - quicksand. The pattern is that they don't discover where the real complexities in education lie until they are in it up to their necks.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Here's some unsolicited advice for engineers and investors who are eyeing EdTech:</span><br />
<ul>
<li><span style="font-family: Arial, Helvetica, sans-serif;">If you think you can crack the code on better education with money, you are wrong</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">If you think you can crack the code on better education with raw intelligence, you are wrong</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">If you think the core challenges in EdTech are technical, you are wrong</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">If you think the silver bullet is in "making learning fun" or "engaging" students, you are wrong</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">If you think the solution is in making clever lessons for each concept, you are wrong</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">If you think you can solve this problem with better graphics, animation, and narrative, you are wrong</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">If you think bringing even all of the above elements to the table *must* be sufficient to crack the code on better education, you are still wrong - though you might be able to generate a positive ROI that way. Or not.</span></li>
</ul>
<div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">Relay Ventures, Andreessen Horowitz, and Emerson Collective (the investors backing Galxyz) - you are welcome to use the above as a litmus test when evaluating EdTech pitches in the future. (Acknowledgement as the source is always appreciated.)</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Don't get me wrong: I strongly believe there is a path to better education. This just isn't it.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">I can hear the incredulous guffaws now. <i>We are on Day 30 and the outlook is blazing - we have an epic promo video and the prize is practically within reach!</i></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">I don't really see any point in debating the matter right now - this is a prediction, not a challenge. Let's check back in a year and see where things stand. I would be pleasantly surprised to be wrong. But </span><span style="font-family: Arial, Helvetica, sans-serif;">I wouldn't bet on it.</span>Anonymoushttp://www.blogger.com/profile/11351479269650780356noreply@blogger.com85tag:blogger.com,1999:blog-6645583842972204443.post-13442462487073118602014-03-21T07:11:00.000-07:002014-03-23T07:20:41.488-07:00Khan Academy: How Does It Measure Up? (Part 2 of 2)<i style="font-family: Arial, Helvetica, sans-serif;">This article is the second in a series. In the <a href="http://theeducationscientist.blogspot.com/2014/02/khan-academy-and-illusion-of.html#.UynJw61dV6B" target="_blank">first article</a>, Dr. Schwartz distinguished authentic understanding from the Illusion of Understanding and introduced five principles from learning science that support the development of authentic understanding. For further reading, check out <a href="http://sloanconsortium.org/jaln/v17n4/khan-academy-illusion-understanding" target="_blank">this article</a> published in the Journal of Asynchronous Networks.</i><br />
<i style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: x-small;"><br /></span></i>
<i style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: x-small;">Note: The original published version of this post was longer. We shortened it in response to reader feedback. If you'd like to read the original version of the post, please contact the blog owner.</span></i><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUbp5Fp7VZYAM9wLCVoKzmB1kYxSDMl0nUd_hRzkrmvMtSd2Hp3lXP70DMpmya1JiOOvCk8TygyMXSOeUrreupW8JaecCMr7pafhmZxn2eQdRz-iSUOmMPFgbEHrpjU0qJYRs-HIYOH-np/s1600/Scorecardv03.png" imageanchor="1" style="float: left; margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUbp5Fp7VZYAM9wLCVoKzmB1kYxSDMl0nUd_hRzkrmvMtSd2Hp3lXP70DMpmya1JiOOvCk8TygyMXSOeUrreupW8JaecCMr7pafhmZxn2eQdRz-iSUOmMPFgbEHrpjU0qJYRs-HIYOH-np/s1600/Scorecardv03.png" height="200" width="197" /></a></div>
<span style="font-family: Arial, Helvetica, sans-serif;">Dr. Marc Schwartz </span><br />
<span style="font-family: Arial, Helvetica, sans-serif; font-size: small;">Professor of Education at the <a href="http://www.uta.edu/coehp/curricandinstruct/research-community/mind-brain/faculty-and-staff.php" target="_blank">University of Texas at Arlington</a> and Director of the <a href="http://www.uta.edu/coehp/curricandinstruct/research-community/mind-brain/" target="_blank">Southwest Center for Mind, Brain, and Education</a></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Dr. Michael Connell</span><br />
<span style="font-family: Arial, Helvetica, sans-serif; font-size: small;">Ed Tech Designer & Visiting Researcher at the University of Texas’ Southwest Center for Mind, Brain, and Education</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
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<br />
<h2>
<span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Introduction</span></h2>
<span style="font-family: Arial, Helvetica, sans-serif;">In <a href="http://theeducationscientist.blogspot.ch/2014/02/khan-academy-and-illusion-of.html#.UxGJlELu3d4" target="_blank">Part 1 of this article</a> I posed a challenge you may still be considering. If you remember the Iceberg Challenge, your goal was to decide what would happen to the water level after all the ice melted. For many years, what nearly all my students found particularly irritating about this challenge (and me) is that I stopped providing the answer. You might be feeling that irritation too. </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span><span style="font-family: Arial, Helvetica, sans-serif;"><b>If you read <a href="http://theeducationscientist.blogspot.com/2014/02/khan-academy-and-illusion-of.html#.UynJw61dV6B" target="_blank">Part 1</a> and tried the challenge, are you feeling this irritation?</b></span><br />
<div class="widget-content" id="widget-content">
<iframe allowtransparency="true" frameborder="0" height="160" name="poll-widget-3608394357461692489" src="http://www.google.com/reviews/polls/display/-3608394357461692489/blogger_template/run_app?txtclr=%23333333&lnkclr=%23007cbb&chrtclr=%23007cbb&font=normal+normal+14px+Arial,+Tahoma,+Helvetica,+FreeSans,+sans-serif&hideq=true&purl=http://theeducationscientist.blogspot.com/" style="border: none; width: 100%;"></iframe></div>
<span style="font-family: Arial, Helvetica, sans-serif;">My goal – then or now – was not to be irritating. My goal is to use our collective experience of the iceberg challenge to clarify what we mean when we use the word <i>understanding</i>, so that we’re all talking about the same phenomenon in the same way with the same expectations. </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">In Part II we introduce an <i>understanding scorecard</i> to help expose the Illusion of Understanding and in turn define what understanding means in the area of math, and finally consider what choices may be available to Khan and all educators, especially those who work online, to better support authentic understanding.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<br />
<h2>
<span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">What do we mean by <i>understanding</i>?</span></h2>
<span style="font-family: Arial, Helvetica, sans-serif;">At one extreme, an understanding might mean that we know something (anything) about a subject, so that we can participate in a cocktail conversation. For example, imagine a person said to you, “I think it makes a difference to coast lines if all the polar ice floating on the oceans melts, but I’m not sure how…” Would you say that person understands Archimedes Principle? </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Alternatively, would you say a person understands Archimedes Principle if they can provide a definition or use a mathematical formula to solve for a missing variable? </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">At the other extreme, would you say a person understands Archimedes Principle who can:</span><br />
<ul>
<li><span style="font-family: Arial, Helvetica, sans-serif;">Recognize deeper connections between situations that seem unrelated on the surface - such as what happens to ice melting in a glass and what happens to a balloon full of oxygen released on Mars (whose atmosphere is predominantly carbon dioxide),</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">Solve a variety of novel challenges like the Iceberg Challenge,</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">Explain their reasoning and articulate why they believe their answers are correct across different contexts, and</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">Recognize how a new concept or formula relates to what they have learned previously, so they can start using it quickly? </span></li>
</ul>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">These three points of view (let’s call them “low,” “medium,” and “high” understanding, respectively) map out positions along a continuum that begin to portray understanding in a richer and more complex way. We may all discover that in the past we have been holding different assumptions when using words like “understanding” (or “learning,” for that matter).</span><br />
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<b><span style="font-family: Arial, Helvetica, sans-serif;">
Do these three points of view frame a continuum that feels useful to you?</span></b><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Using this continuum as a shared point of reference, we can ask a couple of distinct but related questions:</span><br />
<ul>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><b>What outcomes are <i>possible</i>?</b> What is the highest level of understanding that students can theoretically achieve in a given subject area on a large scale in a particular formal education system, given the available resources in that system?</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><b>What outcomes are <i>expected</i>?</b> What level of student understanding should we hold the formal education system accountable for in practice?</span></li>
</ul>
<span style="font-family: Arial, Helvetica, sans-serif;">The two questions above may seem similar but they could hardly be more different. The first question is a question of fact – there is an objective answer independent of what we believe or desire (although it might be difficult to discover that answer – more on that later). While different people might have different beliefs about the answer to the first question, at least one of them is guaranteed to be wrong. The second question is not a matter of fact – it is open-ended and requires a community decision. Different people and communities will certainly have different views about the second question and – as long as they respect the objective limits on what is possible – none of them can be considered wrong because there is no objectively right answer.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Even though the two questions are distinct, they are related. The first question (what is theoretically possible) puts a hard limit on reasonable answers to the second question (what the community demands of its educational system). Two common mistakes that people make when reasoning about education are: </span><br />
<ul>
<li><span style="font-family: Arial, Helvetica, sans-serif;">They assume a low level of understanding is the best that can be achieved at scale in an education system, and – without checking that assumption – they decide to set a low bar for student understanding based on it.</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">Conversely, they ignore the ceiling on what is theoretically possible and make impossible demands of educational institutions. </span></li>
</ul>
<span style="font-family: Arial, Helvetica, sans-serif;">It is not our aim here to argue in favor of or against any particular purpose of education. What is important right now is to know what we mean when we say we want students to understand _______ (and you fill in the blank), and to be clear about which question we are discussing at any given time (what’s possible vs. what's expected).</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
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<h2>
<span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">How do we determine what level of understanding is <i>possible</i>?</span></h2>
<span style="font-family: Arial, Helvetica, sans-serif;">Formal education systems are so complex that it is difficult to analyze them to determine what kind of results are possible from them. How should we measure student understanding given the complexity and unique features of different formal education systems? One way is to create a "scorecard" based on what the learning sciences claim will lead to high levels of understanding. </span><span style="font-family: Arial, Helvetica, sans-serif;">Recall, in particular, the five principles from learning science about the conditions required to develop authentic understanding:</span><br />
<ol>
<li><span style="font-family: Arial, Helvetica, sans-serif;">Authentic understanding depends on hierarchically organized knowledge.</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">Authentic understanding is grounded in direct experience.</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">Authentic understanding is stabilized by practice (generally at every level within the hierarchy).</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">Authentic understanding requires formative feedback.</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">Authentic understanding is context-sensitive.</span></li>
</ol>
<span style="font-family: Arial, Helvetica, sans-serif;">The table below is an "understanding scorecard" that summarizes the principles and offers some examples of how to use each principle as a rating criterion. We invite you to try out the scorecard for the <a href="http://www.khanacademy.org/math/arithmetic/addition-subtraction/basic_addition/v/basic-addition" target="_blank">first lesson Khan created</a> to introduce the notions and elements of arithmetic.</span><br />
<div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div>
<span style="font-family: Arial, Helvetica, sans-serif;">Watching the video takes about 8 minutes. Afterwards, see if rating the video as </span><i style="font-family: Arial, Helvetica, sans-serif;">Low</i><span style="font-family: Arial, Helvetica, sans-serif;">, </span><i style="font-family: Arial, Helvetica, sans-serif;">Medium</i><span style="font-family: Arial, Helvetica, sans-serif;">, or </span><i style="font-family: Arial, Helvetica, sans-serif;">High</i><span style="font-family: Arial, Helvetica, sans-serif;"> on each of the five principles </span><span style="font-family: Arial, Helvetica, sans-serif;">helps you summarize your reflections on the overall level of understanding we might expect from students using the video as an instructional tool. Of course, the more videos you watch, the easier it will be to generate a summary evaluation of the arithmetic curriculum.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
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<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184; width: 449px;">
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<tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="background: #CCFFCC; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 99.9pt;" valign="top" width="100"><div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span style="font-size: 10pt;"><span style="font-family: Arial, Helvetica, sans-serif;">Evaluation
criterion<o:p></o:p></span></span></b></div>
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<td style="background: #CCFFCC; border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 3.75in;" valign="top" width="270"><div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span style="font-size: 10pt;"><span style="font-family: Arial, Helvetica, sans-serif;">Examples
of arithmetic activities supporting “high” understanding<o:p></o:p></span></span></b></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 11pt;">Your_Rating </span></b><span style="font-size: 11pt;">of Khan_Academy <o:p></o:p></span></span></div>
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<span style="font-size: 11pt;"><span style="font-family: Arial, Helvetica, sans-serif;">Arithmetic<b style="mso-bidi-font-weight: normal;"><o:p></o:p></b></span></span></div>
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<span style="font-size: 10pt;"><span style="font-family: Arial, Helvetica, sans-serif;">Learning is grounded in experience<o:p></o:p></span></span></div>
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<span style="font-size: 10pt;"><span style="font-family: Arial, Helvetica, sans-serif;">Hands-on learning experiences using [familiar
objects like] chips, dice, or paper clips to associate physical objects to
ordering, counting and symbols used to represent numbers.<o:p></o:p></span></span></div>
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<br /></div>
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<span style="font-size: 10pt;"><span style="font-family: Arial, Helvetica, sans-serif;">Knowledge is hierarchically developed from the
student’s point of view. <o:p></o:p></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: 10pt;">Concepts learned in a hierarchical way: Understandings
begin as actions (as above), which precede and eventually support
understandings that are representations of actions (writing, speaking or
drawing), which in time support understandings that coordinate numerous
representations to form abstractions (like justice or calculus).<span style="mso-spacerun: yes;"> </span>If you want to know more about hierarchies
of understanding see <a href="http://www.gse.harvard.edu/~ddl/articlesCopy/Schwartz_Fischer_Useful_Metaphors.pdf" target="_blank">this article</a> (pages 3-4).</span><span style="font-size: 10pt;"> </span></span></div>
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<br /></div>
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<span style="font-size: 10pt;"><span style="font-family: Arial, Helvetica, sans-serif;">Provides scaffolded practice (preferably at
every level within the hierarchy)<o:p></o:p></span></span></div>
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<span style="font-size: 10pt;"><span style="font-family: Arial, Helvetica, sans-serif;">The curriculum covers fewer concepts, so students
can spend significant time practicing with physical objects (chips, dice,
etc.) then with drawing pictures, then with symbols.<span style="mso-spacerun: yes;"> </span>The teacher helps them as necessary
(provides scaffolding) during this practice at every level of the hierarchy.<o:p></o:p></span></span></div>
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<span style="font-size: 10pt;"><span style="font-family: Arial, Helvetica, sans-serif;">Provides formative feedback<o:p></o:p></span></span></div>
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<span style="font-size: 10pt;"><span style="font-family: Arial, Helvetica, sans-serif;">As students practice with physical objects
(chips, dice, etc.) then with drawing pictures, then with symbols, their
level of understanding is made visible to themselves and the teacher, which creates opportunities for providing very
specific corrective feedback when a student gets stuck or misunderstands
(this is formative feedback).<o:p></o:p></span></span></div>
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<br /></div>
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<span style="font-size: 10pt;"><span style="font-family: Arial, Helvetica, sans-serif;">Develops connections between abstract
principles and real-world contexts<o:p></o:p></span></span></div>
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<span style="font-size: 10pt;"><span style="font-family: Arial, Helvetica, sans-serif;">The abstract principles are numbers,
operations, and the other symbolic formalisms of math.<span style="mso-spacerun: yes;"> </span>Students spend a lot of time developing
connections between these abstract principles and real world scenarios that they
are used to model. <o:p></o:p></span></span></div>
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<h2 class="title">
<span style="font-family: Arial, Helvetica, sans-serif; font-size: small;"><br /></span></h2>
<h2 class="title">
<span style="font-family: Arial, Helvetica, sans-serif; font-size: small;">How useful does the scorecard seem to you?</span></h2>
<div class="widget-content" id="widget-content">
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<span style="font-family: Arial, Helvetica, sans-serif;">As you complete the scorecard, it might also help to consider some of the following questions (from a first grader’s point of view):</span><br />
<ul>
<li><span style="font-family: Arial, Helvetica, sans-serif;">Do you need to know what an avocado is to make sense of the instruction?</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">How important is it that the avocado looks like an avocado on video?</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">How comfortable does the child already need to be with the idea that the number “2” has a special relationship with the two avocados that Khan draws?</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">What do the symbols “+” or “=” mean as used in Khan’s lesson?</span></li>
</ul>
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<h2 class="title">
<span style="font-family: Arial, Helvetica, sans-serif; font-size: small;">If you’d like, try using the scorecard to assess the highest level of understanding that Khan Academy supports, and then compare your response to others' (using "Show results").</span></h2>
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<h2 class="title">
<span style="font-family: Arial, Helvetica, sans-serif; font-size: small;">Now we invite you to use the scorecard to evaluate a curriculum you're familiar with - at your child's school, the entire school, a program you recently went through, etc. and then compare your response with others'.</span></h2>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">What Do You Think?</span></h2>
<ul>
<li><span style="font-family: Arial, Helvetica, sans-serif;">Does the scorecard help you think more clearly about what you and others mean by “understanding”?</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">How did you rate Khan Academy on the scorecard? Were you surprised by others’ responses?</span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;">How did you rate your own schools on the scorecard? Were you surprised by others’ responses?</span></li>
</ul>
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Anonymoushttp://www.blogger.com/profile/11351479269650780356noreply@blogger.com12tag:blogger.com,1999:blog-6645583842972204443.post-29911966169223393352014-02-20T12:58:00.003-08:002014-03-25T09:15:12.212-07:00Khan Academy: The Illusion of Understanding (Part 1)<a href="https://www.blogger.com/blogger.g?blogID=6645583842972204443" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><br />
<i>Guest blog by <a href="http://www.uta.edu/coehp/curricandinstruct/research-community/mind-brain/faculty-and-staff.php" target="_blank">Dr. Marc Schwartz</a></i><br />
<i>Professor of Education at the University of Texas at Arlington</i><br />
<i>Director of the <a href="http://www.uta.edu/coehp/curricandinstruct/research-community/mind-brain/" target="_blank">Southwest Center for Mind, Brain, and Education</a></i><br />
This post is based on an <a href="http://sloanconsortium.org/jaln/v17n4/khan-academy-illusion-understanding" target="_blank">article</a> by the same name published in the <i>Journal of Asynchronous Learning Networks</i>.<br />
<br />
<span style="font-family: inherit; font-size: large;">The Illusion of Understanding</span><br />
For the past three decades I’ve been working to dispel myself of an illusion that’s hard to recognize and even harder to overcome. I call it the “Illusion of Understanding.” It’s the false belief that we understand something but then we discover we actually don’t. The example problem below will help clarify what I mean. Consider the following…<br />
<span style="font-family: inherit;"><br /></span>
<span style="font-family: inherit; font-size: large;">Iceberg Challenge</span><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHrUFuyrL7TSLK7DbsNj1ADoWLjceqYXDYR6zNIAwXJSyh_gxpL07QVVsd3gcQ7MZF14i38YIE6zN88YHRL5nmImKqM-HjwjQmhdy-K1S25WqOOw8I-QCGM8PReyvMIQ7dDOBtjMmi9BAx/s1600/IceCubeProblem.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="Glass of ice water with ice cubes floating in it" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHrUFuyrL7TSLK7DbsNj1ADoWLjceqYXDYR6zNIAwXJSyh_gxpL07QVVsd3gcQ7MZF14i38YIE6zN88YHRL5nmImKqM-HjwjQmhdy-K1S25WqOOw8I-QCGM8PReyvMIQ7dDOBtjMmi9BAx/s1600/IceCubeProblem.png" height="320" style="float: left; margin-right: 1em;" title="" width="273" /></a><br />
<span style="font-size: 21;">The glass of water in this picture is filled to the brim. One more drop, and water would spill over the edge. When examining the ice you note that the cubes rise just above the surface of the water (like glaciers in the ocean), but do not extend to the bottom of the glass. Now here’s the challenge: Imagine patiently waiting on a hot summer day until all the ice melts. What will happen to the water level? Does it rise and over-flow the glass, remain constant throughout the melting process, or go down? </span><br />
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<h2 class="title">
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<h3>
What do you think will happen to the water level when all the ice has melted?</h3>
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Think about what’s going on for you as you wrestle with this challenge. Do you feel like you know the right answer? How confident are you in your response? Are you, like most people who face this challenge, surprised to find that you aren’t sure of the answer, while also feeling conflicted because you think you should know it? If you answered “Yes” to this last question, then you just experienced the Illusion of Understanding first-hand.<br />
<br />
This is a challenging problem for most people – physics students and adults alike. Yet the problem is based on a principle called Archimedes Principle that most of us encountered at some point in a physical science class.<br />
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As challenging as the problem is for students, consider how much more daunting it is for a science teacher who wants to help students understand the principle so well that even years later they can confidently use that understanding to solve problems like this one. I know how daunting the challenge is, because many years ago I was that science teacher.<br />
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Here’s the dilemma. As a teacher, I can assure you that it’s very, very difficult to help students develop what I call “authentic understanding” – the kind of understanding that would enable them to answer the iceberg challenge correctly and explain why their answer is correct. It’s a great deal easier (although not a conscious goal) for a teacher to leave students with the illusion of understanding – the belief that they understand the relevant principle even though they can’t answer questions based on the principle. I have given the iceberg challenge to hundreds of intelligent, educated adults over many years. Based on their performance I’d say that – despite the best efforts of many capable, dedicated science teachers – authentic understanding in this subject area is relatively rare while the illusion of understanding is quite common. However if you ask people in the grip of the Illusion whether they understood their science teacher’s lesson on Archimedes’ Principle, many would say “yes” without hesitation.<br />
<br />
<a href="https://www.blogger.com/blogger.g?blogID=6645583842972204443" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><span style="font-size: large;">MOOCs to the rescue?</span><br />
Let’s carry our self-experiment one step further to see how deep the Illusion goes in this case. Perhaps Kahn Academy can help you solve the iceberg challenge (assuming schooling has not). Khan’s curriculum on Fluids, <a href="http://www.khanacademy.org/science/physics/fluids/v/fluids--part-5" target="_blank">Part 5</a> and <a href="http://www.khanacademy.org/science/physics/fluids/v/fluids--part-6" target="_blank">Part 6</a>, constitute a formal presentation that, in principle, should allow you to solve the problem as posed above. I invite you to watch those two videos now and try to answer the Iceberg Challenge again.<br />
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(Go ahead and watch the videos now. I'll wait…)<br />
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How did you do? Were you able to resolve the iceberg challenge? Do you feel more or less confident in your answer now? Khan claims that the ability to control the pacing of the video and the opportunity to re-watch the session will help. You may want to test those assumptions. <br />
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<span style="font-size: large;">How to Develop <i>Authentic</i> Understanding</span><br />
I have found that Khan – like the many others who use similar instructional strategies both online and off – are overlooking over a hundred years’ worth of discoveries in the learning sciences. Below, I list five major discoveries that define requirements for achieving authentic understanding (see the <a href="http://sloanconsortium.org/jaln/v17n4/khan-academy-illusion-understanding" target="_blank">companion article</a> published in this month’s Journal of Asynchronous Learning Networks for additional detail):<br />
<ol>
<li>Authentic understanding depends on hierarchically organized knowledge.</li>
<li>Authentic understanding is grounded in direct experience.</li>
<li>Authentic understanding is stabilized by practice (generally at every level within the hierarchy).</li>
<li>Authentic understanding requires formative feedback.</li>
<li>Authentic understanding is context-sensitive.</li>
</ol>
When these insights are ignored, as they are most of the time in online instruction, educators and students risk reinforcing and perpetuating the Illusion of Understanding, which I have observed in many classrooms and in many countries. Typically the illusion unfolds in dramatic fashion when teachers ask students to explain their answers, and the students suddenly realize they can’t. Students find themselves speechless or stuck in a rambling explanation that doesn’t even make sense to them. I have even observed students give a correct explanation and then admit they didn’t understand what they just said. Now, as the teaching and learning enterprise unfolds on a world stage through a variety of online platforms, we face the risk that the Illusion will be even more widespread and difficult to dispel than ever.<br />
<br />
Assuming that your struggle with the above iceberg challenge is no different than almost everyone who attempts the challenge, which of the five observations seem relevant? Did you feel that you lacked the perquisite experiences to reach an answer? Did your past experiences feel relevant yet unconnected or unreliable? Did you feel like you needed to practice some kind of mental exercise but did not know which or how? These questions all underlie the complicated teaching and learning environment that lead to authentic understanding. I don’t claim that the process is easy, but the investment is necessary. The challenge here should also underscore another illusion- that is, the illusion that achieving expert status in one discipline - as a hedge fund manager, for example - automatically transfers to another discipline, such as teaching. Teachers, like hedge fund managers, spend decades to become competent at their craft.<br />
<br />
If you do watch the videos, which of the five observations seem to be relevant to your experience of understanding? You will note that Khan does use a similar challenge in parts five and six of his video series, but the context is different. Does that matter? In <a href="http://theeducationscientist.blogspot.com/2014/03/khan-academy-how-does-it-measure-up.html" target="_blank">Part II</a> we explore in further detail the Illusion of Understanding in the area of math and explore what choices may be available to Khan and all educators, especially those who work online, to better support authentic understanding.<br />
<br />
(Continued in <a href="http://theeducationscientist.blogspot.com/2014/03/khan-academy-how-does-it-measure-up.html" target="_blank">Part II which is available here.</a>)Anonymoushttp://www.blogger.com/profile/11351479269650780356noreply@blogger.com298tag:blogger.com,1999:blog-6645583842972204443.post-67405716388866860092014-01-28T10:33:00.002-08:002014-10-29T04:03:31.417-07:00Teaching Math with Minecraft #2: Understanding Addition, Multiplication, and the Commutative Property<div class="separator" style="clear: both; text-align: left;">
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<span style="color: #666666; font-family: 'Trebuchet MS', Trebuchet, Verdana, sans-serif; line-height: 18px;">In a </span><span style="color: blue; font-family: 'Trebuchet MS', Trebuchet, Verdana, sans-serif; line-height: 18px;"><a href="http://theeducationscientist.blogspot.com/2013/08/teaching-math-with-minecraft-impromptu.html" target="_blank">previous post</a></span><span style="color: #666666; font-family: 'Trebuchet MS', Trebuchet, Verdana, sans-serif; line-height: 18px;">, we ran an impromptu learning experiment using <a href="http://www.minecraft.net/" target="_blank">Minecraft</a> to explore different kinds of numbers (even, odd, prime, and square). </span><br />
<span style="color: #666666; font-family: 'Trebuchet MS', Trebuchet, Verdana, sans-serif; line-height: 18px;"><br /></span>
<span style="color: #666666; font-family: Trebuchet MS, Trebuchet, Verdana, sans-serif;"><span style="line-height: 18px;">That first video prompted a number of very interesting conversations. One question that many adults ask is, "elementary arithmetic is so simple, what is there to really understand beyond memorizing a bunch of math facts?" </span></span><br />
<span style="color: #666666; font-family: Trebuchet MS, Trebuchet, Verdana, sans-serif;"><span style="line-height: 18px;"><br /></span></span>
<span style="color: #666666; font-family: Trebuchet MS, Trebuchet, Verdana, sans-serif;"><span style="line-height: 18px;">Actually, there's an awful lot to understand. Memorizing math facts develops fluency, which is important. But conceptual understanding is altogether different - and equally important. </span></span><br />
<span style="color: #666666; font-family: 'Trebuchet MS', Trebuchet, Verdana, sans-serif; line-height: 18px;"><br /></span>
<span style="color: #666666; font-family: 'Trebuchet MS', Trebuchet, Verdana, sans-serif; line-height: 18px;">In an effort to give a concrete example of what "understanding" looks like and how it is different from memorizing facts, I invited Swifty7777 back for a second conversation.</span><br />
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<span style="background-color: white; color: #666666; font-family: 'Trebuchet MS', Trebuchet, Verdana, sans-serif; line-height: 18px;">In this episode, we dig in to some more advanced topics in arithmetic:</span><br />
<ul>
<li><span style="background-color: white; color: #666666; font-family: 'Trebuchet MS', Trebuchet, Verdana, sans-serif; line-height: 18px;">What is addition?</span></li>
<li><span style="background-color: white; color: #666666; font-family: 'Trebuchet MS', Trebuchet, Verdana, sans-serif; line-height: 18px;">What is multiplication?</span></li>
<li><span style="background-color: white; color: #666666; font-family: 'Trebuchet MS', Trebuchet, Verdana, sans-serif; line-height: 18px;">What is the relationship between addition and multiplication?</span></li>
<li><span style="background-color: white; color: #666666; font-family: 'Trebuchet MS', Trebuchet, Verdana, sans-serif; line-height: 18px;">What is the commutative property of addition? Of multiplication?</span></li>
<li><span style="background-color: white; color: #666666; font-family: 'Trebuchet MS', Trebuchet, Verdana, sans-serif; line-height: 18px;">How is commutativity similar and different for addition and multiplication?</span></li>
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<span style="color: #666666; font-family: Trebuchet MS, Trebuchet, Verdana, sans-serif;"><span style="background-color: white; line-height: 18px;"><br /></span></span><span style="color: #666666;"><span style="background-color: white; font-family: Arial, Helvetica, sans-serif; line-height: 18px;"><b>What reactions, questions, or insights does this video generate for you? </b></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>If you liked this "learning with Minecraft" video, check out these others:</b></span><br />
<a href="http://theeducationscientist.blogspot.com/2013/08/teaching-math-with-minecraft-impromptu.html#.VFDCTPTF8QR"><span style="font-family: Arial, Helvetica, sans-serif;">Minecraft Math #1: Numbers - Even, Odd, Prime & Square Root</span></a><br />
<a href="http://theeducationscientist.blogspot.com/2014/10/minecraft-scientists-STEM-education-ep1.html"><span style="font-family: Arial, Helvetica, sans-serif;">Minecraft Scientists Ep. #1: Fishin' In The Rain</span></a><br />
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Anonymoushttp://www.blogger.com/profile/11351479269650780356noreply@blogger.com10tag:blogger.com,1999:blog-6645583842972204443.post-41064316036542689642013-12-19T09:52:00.001-08:002013-12-19T10:00:41.999-08:00What We Know About How Children Learn Math - And How It Can Help Us Close the Achievement Gap(This week's post is the first half of a two-part article I wrote for Footnote1.com.)
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When it comes to math, American students lag behind their counterparts in many European and Asian countries, as do American adults. Our nation’s fourth graders are outperformed in math by students from Singapore, Korea, Japan, Northern Ireland, and Hong Kong, while the U.S. ranks 19th in adult math skills among advanced democracies. These problems exist despite the fact that we spend $1.3 trillion a year – nearly 9% of the American GDP – on education.
Why is such a promising system failing its students?
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<a href="http://footnote1.com/what-we-know-about-how-children-learn-math-%E2%80%93-and-how-it-can-help-us-close-the-achievement-gap/"><span style="color: blue;">Read the full article..</span>.</a>Anonymoushttp://www.blogger.com/profile/11351479269650780356noreply@blogger.com9tag:blogger.com,1999:blog-6645583842972204443.post-52725662402637523292013-09-12T19:04:00.000-07:002013-09-13T07:10:07.815-07:00What's Holding Education Back? (Hint: Check Your Assumptions about Learning & Teaching)<div class="separator" style="clear: both; display: none; text-align: center;">
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<a href="http://commons.wikimedia.org/wiki/File%3AOrlando-Ferguson-flat-earth-map_edit.jpg" title="By Orlando Ferguson [Public domain], via Wikimedia Commons"><img align="left" alt="Orlando-Ferguson-flat-earth-map edit" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Orlando-Ferguson-flat-earth-map_edit.jpg/512px-Orlando-Ferguson-flat-earth-map_edit.jpg" width="300" /></a>
<h3>
The World Has Moved On, But Education Hasn’t </h3>
The world has changed dramatically during the past century. Most domains have changed right along with it, thanks in part to major advances in science and technology. Architecture, for example, has evolved with the invention of new kinds of materials, powerful computer-based design tools, and more sophisticated models of environmental impact.<br />
<br />
Modern medicine, with innovations like brain scanners, artificial hearts, and gene therapy, would be virtually unrecognizable to a physician from the 1900’s. We could tell similar stories about the transformation of engineering, agriculture, and even business administration. Take a practitioner from the 1900’s in any of these fields and bring them into the present day and they would be thoroughly bewildered and unable to perform the job.<br />
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But what about education? If we transported a teacher from the 1900’s and put her in front of a classroom today, she would be able to take over the class without much trouble. There have been some changes, of course. Whiteboards and projectors have replaced blackboards, for example, and students now use laptops and iPads instead of slates. In World History, there’s over a century’s worth of new material to cover. But changes like these are largely cosmetic. Superficial differences aside, the way we educate today is fundamentally the same as it was one hundred and fifty years ago.<br />
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<h3>
What’s Holding Education Back? </h3>
Why has education stayed basically the same for so long while other domains like architecture and medicine have been completely transformed?<br />
<br />
One possible explanation is that there’s simply no room for improvement – that education is already as good as it gets. We’ve explored this in previous posts, though, and based on the evidence I’d say this can’t possibly be true (for example, read <a href="http://theeducationscientist.blogspot.com/2013/07/can-we-make-education-better-or-is-this.html#.UjJuHaVK6MM" target="_blank">this</a>, <a href="http://theeducationscientist.blogspot.com/2013/08/how-can-less-studying-produce-more.html" target="_blank">this</a>, and <a href="http://theeducationscientist.blogspot.com/2013/08/teaching-math-with-minecraft-impromptu.html" target="_blank">this</a>).<br />
<br />
A second possibility is that we don’t know enough yet – that we are still waiting for the big breakthroughs in science and technology that will enable education to advance the way architecture and medicine have. But the fact is that we already <i>know</i> far more about effective learning and teaching than we actually <i>apply</i> in mainstream educational practice. The root problem does not seem to be a lack of good ideas or proven methods.<br />
<br />
I’d like to suggest a third possibility. What if education is being held back by a number of common assumptions about learning and teaching that seem completely obvious to most people but that are nonetheless completely and utterly <i>wrong</i>? What if these assumptions are so obvious and so deep-seated that many people aren’t even aware they are assumptions, and what if education can’t move forward until we surface these assumptions, examine them critically, and get people to revise them?<br />
<br />
If this sounds far-fetched, consider these cases from the history of science:<br />
<br />
<ul>
<li><b>Geography & Navigation</b>: People assumed the earth was flat because if you look around it’s obvious to anyone that it <i>is</i> flat. Because of this assumption, sailors wouldn’t sail out of sight of land for fear of falling off the edge. Challenging this assumption freed people up to sail anywhere – it opened up the whole world to humanity.</li>
<li><b>Astronomy</b>: People assumed the earth is stationary and sits at the center of the universe. Just look up in the sky – the earth is obviously holding still and everything else is circling around it (otherwise we’d all feel pretty dizzy, right?). Even after this assumption was challenged and evidence collected to demonstrate how wrong it was, it took a few centuries to bring everyone around. Changing it opened up the heavens to humanity. Space exploration and communications satellites are just two technologies that would not be possible today under the original (obvious but erroneous) assumption.</li>
<li><b>Biology & Medicine</b>: Quite recently – at least as late as the 19th century - people generally assumed that a disease epidemic like cholera or the Black Death could be caused by a miasma – a cloud of toxic air released by rotting material. After all, if there is a bad smell in the air where a lot of people are getting sick, the most obvious explanation is that the air causing the bad smell must also be causing the bad illness. Once again: obvious, but wrong. Public health has improved greatly since people stopped trying to avoid miasma and started trying to avoid physical contact with people who are carrying disease-causing viruses and bacteria.</li>
</ul>
<br />
The list goes on and on…<br />
<br />
So - what about education today? Is it possible that humanity is at this very moment living with some assumptions about learning and teaching that are so obvious and so deep-seated that they are not even recognized as assumptions but taken as incontrovertible facts?<br />
<br />
I believe we are.<br />
<br />
And not just <i>one</i> such assumption – <i>loads and loads </i>of them. And I propose that these obvious, virtually universal, and yet entirely misleading assumptions are a major reason education has stalled while nearly every other major domain of human endeavor has raced ahead. The same way that the flat earth assumption left most of the world unexplored, these assumptions lead us to educate students in ways that leave most of the subject matter unlearned.<br />
<br />
These are bold claims. Let me provide a specific example.<br />
<br />
It’s obvious to most people that engagement drives learning. It’s a very widespread assumption. In fact, it’s what leads people to take boring materials like math or chemistry flashcards and routinely attempt to inject “fun” into them by adding unrelated cartoons, competitions, sticker prizes, and the like.<br />
<br />
But what if that obvious and deep-seated assumption is wrong? What if the <i>learning</i> actually drives the <i>feeling of engagement</i> instead of the other way around? Moreover, what if trying to artificially inject fun into the mix only gives the illusion of successful education – while actually <i>degrading</i> the quality of learning? There are reasons to believe that this is, in fact, the case.<br />
<br />
<h3>
Do Our Assumptions Really Make a Difference? </h3>
You might well ask, "Does it really matter which is true - whether learning drives engagement or engagement drives learning?"<br />
<br />
Yes, it matters a lot. To see why, let’s pose a similar question about one of our historical examples: “Does it really matter whether we assume the earth is flat or round?”<br />
<br />
Consider:<br />
<br />
If the earth is flat, then we should stay close to shore.<br />
If the earth is a sphere, then we can sail anywhere.<br />
<br />
Similarly:<br />
<br />
If engagement drives learning then we should be able to produce high-quality learning even if we start with low-quality material by over-compensating with fun.<br />
<br />
On the other hand…<br />
<br />
If learning drives engagement, then we actually have to start with high-quality learning experiences if we expect to produce high-quality learning outcomes. Instead of “injecting” fun to make the learning happen, we’ll know the learning is happening when we see students engaging deeply with the subject matter itself. In this view, “fun” (or engagement) is not something one puts <i>into the teaching</i> so much as something one expects to see <i>coming out of the learning</i>.<br />
<br />
The two different assumptions lead to two contradictory conclusions about how to educate effectively. Assumptions are important because they determine the strategies we use to pursue our goals, and some strategies work much better than others.<br />
<br />
As the historical examples cited above illustrate, one way to change the world is to change widespread assumptions that seem obvious to everyone but in fact are simply wrong. It may be that easy – and that difficult – to start bringing education into the twenty-first century.<br />
<br />
<h3>
What do <u>you</u> think?</h3>
Anonymoushttp://www.blogger.com/profile/11351479269650780356noreply@blogger.com15tag:blogger.com,1999:blog-6645583842972204443.post-17885724351166908222013-08-28T04:35:00.000-07:002014-10-29T03:43:42.120-07:00Teaching Math with Minecraft (An Impromptu Education Experiment)<div class="separator" style="clear: both; display: none; text-align: center;">
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In a <a href="http://theeducationscientist.blogspot.com/2013/08/how-can-less-studying-produce-more.html">previous post</a>, we explored the following question:<br />
<br />
<b>How can less studying produce more learning?</b><br />
<br />
We considered examples from chemistry, arithmetic, and foreign language studies where small differences in approach could produce large differences in learning outcomes - on the order of twice the learning in half the time (or better).<br />
<br />
This week, I wanted to push this thinking one step further to explore the related question:<br />
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<b>How difficult is it to design experiences that reliably produce more learning with less studying?</b><br />
<b><br /></b>
To do this, I set up an impromptu experiment. I chose some core math concepts as the subject matter and <a href="https://minecraft.net/" target="_blank">Minecraft</a> as the learning medium. I spent about an hour preparing. I invited a second-grader known as "Swifty7777" (his Minecraft handle) to join me for a conversation, which I recorded. The full conversation (excerpted below) lasted more than half an hour and covered a lot of ground - from the definition of "number" to the commutative property of addition to the relationship between addition and multiplication. We explored some topics, like square roots, that were not part of my original plan but that emerged during the conversation. We both had fun and the time flew by.<br />
<br />
The video below is a shorter excerpt of our conversation in which we explore five questions:<br />
* What is a number?<br />
* What is an even number?<br />
* What is an odd number?<br />
* What is a prime number?<br />
* What is a square root?<br />
<br />
<iframe allowfullscreen="" frameborder="0" height="400" src="http://www.youtube.com/embed/IDr6v9HsmxQ?feature=player_detailpage" width="512"></iframe><br />
<br />
What do you think of this experiment?<br />
What do you think we can learn from it?<br />
<br />
<b>If you liked this "learning with Minecraft" video, check out these others:</b><br />
<a href="http://theeducationscientist.blogspot.com/2014/01/teaching-math-with-minecraft-2.html">Minecraft Math #2: Understanding Addition, Multiplication & Commutativity</a><br />
<a href="http://theeducationscientist.blogspot.com/2014/10/minecraft-scientists-STEM-education-ep1.html">Minecraft Scientists Ep. #1: Fishin' In The Rain</a>Anonymoushttp://www.blogger.com/profile/11351479269650780356noreply@blogger.com11tag:blogger.com,1999:blog-6645583842972204443.post-44856697994106942962013-08-19T07:10:00.000-07:002014-02-20T13:48:26.294-08:00Children and Technology: How Should We Manage Kids' Screen Time?<a href="http://commons.wikimedia.org/wiki/File%3AWilcox.jpg" title="A Child's Garden of Verses, By Jessie Willcox Smith (1863 – 1935) (en:Image:Wilcox.jpg) [Public domain in the US and the country of origin], via Wikimedia Commons"><img align="left" alt="Jessie Willcox Smith, A Child's Garden of Verses" src="//upload.wikimedia.org/wikipedia/commons/e/ee/Wilcox.jpg" width="200" /></a>
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(Originally posted at <a href="http://www.nativebrain.com/2012/08/is-technology-good-or-bad-for-young-children/" target="_blank">nativebrain.com</a>)<br />
<strong style="font-size: 16px;">Is technology good or bad for my child?</strong></div>
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This question is on a lot of people’s minds. If you’ve ever seen a child with a touchscreen computer like a smartphone or an iPad, it’s easy to understand why. The devices seem to enchant kids like few things that have come before – reliably absorbing them for a surprisingly long time. And good luck taking one away!</div>
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Many parents experience conflicting feelings about their kids’ powerful attraction to touchscreen computers. On one hand, it can be challenging (and exhausting) trying to keep a child content all day long – especially during long car trips or waits at restaurants and the doctor’s office. Having a reliable “high tech pacifier” sometimes comes in very handy. And the fact that kids can engage with interactive apps instead of just passively viewing videos means that they might even benefit somehow, by learning problem solving skills through games, for example, or expressing themselves through digital finger painting.</div>
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On the other hand, many parents worry about the opportunity costs of “screen time” – that is, time when kids aren’t exercising their bodies, interacting with other people, or experiencing the “real” world. Others fear that the devices may in fact be <em>too</em> engaging – that once a child has visited the world of Angry Birds and Fruit Ninjas they might never want to come back…</div>
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<strong>The apparent paradox of digital technology</strong></div>
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Parents are all over the map on how to manage their kids’ access to touchscreen computers. At one extreme, some kids have unrestricted, unmonitored use of their own personal devices and spend tens of hours each week with them. At the opposite extreme, some families try to keep their kids completely “screen-free” for as many years as possible.</div>
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Parents frequently ask some version of the following question:</div>
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<em>How should I manage my child’s time in the digital world so it doesn’t interfere with their understanding and appreciation of the “real” world?</em></div>
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In this post, I want to explore how this question sheds light on the conflict many parents experience concerning their children’s use of technology, and how we might reframe the issue in a way that can help us move beyond that conflict.</div>
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I find it interesting that at the heart of this question is a kind of paradox, in that the “digital” world is at the same time seen as somehow <em>less real</em> yet <em>more compelling</em> than the offline (or “real”) world.</div>
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Think for a moment: what else in our lives is both less real and also more compelling than the alternatives? Junk food and Ponzi schemes come to mind. Junk food is less nutritious than whole food, but when given a choice, people – especially kids – often find the junk food more appealing. Ponzi schemes are financially disastrous compared to legitimate financial investments and yet many people are lured by their false promise of quick riches. If these are the kinds of associations that come to mind for people when they think about children and touchscreens, then it’s no wonder they experience ambivalence and uneasiness regarding children’s use of the technology!</div>
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If we stop for a moment and reflect, though, we realize that such comparisons can’t possibly be appropriate. Touchscreen computers are simply a means for distributing content, like dinner plates or printer paper. Dinner plates can deliver either junk food or whole food. Printer paper can deliver a contract for shares in a Ponzi scheme or a U.S. government bond. Similarly, touchscreen computers can deliver effective, developmentally appropriate learning experiences or “chewing gum for the eyes.” In all three cases, to label the plate, the paper, or the touchscreen computer as “good” or “bad” in absolute terms is to confuse the delivery medium with the contents delivered.</div>
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In short: it stands to reason that touchscreen computers are not inherently good or bad for children, any more than dinner plates or printer paper are inherently good or bad for them. It doesn’t, for example, make sense to compare the devices directly to junk food or to whole food; they can be used to <em>serve up</em> the digital equivalent of either type. It all depends on how we choose to use them.</div>
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<strong>So what’s a parent to do?</strong></div>
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While this shift in perspective does not provide hard guidelines for how to manage kids’ access to digital technology, it can help shift the questions that are generating conflict in parents’ minds. In particular, the either-or question “Is digital technology good or bad for my child?” causes ongoing stress for parents because there appear to be big consequences for getting the answer wrong – but the question stated that way doesn’t actually have an answer. The result is that parents constantly agonize over whether they are doing the right thing for their child, with no relief in sight.</div>
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A variation of that question asks, “How much screen time is OK for my child?” This question certainly makes it easier to provide specific guidelines – various organizations have come out with clear recommendations such as “no screen time through age two,” or “limiting screen time to one hour per day is OK,” etc. But this is like asking “how long should my child spend at the table with a dinner plate in front of her during the day?” Setting an arbitrary time limit doesn’t make a whole lot of sense. The important question is: <em>What are they consuming from that dinner plate and how much of it?</em></div>
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Similarly, a more useful question regarding technology for parents is: “What are your kids doing on the touchscreen computer, and how much of each type of activity is appropriate?” If all the child wants to do is watch nonsensical cartoons on an iPad, then a parent might reasonably decide to limit the daily amount of time spent on that activity. But what about the case of a three-year-old boy I know, who became so completely engrossed in learning all the countries of the world, their capitals, and where to place them on a map, that he rapidly <em>mastered them all</em>. Ask yourself: would you allow the child to spend hours – even an entire day – studying geography using a paper atlas or a globe? Now ask yourself: do you have a principled rationale for arbitrarily limiting his time engaged in the same activity on an iPad? If you do, then well and good. If you don’t, then imagining how you would manage the activity off the device can be a good guide for deciding how to manage their activity on the device.</div>
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<strong>Summary and Take-Aways</strong></div>
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Parents want the best for their kids, and they experience unpleasant stress when they don’t know what course of action is best. Here’s a quick summary on this issue with regard to children’s use of touchscreen computers:</div>
<ul style="color: #333333; font-family: Lora, Georgia, 'Times New Roman', Times; font-size: 16px; line-height: 25px; margin: 0px; padding: 0px 0px 20px;">
<li style="background-image: url(http://www.nativebrain.com/wp-content/themes/focus/images/icon-right.png); background-position: 2px 7px; background-repeat: no-repeat no-repeat; list-style-type: none; margin: 0px 0px 5px 20px; padding: 0px 0px 0px 20px;">Avoid the question, “Is technology good or bad for my child?” It’s a trap with no way out.</li>
<li style="background-image: url(http://www.nativebrain.com/wp-content/themes/focus/images/icon-right.png); background-position: 2px 7px; background-repeat: no-repeat no-repeat; list-style-type: none; margin: 0px 0px 5px 20px; padding: 0px 0px 0px 20px;">Move beyond the question, “How much screen time is OK for my child?” It’s like asking how long your child should sit at the dinner table – not very meaningful.</li>
<li style="background-image: url(http://www.nativebrain.com/wp-content/themes/focus/images/icon-right.png); background-position: 2px 7px; background-repeat: no-repeat no-repeat; list-style-type: none; margin: 0px 0px 5px 20px; padding: 0px 0px 0px 20px;">Let this question be your guide: “How much do I value what my child is doing and learning from a particular experience (whether they are doing it online or offline)?” Each parent is in the best position to answer that question for their child and to make a judgment about how much time they think is appropriate based on their values. It may not be quite as easy as setting arbitrary time limits for your child based on third-party recommendations, but at the end of the day it should leave you feeling more empowered to make good decisions on your child’s behalf and less stressed about whether you are doing the “right thing” for them.<div class="separator" style="clear: both; text-align: center;">
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Anonymoushttp://www.blogger.com/profile/11351479269650780356noreply@blogger.com6tag:blogger.com,1999:blog-6645583842972204443.post-1007040927173556622013-08-07T14:12:00.001-07:002014-02-20T13:18:49.905-08:00Why a touchscreen (tablet or iPad) is better than a mouse and keyboard for young learners<a href="http://commons.wikimedia.org/wiki/File%3AWir_gratulieren_Illustration_2.jpg" title="By W. Christian, Wir gratulieren! Eine Sammlung von Kinderglückwünschen für Geburts-, Neujahrs- und Festtage nebst einem Anhang, Löwensohn, Fürth (c. 1900) [Public Domain in the US and the country of origin], via Wikimedia Commons"><img align="left" alt="W. Christian Wir gratulieren" src="//upload.wikimedia.org/wikipedia/commons/e/e2/Wir_gratulieren_Illustration_2.jpg" width="256" /></a>
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(This article was originally posted at <a href="http://www.nativebrain.com/blog">http://www.nativebrain.com/blog</a>.)</div>
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<strong>The Idea, In Brief</strong></div>
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As schools acquire significant numbers of tablets (Androids and iPads), administrators face questions regarding how these devices relate to the other learning technologies they already own. In particular, should tablets be thought of as a less expensive and more portable version of desktop and laptop computers? Or should they be thought of as a new type of educational technology altogether?</div>
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In this article, I argue that although today’s tablet computers are probably incremental innovations when it comes to adult productivity (“getting work done”), they are better thought of as major innovations when they are used as learning technologies, especially for children. <span id="more-448"></span>I highlight two issues in particular:</div>
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<li style="list-style-type: decimal; margin: 0px 0px 0px 35px; padding: 0px;">Touchscreen computers enable many children as young as one year old (and in some cases even younger) to engage in <em>independent learning activities</em> on the computer <em>for the first time</em>, and</li>
<li style="list-style-type: decimal; margin: 0px 0px 0px 35px; padding: 0px;">Although there is not yet much empirical data on the relative benefits of touchscreen computers compared to desktop and laptop models, learning theory suggests we can expect <em>faster learning</em> and <em>greater knowledge transfer</em> from learning on a touchscreen computer compared to one equipped with a keyboard and mouse.</li>
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<strong>A Brief History of Educational Technology</strong></div>
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Major technological innovations have arrived in waves over the past century, each bringing with it new opportunities and challenges for educators.</div>
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<em>The Broadcast Epoch</em></div>
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Early technologies included radio and television. These broadcast media opened up new possibilities for educators, but were highly inflexible and therefore difficult to incorporate into lessons. The invention of recording and playback technologies – especially videocassettes and laser disks – gave teachers control over the time and place of presentation so that they could incorporate them systematically into their teaching plans. Despite some clever and heroic efforts to make these technologies interactive, however, their capacity for interaction and adaptation were very limited and consequently they were still used mostly to “push” the same set of canned programs to all learners.</div>
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<em>The Interactive Epoch</em></div>
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The emergence of affordable personal computers changed the game. First, the desktop computer arrived in the late 1970’s, followed a few years later by smaller and more portable laptop models. Computers were different from broadcast technologies in many ways, perhaps most notably from an educational standpoint in terms of their ability to respond to user input. That is, unlike broadcast television and audio programs, computer programs could change their behavior in response to different user actions, opening the door to more interactive, individualized, and dynamic learning experiences.</div>
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<em>The Networked Epoch</em></div>
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The World Wide Web became mainstream in the 1990’s, ushering in the era of massively networked communication. The Web created opportunities to aggregate data across users and analyze patterns to provide a more social, customized, and targeted experience – consider, for example, the targeted book recommendations from Amazon.com, the free self-study courses available via iTunes University, and the massive information sharing among educators and other stakeholders taking place on blogs, Facebook, and Twitter.</div>
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In each technology epoch there have been major shifts – such as the rise of personal computing and the emergence of ubiquitous social networks – that have created qualitatively new kinds of experiences and opportunities, and there have been more incremental advances – such as the laser disk following VHS and the laptop following the desktop computer – that have not so much enabled truly new experiences as they have expanded the availability, usefulness, and flexibility of existing opportunities in more modest ways.</div>
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Currently, in the second decade of the twenty-first century, we are experiencing the rapid global adoption of touchscreen devices like smartphones and iPads. Which raises the question…</div>
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<strong>Are touchscreen computers incremental extensions of desktop and laptop computers or a qualitatively new category of technology?</strong></div>
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I would suggest they are both, but for different audiences.</div>
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For many adults, in particular, the jury still seems to be out on this question. <a href="http://www.guardian.co.uk/technology/2012/apr/25/tablet-pc-market-analysis" style="color: text-decoration: none;" target="_blank">Tablet sales are growing fast</a>, but few adults who use their computers for production work such as word processing, software development, or video editing are <em>replacing </em>their laptop or desktop computers with tablets. <a href="http://news.cnet.com/8301-1035_3-57471581-94/could-i-really-ditch-my-laptop-for-an-ipad/" style="text-decoration: none;" target="_blank">The devices are still underpowered and the touchscreen interface tends to make them awkward to use for those types of tasks</a>. Most such people are evidently buying tablets <em>in addition to</em> their primary computer and using them for lighter, more consumption-oriented tasks like surfing the web, reading email, and playing games. From an adult’s perspective, touchscreen computers appear to be more like incremental extensions of desktop and laptop computers.</div>
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And that’s the trap – the fact that adults experience tablet computers as less powerful but more portable versions of laptop computers is likely to blind them to the fact that for young children, touchscreen computers are truly revolutionary innovations – in the sense that they have the potential to enable entirely novel kinds of experiences. Two important benefits of touchscreen computers as learning technologies are that they enable <em>access to independent learning activities</em> to some groups of learners for the first time and they support <em>faster learning that is also more transferable to the “real world.”</em></div>
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<strong>In terms of accessibility, touchscreen computers represent the first personal computer revolution for children</strong></div>
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For the youngest children, who can’t effectively use a keyboard or mouse, the arrival of tablet computers is analogous to the arrival of the first personal computers for adults in the 1970’s. Tablets make personal computing – with all of its interactivity, adaptiveness, and dynamism – fully accessible to millions of young children for the first time. Why? Because the tap and swipe gestures used to manipulate virtual objects on a tablet computer can be made very similar to the kinds of gestures that children would spontaneously use on physical objects in the real world.</div>
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Using a keyboard or mouse requires learning a new skill, and that skill is both counter-intuitive and idiosyncratic to the domain of computer use. Where else in life, for example, do we touch something in one place (the left mouse button, for example) while looking in a completely different place for the effect of that action (a point on the computer monitor that is three feet away from the hand doing the pressing)? This situation is not only unnatural – it also involves <em>applying a skill that is unrelated to the task at hand and – for young children at least – is generally more complex than the task they are actually trying to accomplish in the first place</em>.</div>
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Think about that for a second. If the game we are playing with a child is to identify which of three objects is a particular color (“which one is blue?”), then the response we want from them is not terribly complex – they should, for example, point to or grab the one blue object out of the three different colored objects arrayed in front of them. Such a response generally requires only very gross motor control, and the action is very intuitive – they look at the object and then grab at the same spot where they are looking. Our brains evolved to handle this kind of task almost reflexively very early in life.</div>
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If we expect the child to respond using a mouse, however, suddenly the task requires not only fine motor control – placing the tiny cursor on the virtual blue object using the mouse – but also a complex coordination of counterintuitive fine motor actions: look straight ahead at a cursor moving on a vertically oriented screen while moving a mouse sitting off to your side across a horizontally oriented table, and then hold the mouse perfectly steady while pressing the correct button on it to indicate your selection. The child can know the right answer while being completely unable to express it using this complex interface, which can make a straightforward, enjoyable learning activity both puzzling and frustrating.</div>
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For children, the touchscreen is the first computer interface that does not automatically add a high barrier to entry for engaging in an activity that is completely unrelated to the activity itself. Consequently, many more children can engage in a greater range of independent learning activities than ever before.</div>
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<strong>Touchscreen interfaces support learning that is far more transferable to the “real world” than keyboards and mice</strong></div>
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Beyond making the interactive capabilities of computers fully accessible to many children for the first time, however, there is an even more important educational benefit of touchscreen computers compared to their desktop and laptop cousins. Learning theory suggests that we can expect the natural gestures used with the touchscreen interface to support <em>faster learning</em> and<em>greater knowledge transfer</em> from computer to real world than an otherwise identical activity accessed on a desktop or laptop computer via keyboard and mouse.</div>
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To illustrate why this is true, imagine a boy who dreams of being a great chef but grows up in a small apartment with limited facilities. The only kitchen appliances are a fridge/freezer and a microwave oven. The boy helps his parents prepare food every day – a combination of frozen meals and dishes improvised from fresh ingredients. Over time, his skill grows, so that he can successfully prepare a variety of dishes with hardly a glance at recipes or recommended preparation instructions. The boy loves to cook and he has received a lot of positive feedback for his skill at operating the microwave.</div>
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Now imagine that this same boy lands his first job – as a sous chef in a restaurant. He shows up for his first day eager to build on his skills only to find that he doesn’t know how to perform even the most basic tasks like slicing and dicing vegetables or pre-heating the conventional oven – and he is alarmed to see people putting metal containers into it! What is going on? The boy’s knowledge of food preparation is all mixed up with the peculiarities of the tool he uses for cooking – the microwave oven.</div>
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Similarly, when children engage in certain types of learning via keyboard and mouse, the peculiarities of the interface can become mixed up with the subject matter they are learning. For example, imagine a child is working on developing her visual spatial skill by playing a “Tangrams” type puzzle game that involves dragging and rotating pieces into position. She uses the “Tab” key to select a puzzle piece, the space bar to pick it up, the arrow keys to move it into position, and then the “[” and “]” keys to rotate the piece left and right. The girl might become very proficient at this type of task. But how much will proficiency in this activity transfer to physical challenges in the real world where the actions required to drag and rotate pieces into place are completely different, and where there are no space bars or arrow keys? The child in this scenario is like the boy who steps into a fully equipped kitchen for the first time – she is likely to find that her keyboard-and-mouse knowledge does not apply readily to real-world situations.</div>
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The advantage of the touch screen is that the actions required to complete a task can be made much more similar to actions taken on physical objects – dragging a virtual object requires touching the object and dragging it with one or more fingers, for example, and rotating the object can be done by rotating one’s fingers on the screen.</div>
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The actions are of course not exactly the same as they would be with physical objects, but the point is that they are much more similar and that should support both faster learning and greater transfer. In fact, by combining the benefits of real-world interaction with the adaptive affordances of computer technology, in some cases touchscreen computers like iPads can provide entirely novel learning experiences that would not be possible in either the real world or on a computer with keyboard and mouse.</div>
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But don’t take my word for it – check out some examples of young children using iPads:</div>
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<a href="http://www.youtube.com/watch?v=MGMsT4qNA-c" style="text-decoration: none;" target="_blank" title="YouTube video: 2-year-old child using iPad">Two-year-old drawing and using apps</a></div>
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<a href="http://www.youtube.com/watch?v=IHqbcGgf90o" style="text-decoration: none;" target="_blank" title="YouTube video: 14-month-old baby using iPad">14 month old baby playing Angry Birds</a></div>
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<a href="http://www.youtube.com/watch?feature=player_detailpage&v=2Iy0y_XeKhU#t=60s" style="text-decoration: none;" target="_blank" title="YouTube video: 15-month-old baby using iPad">15 month old baby playing Garage Band</a></div>
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You won’t see them doing that on a laptop computer!</div>
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The iPad has only been around for a little over two years. As of this writing, empirical research on children’s use of tablet computers is scant. As one can plainly see from videos like those above, however, touchscreens have made computers accessible to a large number of children in unprecedented ways. Even more exciting, learning theory suggests that tablet computers like the iPad can support <em>higher quality learning</em> than desktop or laptop computers.</div>
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Adults would do well to keep these considerations in mind when making choices on behalf of the children in their care. Despite appearances, all learning technologies are <span style="text-decoration: underline;">not</span> created equal.</div>
Anonymoushttp://www.blogger.com/profile/11351479269650780356noreply@blogger.com4tag:blogger.com,1999:blog-6645583842972204443.post-36223980809985187472013-08-05T05:54:00.000-07:002013-08-05T05:54:38.799-07:00How Can Less Studying Produce More Learning? <a href="http://commons.wikimedia.org/wiki/File%3AFrederick_Alfred_Slocombe_Wandering_thoughts.jpg" title="By Frederick Alfred Slocombe (1847-c. 1920) (Bonhams) [Public domain], via Wikimedia Commons"><img align="left" alt="Frederick Alfred Slocombe Wandering thoughts" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/86/Frederick_Alfred_Slocombe_Wandering_thoughts.jpg/256px-Frederick_Alfred_Slocombe_Wandering_thoughts.jpg" width="256" /></a>
<span style="font-family: Verdana, sans-serif;">In a <a href="http://theeducationscientist.blogspot.com/2013/07/can-we-make-education-better-or-is-this.html" target="_blank">previous post</a>, I introduced two notable examples of applied learning science: SHERLOCK and <i>RightStart</i>. They demonstrate that the difference between an average instructional design and an optimal design can be huge - much bigger than most people realize. In this post, I use those examples as a jumping off point to explore two questions:</span><br />
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<span style="font-family: Verdana, sans-serif;">1) What could cause such large differences in learning outcomes if the basic "subject matter" being taught doesn't change?</span><br />
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<span style="font-family: Verdana, sans-serif;">2) How unusual are the SHERLOCK and </span><i style="font-family: Verdana, sans-serif;">RightStart</i><span style="font-family: Verdana, sans-serif;"> results? In particular, should we only expect those kinds of results from formal, long-term, well-funded research studies?</span><br />
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<span style="font-family: Verdana, sans-serif;">But first, I need to introduce the following key insight.</span><br />
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<span style="font-family: Verdana, sans-serif;">Key Insight: Don't Mistake <i>Subject Matter</i> for <i>Knowledge</i></span></h3>
<span style="font-family: Verdana, sans-serif;">When I was in high school, I ran a tutoring business. I loved helping my peers learn about subjects like math, science, and writing. As a bonus, not only did I deepen my own understanding of these subjects, but I also learned a ton about how other people come to understand them.</span><br />
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<span style="font-family: Verdana, sans-serif;">One of the more interesting insights I gleaned was this:</span><br />
<span style="font-family: Verdana, sans-serif;">Subject matter <i>taught</i> is not the same as subject matter <i>learned</i>. </span><br />
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<span style="font-family: Verdana, sans-serif;">Let me illustrate with an example based on actual events. </span><br />
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<span style="font-family: Verdana, sans-serif;">One of my tutoring clients was a good friend named Susan. She was a diligent student in all subjects and a strong writer, but she struggled with math and science. One day we were studying math at her house. As I was packing up to leave at the end of the hour, Susan groaned, "Now I have to study for tomorrow's chemistry test. I <b>hate</b> chemistry."</span><br />
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<span style="font-family: Verdana, sans-serif;">"Why?" I asked.</span><br />
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<span style="font-family: Verdana, sans-serif;">"There's too much to remember!" she complained.</span><br />
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<span style="font-family: Verdana, sans-serif;">"Show me," I said.</span><br />
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<span style="font-family: Verdana, sans-serif;">She pulled out a stack of homemade flashcards and flipped the first one onto the table. Written on it was the formula for the "Ideal gas law" in chemistry:</span><br />
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<span style="font-family: Verdana, sans-serif;">PV = nRT</span><br />
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<span style="font-family: Verdana, sans-serif;">"There are all these formulas," Susan said, "and I can't keep them straight in my head because they all look alike." Then she dealt out a bunch more cards to illustrate her point:</span><br />
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<span style="font-family: Verdana, sans-serif;">P = nRT / V</span><br />
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<span style="font-family: Verdana, sans-serif;">V = nRT / P</span><br />
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<span style="font-family: Verdana, sans-serif;">n = PV / (RT)</span><br />
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<span style="font-family: Verdana, sans-serif;">R = PV / (nT)</span><br />
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<span style="font-family: Verdana, sans-serif;">T = PV / (nR)</span><br />
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<span style="font-family: Verdana, sans-serif;">I stared at the cards. "Susan, that's algebra." </span><br />
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<span style="font-family: Verdana, sans-serif;">"No, this is for my chemistry test," she insisted.</span><br />
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<span style="font-family: Verdana, sans-serif;">"No, I mean those aren't six different formulas," I explained, "It's the same formula written six different ways. If you start with any one of them you can get to all five of the others using simple algebra. In fact, you just used the same algebra in some of your math homework during the last hour."</span><br />
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<span style="font-family: Verdana, sans-serif;">Her eyes widened with dawning recognition. "Oooohhhhhh - I never realized you could use algebra in another subject like that!"</span><br />
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<span style="font-family: Verdana, sans-serif;">No wonder chemistry was so hard for her! She had to memorize about five times as much subject matter as the student sitting next to her who realized he could use algebra there. Note that both students would have been exposed to the same <i>subject matter</i> - algebra and chemistry. It would have been their <i>knowledge</i> (or <i>understanding</i>) of the two subjects that was organized slightly differently. But the implications for future learning were not slight at all - they were quite huge. Huge on the scale of SHERLOCK and <i>RightStart,</i> in fact. The picture below illustrates this scenario.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiS0ngrB2_p1DS-THkPtwZIt3to1hjYqKfUnS5fLJFfkgM4kBCES6w24Jn40No6nYuayRHwuz-lidCxWWIvokwg_kZP_0Qxg8kQpIOlMOrwIXHN20XZRUp-r8Kv52wErC4MvSF7NFSoUhrE/s1600/IdealGasLaw_Comparison.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiS0ngrB2_p1DS-THkPtwZIt3to1hjYqKfUnS5fLJFfkgM4kBCES6w24Jn40No6nYuayRHwuz-lidCxWWIvokwg_kZP_0Qxg8kQpIOlMOrwIXHN20XZRUp-r8Kv52wErC4MvSF7NFSoUhrE/s1600/IdealGasLaw_Comparison.png" height="368" width="640" /></a></div>
<span style="font-family: Verdana, sans-serif;"><br /></span><span style="font-family: Verdana, sans-serif;">This example also suggests a way to think about how SHERLOCK and RightStart could produce such large gains compared to other curricula covering similar subject matter. </span><span style="font-family: Verdana, sans-serif;">In particular, if we imagine two students taking the exact same classes at the exact same time, we can see how one student could easily spend <i>twice as much time</i> as the other student to learn <i>half as much material</i> with <i>less understanding</i>. It stands to reason that a curriculum designed to ensure that every student has mastered key concepts and skills before moving on could produce dramatically better learning outcomes than a curriculum that leaves it up to each student to find their own way - even if the subject matter is ostensibly the same in both designs.</span><br />
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<span style="font-family: Verdana, sans-serif;">And we should note that even though Susan eventually made the connection between algebra and chemistry, she had already suffered (unnecessarily) through years of tedious studying just to make a passing grade in science while watching some of her peers seem to breeze through with top marks. How often does a single, critical misstep like this prevent a student from pursuing - or even exploring - entire categories of career? The stakes are very high in education - people's life outcomes hang in the balance.</span><br />
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<span style="font-family: Verdana, sans-serif;">Example: Arithmetic</span></h3>
<span style="font-family: Verdana, sans-serif;">The chemistry example is not unique - far from it. Consider a similar example from arithmetic - memorizing the times tables from 1x1 up to 12x12.</span><br />
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<span style="font-family: Verdana, sans-serif;">Memorizing all of these multiplication facts would involve 144 flashcards: 1x1, 1x2, 2x1, 2x2, and so on, all the way up to 12x12 (as shown in the left panel of the next figure).</span><br />
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<span style="font-family: Verdana, sans-serif;">But if the student knows the commutative property of multiplication (which means, for example, that 1x2 = 2x1) then suddenly there are only 78 facts to remember (plus one rule), as shown in the right panel in the figure below. The student who doesn't understand the commutative property has to memorize nearly <i>twice as much information</i> as the student who does. The same observation applies to learning the addition tables.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWl45ZBIcSCOznLKWtj7RIwjJeMLZid5S7VRAEF8DRD37wS5uaRLJOHE6VrilRH3RaEcLZB0NZj9LQDyqb_1QhNYnIk0QGkYnI4c61vJ_y0rf_C23tPlF0XmpMzQsgcHOo7I3lcEN7pFxx/s1600/TimesTables_comparisonWithLabels.png" imageanchor="1" style="clear: left; display: inline !important; float: left; margin-bottom: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWl45ZBIcSCOznLKWtj7RIwjJeMLZid5S7VRAEF8DRD37wS5uaRLJOHE6VrilRH3RaEcLZB0NZj9LQDyqb_1QhNYnIk0QGkYnI4c61vJ_y0rf_C23tPlF0XmpMzQsgcHOo7I3lcEN7pFxx/s1600/TimesTables_comparisonWithLabels.png" height="338" width="640" /></a><br />
<br />
<h3>
<span style="font-family: Verdana, sans-serif;">Example: Foreign languages</span></h3>
<span style="font-family: Verdana, sans-serif;">The problem is not limited to math and science, either. Consider foreign language studies. Linguists use the term "cognate" to describe words in different languages that derive from the same origin. For example, "university" in English and "universidad" in Spanish are cognates, as are "city" / "ciudad" and "accident" / "accidente." The Spanish student who recognizes the general patterns by which cognates are related (for instance: "-ty" in English becomes "-dad" in Spanish and vice versa) will have quite a bit less to learn than the student who doesn't pick up on those patterns.</span><br />
<br />
<h3>
<span style="font-family: Verdana, sans-serif;">Just the tip of the iceberg...</span></h3>
<span style="font-family: Verdana, sans-serif;">As these examples from familiar school subjects illustrate, knowing what (or how much) subject matter is being taught doesn't tell us what (or how much) subject matter is being learned. The differences are not on the order of 1% or 10% either - even in these simple cases the swings are closer to 200% to 500%. </span><br />
<span style="font-family: Verdana, sans-serif;"><br /></span>
<span style="font-family: Verdana, sans-serif;">But these simple cases represent just the tip of the iceberg. As the example from Susan illustrates, the differences accumulate and compound as multiple subject areas interact (or not), and as new knowledge is layered on top of old. </span><br />
<span style="font-family: Verdana, sans-serif;"><br /></span>
<span style="font-family: Verdana, sans-serif;">At still deeper levels of analysis where we apply insights from Cognitive Science, we find that issues arise when knowledge is stored in one type of memory system in the brain that should really be stored in a completely different type of memory system. </span><span style="font-family: Verdana, sans-serif;"> For example, a child could memorize the steps involved in tying one's shoes as declarative facts (Step 1: hold the shoelaces apart near the tips, Step 2: cross the right lace over the left and exchange the tips between hands, ...), but to actually <i>tie</i> their shoes effortlessly they will need to transfer that information to procedural memory. That should be obvious in the case of tying shoes, but it applies equally well to the difference between being able to recite the "six key features of a persuasive essay" (declarative facts) and the procedural knowledge required to actually <i>compose</i> an essay that influences people.</span><br />
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<h3>
<span style="font-family: Verdana, sans-serif;">What do you think?</span></h3>
<span style="font-family: Verdana, sans-serif;">In this post we have explored the question of whether the dramatic learning gains documented in projects like SHERLOCK and <i>RightStart </i>are likely to be rare - perhaps only discoverable and accessible through systematic, long-term, and expensive formal research projects - or whether they are more commonplace and readily accessible by teachers in regular classrooms. I think the examples above provide pretty compelling evidence for the latter. </span><br />
<span style="font-family: Verdana, sans-serif;"><br /></span>
<span style="font-family: Verdana, sans-serif;">What do you think? What experiences or examples can you share to push the conversation forward?</span>Anonymoushttp://www.blogger.com/profile/11351479269650780356noreply@blogger.com10tag:blogger.com,1999:blog-6645583842972204443.post-40472932371085209512013-07-29T11:01:00.006-07:002013-07-29T12:34:08.533-07:00How Can Education Experiments Make Education Better?<span style="font-family: Trebuchet MS, sans-serif;"><a href="http://commons.wikimedia.org/wiki/File%3A4_The_Scientists.JPG" title="The Scientists, By Rita Greer, via Wikimedia Commons"><img align="left" alt="The Scientists" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/09/4_The_Scientists.JPG/512px-4_The_Scientists.JPG" title="" width="265" /></a>
</span>
<span style="font-family: Trebuchet MS, sans-serif;">In a <a href="http://theeducationscientist.blogspot.com/2013/07/can-we-make-education-better-or-is-this.html" target="_blank">previous post</a>, I suggested that to make education better we should “Stop arguing about what people <i>think will work</i> in education and start experimenting to determine <i>what actually works</i>.”</span><br />
<span style="font-family: Trebuchet MS, sans-serif;"><br /></span>
<span style="font-family: Trebuchet MS, sans-serif;">There were a number of reader comments (thanks to Jeff, Stacie, and Suzanne in particular) that helped me to understand that the word “experiment” may carry some extra baggage that wasn't part of what I had in mind here. In this post, I’ll try to clarify what I mean and offer an example.</span><br />
<h3>
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></h3>
<h3>
<span style="font-family: 'Trebuchet MS', sans-serif;">How </span><u style="font-family: 'Trebuchet MS', sans-serif;">not</u><span style="font-family: 'Trebuchet MS', sans-serif;"> to run education experiments</span></h3>
<span style="font-family: Trebuchet MS, sans-serif;"><br /></span>
<span style="font-family: Trebuchet MS, sans-serif;">First, a few things I <i>don’t</i> mean when I talk about “education experiments”:</span><br />
<ul>
<li><span style="font-family: Trebuchet MS, sans-serif;">I don’t mean we should bring scientists in white lab coats into the classroom so that they can better understand how our children’s brains work – that is <i>cognitive</i> science, not <i>education</i> science.</span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">I don’t mean we should bring academics in white lab coats into the classroom to test their speculative or radical new math curriculum for the very first time on our children for the benefit of future generations.</span></li>
</ul>
<span style="font-family: Trebuchet MS, sans-serif;">Don’t get me wrong – I think both basic and applied academic research are extremely important and have their place (with appropriate safeguards and informed consent all around). In particular, these kinds of research can benefit society greatly over the long term. But academic research is not what I had in mind here for two reasons:</span><br />
<ol>
<li><span style="font-family: Trebuchet MS, sans-serif;">I am more interested in research that has a good chance of benefiting the <i>participating students</i> in the short term, and</span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">I am interested in research that leverages the <i>teacher’s special knowledge and insight</i> about the capabilities and needs of <i>those particular students</i>.</span></li>
</ol>
<br />
<h3>
<span style="font-family: Trebuchet MS, sans-serif;">A different take on education experiments (with an example)</span></h3>
<br />
<span style="font-family: Trebuchet MS, sans-serif;">What I am proposing is more akin to <a href="http://en.wikipedia.org/wiki/Action_research" target="_blank">action research</a>, or <a href="http://en.wikipedia.org/wiki/Design-based_research" target="_blank">design-based research</a>. To clarify what I have in mind, I’ll give an example from real life. </span><br />
<span style="font-family: Trebuchet MS, sans-serif;"><br /></span>
<span style="font-family: Trebuchet MS, sans-serif;">In my work as an educational designer and consultant, I have the pleasure of talking with some extremely dedicated teachers. Sometimes I meet them when they send a message, out of the blue, with a specific idea or question about how to do more for their students. Below is an example of one such message I received about a year ago.</span><br />
<span style="font-family: Trebuchet MS, sans-serif;"><br /></span>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtZk_sazAuDwIRPXq3T9swsT_ZOVSfB4qvvObcl9C7bm5mQViWyghp48U53umK0rq4tzrwP6al97e4nVW80JoIsPbsBGIj_HR1hGYbi6BYy_e0Rmry13wLbJLQfn1NQg1Bt1qDrIkNrER9/s1600/EducExp1_quote.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Trebuchet MS, sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtZk_sazAuDwIRPXq3T9swsT_ZOVSfB4qvvObcl9C7bm5mQViWyghp48U53umK0rq4tzrwP6al97e4nVW80JoIsPbsBGIj_HR1hGYbi6BYy_e0Rmry13wLbJLQfn1NQg1Bt1qDrIkNrER9/s1600/EducExp1_quote.png" height="195" width="640" /></span></a></div>
<span style="font-family: Trebuchet MS, sans-serif;"><br /></span>
<span style="font-family: Trebuchet MS, sans-serif;">Key points to note about the situation:</span><br />
<ul>
<li><span style="font-family: Trebuchet MS, sans-serif;">This teacher has identified a <b>problem</b>: <i>Something isn’t working right, and my students are struggling in math.</i></span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">This teacher has a <b>hypothesis</b> about the root cause of the problem: <i>I believe some of my students lack number sense, which prevents them from understanding the more complex material in the math curriculum.</i></span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">This teacher has done some research (most likely on her own time) and identified an <b>option</b> that she believes could address the root cause better than the current curriculum alone: <i>I have found an iPad math curriculum that I believe will solve the problem by developing my students’ number sense.</i></span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">This teacher has encountered a <b>barrier</b> that prevents her from trying the option: <i>I don’t have all the technology I need (wifi) to use the app in my classroom.</i></span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">This teacher is actively seeking creative ways to <b>overcome the barrier</b>: <i>Is there a way I can use the app-based curriculum without wifi?</i> (In my experience, teachers are willing to go to great lengths to make something work if they believe it will help their students.)</span></li>
</ul>
<span style="font-family: Trebuchet MS, sans-serif;">This situation has all the trappings of a good old-fashioned experiment. What happens next?</span><br />
<span style="font-family: Trebuchet MS, sans-serif;"><br /></span>
<span style="font-family: Trebuchet MS, sans-serif;">Here are two common outcomes:</span><br />
<ul>
<li><span style="font-family: Trebuchet MS, sans-serif;"><u>Either</u>: The teacher gets no support to overcome the final barrier, she can’t even try out the option she believes will help her students, and her students continue to struggle with math – probably for life (because math <u>mis</u>understanding – like math understanding – is cumulative). Sadly, this is probably what happens to proactive teachers and their students most of the time. The teacher takes the ball to the 99 yard line and for any number of reasons can’t carry it the final yard alone so it sits there. The students miss out. The dedicated teacher gets a little more burnt out – maybe this is even the last straw and she leaves the profession. Everyone loses. </span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;"><u>Or</u>: The teacher finds a creative way around the barrier, tries out the math app with her students this year, and based on her results she decides whether to use it again (or try something else) with her class next year. The teacher goes to great lengths to get her students more of what they need. Her twenty-five students benefit. She feels empowered - maybe she can make a difference through diligence, resourcefulness, and a lot of hard work. But…did her idea work? How well? What’s the evidence that it did or didn't? Did it work for some kids and not others? If so, which ones? What did she do to make it work? That teacher has a lot of valuable, actionable insight as a result of her experiment, but it was a private experiment and so the world will never know about it.</span></li>
</ul>
<span style="font-family: Trebuchet MS, sans-serif;">The answers to those last questions would have been handy six months later when I received this message from another teacher:</span><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSuLx1bloQBQX34Y0zHrR4kMygW28_E5qdevLAPdZqurVnE5PeK4MRNDO2Gt5Y93gxh6keDujzOnZq-OggM9U4BkMbWJZuz1g0QxtPnZUzm294drnPpQTWuSr3mlF6PtgDm_dKuKdunnoM/s1600/EducExp2_quote.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Trebuchet MS, sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSuLx1bloQBQX34Y0zHrR4kMygW28_E5qdevLAPdZqurVnE5PeK4MRNDO2Gt5Y93gxh6keDujzOnZq-OggM9U4BkMbWJZuz1g0QxtPnZUzm294drnPpQTWuSr3mlF6PtgDm_dKuKdunnoM/s1600/EducExp2_quote.png" height="386" width="640" /></span></a></div>
<span style="font-family: Trebuchet MS, sans-serif;">It’s déjà vu all over again.</span><br />
<span style="font-family: Trebuchet MS, sans-serif;"><br /></span>
<span style="font-family: Trebuchet MS, sans-serif;">Key points to note about this situation:</span><br />
<ul>
<li><span style="font-family: Trebuchet MS, sans-serif;">This teacher has <u>independently</u> identified the same <b>problem</b>: <i>Something isn’t working right, and my students are struggling in math.</i></span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">This teacher has <u>independently</u> produced the same <b>hypothesis</b> about the root cause of the problem: <i>I believe some of my students lack number sense, which prevents them from understanding the more complex material in the math curriculum.</i></span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">This teacher has done some research (most likely on her own time) and <u>independently</u> identified the same <b>option</b> that she believes could address the root cause better than the current curriculum alone: <i>I have found an iPad math curriculum that I believe will solve the problem by developing my students’ number sense.</i></span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">This teacher has encountered a slightly different <b>barrier</b> that prevents her from trying the option: <i>I don’t have all the technology I need (iPads) to use the app in my classroom.</i></span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">This teacher is also actively seeking creative ways to <b>overcome the barrier</b>: <i>Is there a way I can adapt the app to a whole-class format so I can make it work with the technology I do have available?</i></span></li>
</ul>
<span style="font-family: Trebuchet MS, sans-serif;">The teacher from California observed a pattern, had a hypothesis, came up with a test of that hypothesis, and – if she was persistent and lucky enough – was able to run the experiment. But no one except perhaps a few colleagues will ever hear about it, whether it was successful or not. As a result, the teacher in Tennessee has to do all of the same work over again, from scratch, without guidance or data to help her make informed decisions. Which raises a few questions:</span><br />
<ul>
<li><span style="font-family: Trebuchet MS, sans-serif;">If these two teachers face the exact same problem with teaching math, how many others are there? Tens of thousands? Hundreds of thousands?</span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">How much teacher time, energy, and good will are we wasting with all of this duplicated effort?</span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">How many <i>more</i> teachers would use an effective option that had already been vetted by another teacher if they knew about it and didn’t have to re-invent it from scratch or take the risk of "being first"?</span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">Looking beyond first grade math, how many students would benefit if every teacher didn’t have to reinvent the wheel like this on every big and little problem they encounter in the classroom? Presumably <i>every single student</i>. That includes your children, and mine.</span></li>
</ul>
<span style="font-family: Trebuchet MS, sans-serif;">Here’s the punch line:</span><br />
<span style="font-family: Trebuchet MS, sans-serif;"><i>This is going on all the time. Millions of such private experiments are presumably being conducted by teachers every day in classrooms across the country and around the globe. The only thing that’s missing to capture the value of that activity is a bit of systematic record keeping and a way to share results.</i></span><br />
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<h3>
<span style="font-family: Trebuchet MS, sans-serif;">Where do we go from here?</span></h3>
<span style="font-family: Trebuchet MS, sans-serif;">I hope that helps clarify what I meant when I said we need to stop arguing about what people <i>think will work</i> in education and start experimenting to determine <i>what actually works</i>. </span><br />
<span style="font-family: Trebuchet MS, sans-serif;"><br /></span>
<span style="font-family: Trebuchet MS, sans-serif;">In fact, I now realize that I mis-spoke when I first said that. We don't need to <i>start</i> <i>experimenting</i> - that part is already happening. As a first step we</span><span style="font-family: 'Trebuchet MS', sans-serif;"> simply need to <i>start</i> </span><i style="font-family: 'Trebuchet MS', sans-serif;">sharing</i><span style="font-family: 'Trebuchet MS', sans-serif;"> what teachers have discovered about what works and doesn't work as they try – sometimes desperately and at significant personal cost – to give our children more of what they need to succeed in school and in life.</span>Anonymoushttp://www.blogger.com/profile/11351479269650780356noreply@blogger.com7tag:blogger.com,1999:blog-6645583842972204443.post-77039549344385182672013-07-22T07:20:00.000-07:002014-07-31T11:33:28.729-07:00Can We Make Education Better, or Is This Really As Good As It Gets?<h2>
<a href="http://commons.wikimedia.org/wiki/File%3AAdriaen_van_Ostade_007.jpg" style="font-family: 'Trebuchet MS', sans-serif;" title="Adriaen van Ostade [Public domain], via Wikimedia Commons"><img align="left" alt="Adriaen van Ostade 007" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/dc/Adriaen_van_Ostade_007.jpg/256px-Adriaen_van_Ostade_007.jpg" width="256" /></a></h2>
I attended a summer conference years ago at Brown University. The conference theme had to do with making brain research more useful in practice. I was a doctoral student at the time, working in the emerging domain of <a href="https://en.wikipedia.org/wiki/Educational_neuroscience" target="_blank">Educational Neuroscience</a>. The field was so new it wasn't even established yet, it was starting to generate some buzz, and this was one of the first conferences of its kind. I was pretty excited to be there.<br />
<br />
One talk was by a cognitive neuroscientist renowned for his brain imaging studies of memory and perception (how we see, hear, etc.). This particular presentation, though, was about a study he was doing on learning. Learning and motivation have been my primary interests for a long time, and so I was keenly interested in the talk. During the Q&A following the presentation I asked, "Do you have ideas about how this kind of brain research might help us make education better?"<br />
<br />
Based on prior experience, I expected one of two answers.<br />
<br />
Either:<br />
"Yes, I have several ideas about how this might be useful down the road. For example..."<br />
<br />
Or:<br />
"No, this laboratory work is too preliminary and too far removed from educational practice for me to speculate about that."<br />
<br />
His actual answer was far more interesting (and surprising). He said:<br />
"I think we do pretty well in education already. I don't really think it's possible to do much better."<br />
<br />
I was taken aback. First, he dismissed my question instead of answering it. But, more importantly – could he really be suggesting that education is about as good as it can possibly be? And that a deeper understanding of the biology and psychology of learning won't lead to better education? At the time it hadn't occurred to me that people - especially people who study learning - could seriously hold that view.<br />
<br />
But he got me thinking…<br />
<h3>
</h3>
<h3>
Why should anyone believe that education could be better than it is? And how much room for improvement is there, really?</h3>
These are quite important questions. After all, if the best-case scenario would be, say, 10% improvement over what we do now, then it probably wouldn’t be worth the extra cost. But if, on the other hand, we could <i>double</i> the return on our educational investment (100% improvement), then that would really be something to get excited about!<br />
<br />
<b>How much more <i>efficient</i> could education be?</b><br />
First, let’s think about educational <i>efficiency</i>. One way to determine that is to compare how long it takes students to master a specific amount of content under different instructional designs. One telling example comes from the SHERLOCK Project, in which cognitive scientists demonstrated that they could replace four years of on-the-job training (in troubleshooting electronics) with 20-25 hours of computer-based training to produce the same expert-level performance. <i>Four years of training compacted into less than three days</i> through the systematic application of Learning Science. The authors of <a href="http://act-r.psy.cmu.edu/wordpress/wp-content/uploads/2012/12/173Chapter_37_Intelligent_Tutoring_Systems.pdf" target="_blank">this article</a> point out that “SHERLOCK achieves this stunning result in two ways, by affording the opportunity for extensive practice and by creating educationally effective instructional conditions” (p. 9).<br />
<br />
So, based on this example, we can estimate that in at least some domains education could be made not just 10% or even 100% more efficient than it currently is through optimal instructional design, but <i>on the order of 100x – or 10,000% – more efficient</i>!<br />
<br />
Wow. I’d say that puts the score at:<br />
Me: 1<br />
Cognitive Neuroscientist: 0<br />
<br />
<b>How much more <i>effective</i> could education be?</b><br />
Now let’s think about educational <i>effectiveness</i>. One way to determine that is to compare levels of student achievement in a subject area like math resulting from different instructional designs. The cognitive scientists behind the <a href="http://www.ascd.org/ASCD/pdf/journals/ed_lead/el200402_griffin.pdf" target="_blank"><i>RightStart</i> project</a> did just that. In one study, they followed three groups of children for about five years (from preschool through third grade), measuring their math achievement each year.<br />
<br />
<ul>
<li>Group 1 was a <i>high-resource</i> group – children from middle- and upper-income homes who attended a magnet school with an enriched math curriculum (not specifically informed by Cognitive Science).</li>
<li>Group 2 was a <i>high-ability</i> group – children from lower-income homes who were identified as having superior math achievement when they arrived at school. They received no special or enriched math instruction.</li>
<li>Group 3 was the <i>experimental (RightStart)</i> group – typical children from lower-income homes with no special aptitude for math. In addition to their regular school curriculum, these children received about 20 hours of intensive supplementary instruction in “number sense” (the conceptual foundations of math). The special number sense curriculum was explicitly informed by Cognitive Science.</li>
</ul>
<br />
The <i>RightStart</i> group started out with the lowest math achievement of the three. Over the course of five years, however, they reached <i>higher levels of achievement</i> than either the high-resource or the high-ability group. Evidently, optimal instructional design based systematically on Learning Science can take the children who would normally sit at the bottom of the class and reliably put them <i>beyond</i> what is currently the top of the class – and they’ll stay there for years.<br />
<br />
Wow again. I’d say that brings the score to:<br />
Me: 2<br />
Cognitive neuroscientist: 0<br />
<br />
<b>Cognitive Neuroscience is not Education Science</b><br />
Based on available evidence, it seems the Cognitive Neuroscientist was just plain wrong in saying that education today is about as good as it gets. But he’s a senior scientist studying learning – so where’s the disconnect?<br />
<br />
I think <a href="http://en.wikipedia.org/wiki/Clarke's_three_laws" target="_blank">Clarke’s first law</a> applies here:<br />
<i>When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong.</i><br />
<br />
What I have further come to understand in the decades since (thanks in no small part to <span id="goog_1756898851"></span><a href="http://ia700204.us.archive.org/8/items/sourcesofascienc009452mbp/sourcesofascienc009452mbp.pdf" target="_blank">this book</a><span id="goog_1756898852"></span> by Dewey) is that there is a vast difference between a Cognitive Neuroscientist who studies learning and an Education Scientist who studies education. Much could be said about the differences between them. For now, I’ll simply point out that the former apply systematic methods of inquiry to <i>describe neurological and psychological </i>processes, while the latter apply systematic methods of inquiry to <i>improve educational </i>processes. The difference is analogous to that between the chemical sciences and the medical sciences. <br />
<br />
I have spent much of the past two decades helping people produce the learning outcomes they desire (education) by applying systematic methods of inquiry (science). I am an Education Scientist. In retrospect, I think the Cognitive Neuroscientist was not wrong to dismiss my question. I think I was wrong to ask it of him - in the same way you wouldn't ask a chemist (even a brilliant one) to prescribe your medication. That's simply not his area of expertise.<br />
<br />
Long experience in the field supported by evidence from programs like SHERLOCK and RightStart have led me to believe that we can make education better across the board. Not a little better - a <i>whole lot</i> better. Imagine, for example, that our schools could produce <i>twice the learning</i> in <i>half the time</i> at a <i>fraction of current cost</i>. I believe this is feasible <i>today</i>, in <i>existing schools</i>, with our<i> current students, teachers, and facilities</i>.<br />
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The way we can make education substantially better is with a straightforward three-step process. This process builds on the one applied successfully by the scientists behind both SHERLOCK and RightStart:<br />
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<li><b>Base educational designs on scientific models of human learning</b>. There's over a century's worth of relevant research (including work in Cognitive Neuroscience) that is hardly being used in educational practice. We need to start using it. </li>
<li><b>Use technology to dramatically expand access to high-quality learning experiences while lowering cost</b>. Today, we could basically create for every learner a "personal-tutor-in-a-box." Students could work at their own pace on a personalized curriculum. The system could collect rich data on student performance. Teachers could spend more time actually teaching.</li>
<li><b>Stop arguing about what people <i>think will work</i> in education and start <strike>experimenting</strike> observing, acting, and sharing more systematically to determine <i>what actually works</i></b>. Simply apply scientific thinking to educational processes the same way we do to every other major domain of human endeavor like engineering, medicine, agriculture, and economics. </li>
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Wash. Rinse. Repeat.<br />
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Today, we have all of the components we need to make education much better. There is definitely a <i>way</i>. The question is, do we have the <i>will</i> to make it happen?Anonymoushttp://www.blogger.com/profile/11351479269650780356noreply@blogger.com9tag:blogger.com,1999:blog-6645583842972204443.post-42863132848544576012013-07-15T09:52:00.000-07:002013-07-15T09:52:52.711-07:00I Believe We Can Make Education Much, Much Better Than It Is Today<a href="http://commons.wikimedia.org/wiki/File%3A1650_Jansson_Map_of_the_Ancient_World_-_Geographicus_-_OrbisTerrarum-jansson-1650.jpg" title="Jan Janssonius [Public domain], via Wikimedia Commons"><img align="left" alt="1650 Jansson Map of the Ancient World - Geographicus - OrbisTerrarum-jansson-1650" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/1650_Jansson_Map_of_the_Ancient_World_-_Geographicus_-_OrbisTerrarum-jansson-1650.jpg/256px-1650_Jansson_Map_of_the_Ancient_World_-_Geographicus_-_OrbisTerrarum-jansson-1650.jpg" width="256" /></a>
<span style="font-family: Trebuchet MS, sans-serif;">Welcome to <b>The Education Scientist</b>. The purpose of this blog is to provide a forum for discussing how we can make education systematically better – especially in the short term – through methods proven to work in other applied domains like medicine and agriculture. </span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif;">I value openness and transparency. This first post is intended to tell you where I stand and where I am headed so you can decide if you are interested in walking with me for a while. The summary below is a 50,000 foot overview of the landscape. I plan to expand on each of these points in future posts.</span><br />
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<span style="font-family: Trebuchet MS, sans-serif;">Here, in a nutshell, is my point of departure:</span><br />
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<li><span style="font-family: Trebuchet MS, sans-serif;">I believe that <u>learning</u> may well be the ultimate Good.</span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">I believe that the purpose of formal education systems (like schools) is to facilitate specific <u>learning outcomes</u> desired by a community.</span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">I believe that compulsory education can be a powerful public Good, but that it brings with it certain <u>moral obligations</u> on the part of those who provide it.</span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">I believe that our systems of education (public and private alike) produce less than 50% of the learning that even the average student is capable of. In particular, I believe that we have the capability to produce <i>twice the learning </i>we are currently producing in <i>half the time</i> at a <i>fraction of current cost</i>.</span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">I believe that if we chose to we could accomplish this <i>today</i>, for the <i>average student</i>, in our <i>existing public and private educational institutions</i>.</span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">I believe that the stakes in this area are very, very high. In particular, children’s life courses are being determined powerfully by the quality of their education. The fate of entire societies will in turn be determined by their citizens’ life courses.</span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">Because the stakes are what they are, I believe that knowing how to provide better education for every child creates a moral obligation to do so – for every child – and to act with all possible haste. Every year another cohort of children – <i>our</i> children, grandchildren, nieces, nephews, and friends – advances through the system without getting what they need to survive and thrive in the world we have created for them.</span></li>
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<span style="font-family: Trebuchet MS, sans-serif;">Education Science is the systematic application of methods of inquiry to drive the educational outcomes that a society desires. I believe that Education Science can enable us to produce dramatically better learning over time, in the same way that Medical Science, Agricultural Science, and Political Science enable us to produce (respectively) better health, global nutrition, and political stability over time.</span><br />
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<span style="font-family: Trebuchet MS, sans-serif;">I believe it is within our capability to make education much, much better than it is today. If you believe this too, then I hope you will walk with me a while by joining in the conversation here.</span>Anonymoushttp://www.blogger.com/profile/11351479269650780356noreply@blogger.com13