Teaching Math with Minecraft (An Impromptu Education Experiment)

In a previous post, we explored the following question:

How can less studying produce more learning?

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).

This week, I wanted to push this thinking one step further to explore the related question:

How difficult is it to design experiences that reliably produce more learning with less studying?

To do this, I set up an impromptu experiment. I chose some core math concepts as the subject matter and Minecraft 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.

The video below is a shorter excerpt of our conversation in which we explore five questions:
* What is a number?
* What is an even number?
* What is an odd number?
* What is a prime number?
* What is a square root?



What do you think of this experiment?
What do you think we can learn from it?

If you liked this "learning with Minecraft" video, check out these others:
Minecraft Math #2: Understanding Addition, Multiplication & Commutativity
Minecraft Scientists Ep. #1: Fishin' In The Rain

Children and Technology: How Should We Manage Kids' Screen Time?

(Originally posted at nativebrain.com)
Is technology good or bad for my child?

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!

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.

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 too engaging – that once a child has visited the world of Angry Birds and Fruit Ninjas they might never want to come back…

The apparent paradox of digital technology

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.

Parents frequently ask some version of the following question:

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?

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.

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 less real yet more compelling than the offline (or “real”) world.

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!

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.

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 serve up the digital equivalent of either type.  It all depends on how we choose to use them.

So what’s a parent to do?

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.

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: What are they consuming from that dinner plate and how much of it?

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 mastered them all.  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.

Summary and Take-Aways

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:

• Avoid the question, “Is technology good or bad for my child?”  It’s a trap with no way out.
• 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.
• 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.

Why a touchscreen (tablet or iPad) is better than a mouse and keyboard for young learners

(This article was originally posted at http://www.nativebrain.com/blog.)

The Idea, In Brief

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?

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.  I highlight two issues in particular:

1. Touchscreen computers enable many children as young as one year old (and in some cases even younger) to engage in independent learning activities on the computer for the first time, and
2. 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 faster learning and greater knowledge transfer from learning on a touchscreen computer compared to one equipped with a keyboard and mouse.

A Brief History of Educational Technology

Major technological innovations have arrived in waves over the past century, each bringing with it new opportunities and challenges for educators.

The Broadcast Epoch

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.

The Interactive Epoch

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.

The Networked Epoch

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.

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.

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…

Are touchscreen computers incremental extensions of desktop and laptop computers or a qualitatively new category of technology?

I would suggest they are both, but for different audiences.

For many adults, in particular, the jury still seems to be out on this question. Tablet sales are growing fast, but few adults who use their computers for production work such as word processing, software development, or video editing are replacing their laptop or desktop computers with tablets. The devices are still underpowered and the touchscreen interface tends to make them awkward to use for those types of tasks.  Most such people are evidently buying tablets in addition to 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.

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 access to independent learning activities to some groups of learners for the first time and they support faster learning that is also more transferable to the “real world.”

In terms of accessibility, touchscreen computers represent the first personal computer revolution for children

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.

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 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.

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.

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.

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.

Touchscreen interfaces support learning that is far more transferable to the “real world” than keyboards and mice

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 faster learning andgreater knowledge transfer from computer to real world than an otherwise identical activity accessed on a desktop or laptop computer via keyboard and mouse.

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.

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.

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.

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.

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.

But don’t take my word for it – check out some examples of young children using iPads:

Two-year-old drawing and using apps

14 month old baby playing Angry Birds

15 month old baby playing Garage Band

You won’t see them doing that on a laptop computer!

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 higher quality learning than desktop or laptop computers.

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 not created equal.

How Can Less Studying Produce More Learning?

In a previous post, I introduced two notable examples of applied learning science: SHERLOCK and RightStart. 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:

1) What could cause such large differences in learning outcomes if the basic "subject matter" being taught doesn't change?

2) How unusual are the SHERLOCK and RightStart results? In particular, should we only expect those kinds of results from formal, long-term, well-funded research studies?

But first, I need to introduce the following key insight.

Key Insight: Don't Mistake Subject Matter for Knowledge

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.

One of the more interesting insights I gleaned was this:
Subject matter taught is not the same as subject matter learned.  

Let me illustrate with an example based on actual events. 

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 hate chemistry."

"Why?" I asked.

"There's too much to remember!" she complained.

"Show me," I said.

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:

PV = nRT

"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:

P = nRT / V

V = nRT / P

n = PV / (RT)

R = PV / (nT)

T = PV / (nR)

I stared at the cards. "Susan, that's algebra." 

"No, this is for my chemistry test," she insisted.

"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."

Her eyes widened with dawning recognition. "Oooohhhhhh - I never realized you could use algebra in another subject like that!"

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 subject matter - algebra and chemistry. It would have been their knowledge (or understanding) 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 RightStart, in fact. The picture below illustrates this scenario.

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. 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 twice as much time as the other student to learn half as much material with less understanding. 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.

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.

Example: Arithmetic

The chemistry example is not unique - far from it. Consider a similar example from arithmetic - memorizing the times tables from 1x1 up to 12x12.

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).

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 twice as much information as the student who does. The same observation applies to learning the addition tables.

Example: Foreign languages

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.

Just the tip of the iceberg...

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%. 

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. 

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.  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 tie 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 compose an essay that influences people.

What do you think?

In this post we have explored the question of whether the dramatic learning gains documented in projects like SHERLOCK and RightStart 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. 

What do you think? What experiences or examples can you share to push the conversation forward?