(2) The Dan gives of an open beginning could be reclassified as an open middle by reinterpreting the starting point and the class objective: imagine you are teaching the students about how to conduct a mathematical investigation or how to ask interesting questions. Then, everyone is given the same starting point (the sheep scenario), the middle is open (what questions they ask, what they explore through those questions), and then you can get a closed end by having some class discussion about what journey each student/group took.

However, I agree this is going to be trickier if you think the objective is to explore a particular technique or mathematical concept. In that case, the teachers who use this approach usually wait until the students have listed a question that follows the path the teachers wanted to take and then focus on that. Always a danger of missing some real golden opportunities if you are too focused on putting them on a predetermined path, though.

(3) There are a lot of stories in math, but they don’t usually appear in how we teach it. For a small example, think of the story of 0 (the numeral). How might it have come into use? Why didn’t the Greeks or Romans make use of it? What are the implications of not having it. How much did it suck to do arithmetic without it? What are the circumstances in which it got (re)introduced into Europe? Etc, etc.

Or, if you don’t like that one, what about Galois? Perhaps the math is a bit too advanced, but Numberphile’s trisection videos show it can be connected to a high school audience.

I know that books and math both can be engrossing, but as Tim pointed out in the comment you highlighted, engrossment comes in at least two types: engrossment in a challenge (like Angry Birds) and engrossment in a story (like the Game of Thrones video game). I think 3-Acts are much more like Angry Birds–most of the time, they don’t have a plot, even though they have an open middle–and I think it’s helpful for the discussion not to conflate the two types of engrossment.

Btw, I have now watched your presentation–nice job. I have one thought about creating the open middle. For me, the challenge is to duplicate a video game’s ability to give feedback on the natural results of students’ strategic choices. For example, you presented a scientific notation question (fill in the blanks using the digits 0-9 to make the largest possible product). In a true Angry Birds-style question, once a student placed her digits in the blanks, the game would probably animate the steps of the computation to show the final product. For example, the game would show turning (9.123*10^4)(5.678*10^0) into 91230 * 5.678 and then multiplying those. Without that, it would be like an Angry Birds game that doesn’t show the projectile flying but instead just says “hit” or “miss” or “too far” or “too short”.

I’ve thought about embedding videos in a Google Form so students can choose their own adventure and see the consequence of their choices. For example, if each pizza is $6 and delivery is $1.50, you could ask how much it would cost to get 2 pizzas delivered. If a student selected $13.50, you’d take them to a video of a single delivery guy bringing 2 pizzas. If the student said $15, you’d show a guy bringing 1 pizza, driving back to the pizza place, and bringing the other pizza separately. But it’s a lot of work and, I think, a critical aspect of making math more like video games.

Relatedly, I thought you had decided that perplexity trumped storytelling:

@ijkijKevin There are other techniques aside from storytelling that can be used to generate perplexity. Different concepts, IMO.— Dan Meyer (@ddmeyer) November 3, 2013

I’m not trying to hold you to some silly standard of perfect consistency. Just wondering where storytelling vs perplexity fit in your thinking right now.

I just wanted to point and say, Hey! Everybody look at Tim’s comment about story. Appropriating the elements of a good story for math class is a great goal. Trying hard over here.

On point two, I’d argue that gaming definitely involves learning, but the point of gaming is entertainment. So it’s learning for the sake of entertainment, whereas what we’re looking for in schooling is entertainment for the sake of learning. HUGE difference, in my opinion. Also huge difference: in gaming, the player chooses which game to achive mastery off, and can choose to stop whenever. Not the case in primary to secondary schools. Does mastery matter as much when it is forced on you? I doubt it. Social recognition does, of course, matter, but I think it is more meaningful when we praise a student’s effort verbally, individually and sincerely, or show their work as a positive example to the class, than when we give out gold stars.

The other thing I disagree with is the separation of gaming and learning. Gaming IS learning. Gaming and schooling are separate, yes, and while school can take a lot from game elements, it shouldn’t be completely the same. But the joy of gaming most often comes from learning the game and striving for mastery – the same as learning in most other contexts.

(b) Demon Souls gets *harder* if you fail?! Wow!

OK, let me ask you, if you will, to dig a little deeper. Why do you persist in the face of such abuse! :) Did someone tell you it is amazing once you get past that? Do you feel like you are getting better even as you fail, better enough that as long as you carry on you will eventually get there? (I imagine the game never says, sorry, game over literally, you can never play again.)

(c) I disagree about gamification being something that can only be used to a small degree, but perhaps that is because I am mentally translating gamification into “recognition of achievement (without ever recording failure)”.

When I get a silly silver badge for factoring binomials and I am pleased, i am pleased about having gotten recognition for mastering (somewhat!) a hard game (math) that I know is not a game, it is serious scholarship. Just as a college football player earning a decal for their helmet is excited about having a great play recognized, not the badge.

If I merely passed at the silver level or made a great open field tackle I would still be pleased, but it would not be the same without the recognition.

I guess this is a long-winded way of saying people are human. :)