For the past three days I have had a unique privilege to be a part of some very interesting conversations with a mix of educators, game designers, TV producers and content distributors. The goal of these conversations was to create a strategy for effective “digital learning objects” for the School of One in NYC. The conference was called Digital Learning Object Academy and it was hosted by PBS in Arlington, VA. I was asked by PBS to present on how I teach mathematics and how I included digital content in my classroom.

Much of the conversation was focused around educational gaming, of which I have never been a big fan. The School of One includes many different modalities in which a learner participates during the course of instruction. Without going in to too much detail, an “algorithm” generates a schedule for every learner, every day. This schedule is based on the current progress up to that day. If a learner didn’t understand whole group, teacher directed instruction on Area, she might then see that same topic in a different modality, say, small group or one-on-one with a tutor. One of these modalities is individual, digital instruction. High quality, self-contained digital learning objects are needed to successfully instruct the learner on a specific skill which must yield results that can be fed back in to the algorithm.

Rather than focus on my negativity toward self-contained digital experiences, I tried to focus my energy on making sure these producers understood good mathematics pedagogy. The title of my presentation was “Building Context: The art of creating situations that demand mathematics; not forcing mathematics on situations that do not want it.” If you have been paying attention to any of the buzz on the internet around math instruction you can see that Dan Meyer was a huge influence on my presentation. I think the idea that most people came away with my presentation was the idea of context vs. pseudo-context. I was happy to hear people ask me about the ways in which they were instructing mathematics. I was also happy to tell them when I thought what they were doing was crap but I think they definitely understood what I need in a good math problem— perplexity.

One of the hardest aspects of this challenge is to reconcile what we know about game design vs. the realities that are needed in a classroom. Games are very educational but are rarely explicit about it. They allow us to use our intuition to solve problems within the context of the game. I am going to use Angry Birds as an example because of its obvious popularity and addictive qualities but also, because we used it throughout the three days as an example to to build a model around. Angry Birds is a game of using physics and math to solve problems; mainly, shooting birds out of a sling shot at a certain angle in order to knock down a structure, killing other birds (or pigs?). Angles, projectile motion, center of mass; there is potential to learn about those skills from playing this game. The problem is formalizing the knowledge from the skills.

During a conversation with Nicholas Fortugno, a game designer for Playmatics, I was trying to stress the need for extracting formal mathematics from the skills attained by playing the game. The whole purpose was to assess a specific skill learned from the experience that translates into a test question. That is a tall order given that there are certain qualities that make games fun and once you add the layers of formal mathematics, it loses some of those qualities. That fact reminded me of Dan Meyer’s TED talk. In it, he talks about a method to build “patient problem solvers” by ripping apart textbook problems. He talks about the typical word problem in a textbook as having different layers that should only be applied when the learner needs it. Here is the textbook problem:

He then decompresses the layers,

- the visual
- the question
- the structure
- the steps

Now imagine this process applied to game design. Nicholas proposed this solution as a result of a conversation around making specific skills more explicit in the game.

- Informal
- Informal (formal)
- Formal (informal)
- Formal

This process will hopefully be obvious by the following mock-up of angry birds.

Informal

Users play the game based on their intuition and experience playing the game. The sling shot is interactive.

Informal (formal)

The users continue to interact with the game in the same way, however, data is now displayed on the screen but is not needed for game play.

Formal (informal)

This is probably the biggest transition. No longer can you manipulate the sling shot with the mouse. You must input data into textboxes. The user must translate her intuition into formal data.

Formal

In this phase, all interface is removed and you are given what is essentially a test question in which the user needs to use formal mathematics.

Each level would have increasing complexity governed by a concept well known to game designers as Dynamic Difficulty Adjustment or DDA. The learner would be pushed into more complex situations but would get bumped back when there is lack of progress. DDA might control the progress within each level and the promotion to the higher level. In games, from my experience, this is invisible. The gamer isn’t consciously aware this is happening. This seems like a valid approach to educational game design as well.

I am not saying that we should rush to make this new Angry Birds game nor do I think my illustrations even describe a good game. This was only meant to uncover the parallels between what we do to solve math problems and how we play games. This parallel, I hope, can be used to create fun and addicting educational games about mathematics.

What do you think?

Thanks for posting this summary, Thomas. The Informal -> Formal demonstration via Angry Birds made a lot of sense to me. Compelling stuff.

Thanks Dan. I feel like this idea and your pseudo-context have really informed the way I talk about math education.

Great summary, Thomas. Thanks for the post, and thanks as well for including the TED talk and the diagram of the layers of the math problem. It was a great workshop – mainly because years of work in educational game design have never pushed me that hard to actually get to an explicit interaction with a school-formulated problem or so demonstratively show specific skill learning. You were indispensible to thinking this through. Let’s keep in touch as we develop this out.

[…] This post was mentioned on Twitter by Amy Jo Kim, jonathan reed. jonathan reed said: RT @amyjokim: RT @MargaretWallace Games in math education: http://ow.ly/3YyOj […]

Hi –

As an educator and grandfather, I am very excited about the possibility of creating and using”fun and addicting educational games about mathematics.”

Mike

(p.s. – I am a different Mike Eisenberg than the professor at the University of Colorado).

Thanks for the comment Mike (not the professor at UC). If you want to play a compelling game try this one: http://labyrinth.thinkport.org/www/educators.php

One of the presenters at the academy demonstrated this game and it was definitely addicting.

I’m a game designer passionately interested in games for math education. Like you I was impressed by Dan Meyer’s TED talk. Inspiring, and clearly straight out of real classroom experience. I really like your/Nick’s idea of making the transition from concrete to abstract more gradual, by inserting intermediate steps. Reminds me strongly of an idea I heard from math manipulative pioneer Mary Laycock: she has students learn every idea first through manipulatives, then has them move to drawings, words and finally notation. The result is that kids have safety nets: if they don’t understand an idea in one representation, they can always fall back on a more concrete representation. To merge your and Dan Meyer’s ideas, having kids jump too quickly from concrete to abstract is like giving them a ladder with rungs that are ten feet apart, and lifting them up and placing them up on the upper rung instead of letting them climb up themselves. The result is kids who can hang out on the upper rung, but can’t get back down to earth with confidence.

After looking at a few of the blog posts on your website, I seriously appreciate your way of writing

a blog. I book marked it to my bookmark site list and will be checking back in the near future.

Please check out my website too and let me know what you

think.