**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

WOW!!I need to watch this a dozen more times to capture the fantastic micro-skills/processing that occurred. Wouldn’t it be great if we had a way to capture, in a visual graphic, what students are thinking in real time! I agreed with the previous posts about time children spend with technology as well as usefulness of games…but still I have to re-think my use of games in the context of “learning”… This interaction can be used as an exemplar of informal learning; AND I could absolutely see using this in the classroom EXCEPT (teacher colleagues, don’t hate me) I don’t trust that most teachers will engage in the same dialogue with their students as you did Dr. Connell. I have seen too many teachers use Power Point in a press-and-play/assume-they-learn model. I have been in those classes myself as a student. BUT…this idea (not trusting teachers) is one thing that prevents teachers who are innovative from moving forward if administrators don’t allow technology to be used WITH guidance, TRAINING, and accountability.

ReplyDelete> Wouldn’t it be great if we had a way to capture, in a visual graphic, what students are thinking in real time!

DeleteHaha - we do! http://www.nativebrain.com/dashboard

Yes you do! And wouldn't it be great if there were more like this for different content areas. There ARE tons and tons of programs (software, web-based, apps, etc.) that provide visual graphics in real time. The problem is how the data is used and interpreted. Most programs don't include suggested instructional models for remediating or enriching learning based on the data; it is simply a "report card" of sorts. But, that is not true of the app on www.nativebrain.com! If there are other programs like this, we teachers need them. Beyond that, curriculum and instruction administrators need to know about them!

ReplyDeleteNow wonder kids get confused. Number, as word or symbol, represents quantity is dimensionless; the numerosity of a set - see the work of Stanilas Dehaene. To use Minecraft to mimic the manipulation of Cuisenaire Rods is beneficial in so far as the unit cubes cannot get lost or thrown. However, this young learner's concept of 2 x 2 arrangement being a square is problematic. Cuisenaire Rod arrangements form solids, not shapes. The teacher did not clarify WHAT was being counted, and reinforced that the uppermost face of the arrangement was square. Consider the arrangement of 4 Cuisenaire Rods to form a line. Would the child or the teacher recognise this represents a perfect square? Yet, irrespective of the configuration "4" is a square number. This demonstration is offering neither deep-learning nor comparative reasoning. There is no contextual offering of the role of primes in our number system. This demonstration achieves no value-adding over Cuisenaire rods. Another embedded confusion is that a 'square' is different to 'rectangle'. This misconception starts somewhere in primary school, travels through high school and becomes a blight when the calculus student is solving max-min problems, such as given X linear metres of fencing design a yard with maximum area.

ReplyDeleteHi, GoKart. Thanks for joining the conversation.

DeleteYou touch on several important issues. I'll just focus on one.

> Consider the arrangement of 4 Cuisenaire Rods to form a line. Would the child or the teacher recognise this represents a perfect square? Yet, irrespective of the configuration "4" is a square number.

Historically speaking, a number N is a square if you can arrange N objects into a square shape. So although you are right that "4" is a square number no matter how you arrange those four objects, it qualifies as a square by virtue of the fact that you *can* arrange those four objects into a square shape, which is all that is said in the video.

See, for example, these two discussions:

http://en.wikipedia.org/wiki/Square_number

http://mathforum.org/library/drmath/view/52368.html

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ReplyDeleteติว igcse