The game itself is the stand-alone iPhone/iPad app (other versions will follow). Social media and multiplayer aspects will be provided on the website that supports the game. The intention is to have a whole series of mobile games that connect to the same website.

]]>You’ve not addressed the social aspect. Perhaps your game could include what many games include – some sort of online discussion space for player? This way when questions about process do come up, the players (learners) have somewhere to go to address them, and perhaps some of the misconceptions about process can be addressed through peer to peer interactions.

]]>David, As it happens I co-founded a small mobile games company to produce games that try to do exactly what you suggest. (This goal is also why my recent MOOC focused on mathematical thinking, rather than a set of curricular points.) We secured an initial round of angel investment a few months ago, and our first game should be released some time early next year. And we teamed up with an existing mobile game company with some successful social games to their credit in order to incorporate the social aspect and facilities/encourage group activity (and hence group learning). I doubt we’ll get everything right with version 1.0, but we will be gathering and analyzing the player data from day 1 onwards, and that will let us iterate and improve as we learn from our players. We also have some stellar math ed researchers lined up to help us with the learning side. The process-used issue is a huge one for any automated learning environment. The only solution I know of is to involve teachers in the loop. We have ideas about that, but implementing (and then testing) them will have to wait until our game (in fact, more than one) is out.

I’ll pass on your Khan Academy question, as any remark about KA brings out the trolls, and then I’ll have to close comments.

]]>1. It is assumed that we want to design a video game to teach specific math concepts. What if instead of teaching specific curricula mathematics, we wanted students to learn mathematical habits of mind?

2. Is it possible to create an environment which rewards mathematical thinking, rather than necessarily the product of that thinking? It seems to me obvious that if we reward the product rather than the process that we then necessarily will run into people who use a different process… perhaps even a completely incorrect process.

3. What would happen if we included a social aspect to these games (or frameworks for learning) so that instead of trying to learn in isolation, we have to be able to explain our reasoning to other people, during which (hopefully) our misconceptions become addressed?

4. How does this information apply to the Khan Academy?

]]>For me the lesson is that there are many more components to knowledge that us, who already have the knowledge, tend to realise.

To us, we know “10” in terms of counting out ten items. We also know “10” in terms of what it means to subtract ten items from a larger quantity of items. And we know that the “1” in “18” is the same thing.

We can use our knowledge so fluidly that it just seems like it’s the one bit of knowledge about “10” in all three contexts. The Cena video shows us that it isn’t. At one point we had to learn these separate things, but we have no memory of that experience (and we no doubt weren’t consciously aware of it at the time).

To me one of the most important goals of education is to understand what these underlying components of knowledge are.

If we know what they are we can test for them. And hopefully if we know what they are we can write mechanised tests for them. That way we could have mechanised ways of knowing what the player, or student, is learning.

]]>Belinda: I definitely agree as to the difficulty of embedding tasks into video games that require real mathematical thinking. Mind you, it’s not easy getting them into the classroom either. Thanks for your comment.

]]>I’ve worked on designing some video games, and in my opinion it is deceptively difficult to incorporate actual mathematics. My team had several conversations with game programmers about the difference between players interacting with a demonstration of math concepts and players using math concepts in a meaningful way. Having been a middle school math teacher and a teacher coach, I’ve seen many lessons in which manipulatives were used similarly: to demonstrate math rather than being used to engage with concepts. It’s an interesting challenge to try to embed math concepts in a game without skewing toward a mere demonstration for which Cena, Benny, and their classmates think the game is about trying to guess the rules. ]]>

Andrew: Thanks for writing.

Two examples of failure to properly master elementary concepts that endure into adulthood come to mind from personal experience.

One, as a university professor, I often found that students in advanced calculus were hampered by not having understood addition of fractions, both in terms of the mechanics and the rationale behind those mechanics. It causes problems in coming to terms with the definition of the derivative.

The other is one I’ve commented on a lot, namely the failure to understand multiplication. Admittedly multiplication is a very complex operation, though the fact that many adults do not even recognize that is worrying.

I have had exchanges with graduate students and occasionally professors who do not see multiplication as fundamentally different from addition. The troubles me because it is after all one of the two fundamental operations on numbers! So some conceptual misunderstandings or failures to fully grasp a concept do endure.

So while I would agree with you that in many (most?) cases, most of us manage to get most concepts right in the end, it is not always the case. And for the concepts we do eventually master, how many of them did we “get” because of the intervention of a good teacher?

Benny did not correct his massive misunderstandings despite many years of working on IPI (without teacher intervention).

In terms of significantly higher math, large numbers of people, including many professors of mathematics, fail to fully understand the Recursion Principle. I wrote about this in my MAA column last year: http://devlinsangle.blogspot.com/2011/11/how-multiplication-is-really-defined-in.html. (The focus is on recursion; multiplication is just a convenient example.)

There are others. I myself carried a major misunderstanding well into my research career, and it was only pointed out to me when a referee was evaluating a research paper I’d written. (I did manage to rescue the main proof.)

And what about all the people who submitted false proofs of Fermat’s Last Theorem that assumed unique factorization?

The trouble is, it usually takes someone else to point our our misconceptions.

KD

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