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# Case Study: An appcessory for early math concepts

When my kids were younger, I played a math game that never ceased to amuse them (or me, at least). The “game,” if you can call it that, consisted of grabbing a handful of Teddy Grahams snack crackers (usually off of their plate) and counting them out, one by one. I’d then do simple grouping exercises, moving crackers between two piles or counting by placing them into pairs. The real fun kicked in when we’d play subtraction. “You have seven Teddy Grahams. If Daddy eats one Teddy Graham, how many do you have left?” I think I enjoyed this more than my kids did (to be fair, I’d also make a few additional Teddy Grahams appear out of nowhere, to teach addition). All in all, this was a great way to explore early math concepts such as counting, grouping, subtraction, and addition.

So, how does this game stack up on the design principles? The learning is playful (if not downright mischievous). And the Teddy Grahams are tangible. On these two attributes my game is successful. However, the game doesn’t fare so well on the remaining principles: although my presence is not a bad thing, this doesn’t encourage self-directed learning, and the correction comes entirely from me and is not discovered. As for the intelligence, it’s dependent on my presence.

This left me wondering if this simple game, not all that effective without my presence, could be translated into the kinds of experiences I’m describing here? Could this be improved, to satisfy the identified five design principles?

Here’s my concept: what if we combined my pre-math Teddy Graham game with an iPad? As depicted in Figure 5-7, what if we exchanged the crackers for a set of short cylinders (like knobs on a stereo), and what if we figured out how to get these knobs talking to the iPad. Could that work? Is that possible? Even though this could be accomplished with a set of Sifteo blocks, the costs would be prohibitive for such a singular focus, especially where you’d want up to 10 knobs. I’m treating these as single-purpose objects, with the brains offloaded to the device on which they sit (in this case the iPad). Hence, the “appcessory” label.

Figure 5-7. Appcessory concept and walkthrough

Here’s a walkthrough of how the interactions might work:

• ? Placing one of these knobs onto the surface of the iPad would produce a glowing ring and the number 1.
• ? Adding a second knob in close proximity would make this ring larger, encircling both knobs (and changing the number to 2).
• ? Let’s suppose you added a third knob farther away, which would create a new ring with the corresponding number 1.
• ? Now you have two rings, one totaling 2, the other totaling 1. If you slide the lone knob close to the first two, you’d end up now with one ring, totaling 3. In this manner, and as you start to add more knobs (the iPad supports up to 10, double that of other platforms), you start to learn about grouping.
• ? In this case, the learning is quite concrete, with the idea of numeric representations being the only abstract concept. You could then switch to an addition mode that would add up the total of however many groups of knobs are on the surface.

I could go on, but you get the idea. By simply placing and moving knobs on a surface the child begins to play with fundamental math concepts. As of this writing, we have proven out the functional technology, but have yet to test this with children. Although the app I’m describing could be built very quickly, my fundamental thesis is that by making these knobs something you can grasp, place, slide, move, remove, and so on, learning will be multimodal and superior to simply dragging flat circles behind glass.

How does this stack up on the five principles?

As with the earlier Teddy Grahams version, it is interactive and tangible. Moving this game to a tablet device allows for self-directed learning and feedback loops in the form of the rings and numerical values. As far as intelligence goes, there is no limit to the kinds of data one could program the iPad to monitor and act upon.

So where might this thinking lead, one day?

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