Video Games & Making Math More Like Things Students Like

Here is the talk I gave at CMC-North last weekend: Video Games & Making Math More Like Things Students Like.

Students generally prefer video games to our math classes and I wanted to know why. So I played a lot of video games and read a bit about video games and drew some conclusions. I also asked my in-laws to play two video games in front of a camera so we could watch their learning process and draw comparisons to our students.

These are the six lessons I learned:

  1. Video games get to the point.
  2. The real world is overrated.
  3. Video games have an open middle.
  4. The middle grows more challenging and more interesting at the same time.
  5. Instruction is visual, embedded in practice, and only as needed.
  6. Video games lower the cost of failure.

Featured Comments:

Tim brings storytelling to the conversation:

As one of those weird AP Lit and AP Calc teachers – and a gamer – I think “story” is key in video gaming. Psychologists (like Willingham) and sociologists talk about the “story bias” of the brain. Nearly all long video games have a heavy story element. You are a character embedded in a story, be it open-ended or scripted. So often when I’m frustrated with bad game design I’ll push through because I’m committed to the story. So often when I finish the “missions” I give up on the well-designed “side-quests” because the story has rushed out of the game and it’s just a task-garden again.

I’ll play Angry Birds for a few minutes. I’ll play Temple Run till I beat my friend’s score. But I won’t put 20 hours into a game until I find a story I want to be invested in. (In the same breath, I’ll say that – in the sense of “story” that Willingham uses it – Angry Birds and Temple Run have their stories, too. Far more than many “story” problems in math books like to pretend that have.)

Not sure how you get rich story into math. How to become characters whose adventures we become invested in, not the scripted Jane who is trying to maximize the area of his pasture or the open-ended John who is trying to find a good way to estimate the number of people in a photo.

Anyway – the first lesson I learn from video games is: humans will spend hours on a good yarn.

My Panama Canal metaphor was just a joke from the onset so I had to admire Joshua Greene’s continued debunking.

About 
I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. More here.

46 Comments

  1. I am not much of a vg’er, but…
    They are fun.
    They have a built-in progress monitor–points.
    There are bonus points.
    There is a social aspect–comparing and consulting with others.
    You can repeat/re-try.
    You can venture to new levels.
    They are engaging and allow the user to escape a bit.

  2. If you want to know what it would like for math to be like Angry Birds (or Gran Turismo), just visit tiltonsalgebra dot com, specifically the “Missions” section.

    You do not even have to register, but then of course missions passed will disappear if you end the session. (We are still actively developing!)

    One *can* unlock missions early by clicking “show future”, but I might disable that. I try to let kids make their own decisions, but those game people sure know a lot. (So don’t be surprised if I have that turned off by the time you do not get there. )

    Nice features:
    — “Personal Best” certificate if you fail a mission less badly than ever.
    — “Abandon mission” option if you blow a couple early Qs and don’t like your odds of passing.
    — If the engine says you are wrong and you disagree, click the Study Group icon to automatically post the problem to the group and make your case.

    I think I heard someone in the audience say Angry Birds in math class would be like playing without birds because one would not know the results immediately. Quite astute. My analogy is juggling without beanbags, sending in a videotape for scoring the next day. (“You dropped the bags at 1:42, 2:38, 3:17…”)

  3. I’ve been going through a similar analysis and I would add two things:

    1. Agency – player feels in control of the action.

    2. Progressive challenge – the first levels of a video game are exceedingly easy. The early success helps draw you into the game. We need to do that in math class. Early success builds confidence and increases stamina to tackle the meatier parts of a problem.

    A corollary to #2 is how well-designed video games turn up the difficulty at just the right pace to maintain the players belief that they can succeed. As long as the game feels doable, but just out of reach, you will keep playing. Our challenge is to design math tasks like that.

  4. @josh I think you are right about the realism. Angry Birds, driving games like my fav Gran Turismo, snowboarding games inter alia all rely critically for play value on realistic physics engines.

    In MMORPGs, the social aspect is quite realistic, forcing players to cooperate with real other players to level up.

    And you are right: there *is* a real risk in not mastering an Algebra game, but that is a given. We want to structure the game experience with painless failure to draw our young scholars in and tap the resiliency they display in non-educational gaming, knowing that, in the end, hey, Algebra is not all that hard.

    If we draw them in with painless failure, sound effects, gamification, self-assessment (so they know if they will pass the real test) and even social aspects as my app does, I expect real-world success will follow.

  5. Brother.

    So far I’ve got an extended ad for a commercial product and an extended critique from someone who hasn’t watched the talk [now deleted on request of the commenter –dm]. It’s up from here?

  6. Thanks. Enjoyed the talk. Some comments:

    – I miss some on the already existing body of knowledge (Gee, for example) but in particular that of your colleague Devlin who wrote a whole book about this with many more suggestions and principles (I thought more than 20) and even a game (Wuzzit Trouble). Now, there are several things that might be missing there as well but it’s not as if there is nothing. Also the psychology of play.

    – The games mentioned are probably more ‘social games’ rather than full games, with the exception of Portal (Portal 2 is even better). There is a wider range of games and it would be good if these were covered as well, especially if the introduction mentions games like GTA.

    – What should be researched more is WHAT mathematics is learned with these games. I have a vague idea for most of the games, but if there is no connection to, for example, the curriculum one could argue ‘what is the point’. One very sensitive issue here is intrinsic/extrinsic motivation, or the question whether successful games outside the maths lesson will actually be successful in it or not.

    – There is extensive research on impact of games on maths from neuroscience perspective, especially from the spatial aspect. I would probably say that that link might be the strongest.

    – There also is a long history of games and mathematical elements. Remember gorilla.bas in Quickbasic: parabolas. I don’t really see too many differences with longer ago except (i) social gaming, (ii) technology changes. But indeed: still no clear picture of what works or not.

  7. By the way, I saw one short clip of Braid. Interesting to note that rewinding the game in that game is actually part of the gameplay itself, rather than ‘replay only’. That makes it such a great game! :-)

  8. @Dan

    Hi. I am the one who listened to your talk.

    You seem to think “commercial” is a dirty word. I understand: the vendor likely has a conflict between profits and honesty and/or quality of product, so we cannot believe a word they say. I feel the same when I am on the other side of the buy/sell fence.

    Thanks for tolerating me on your blog.

    Anyway, how *are* you going to achieve game dynamics without automation? It seems to me one entails the other, or as Bloom assumed was financially infeasible, a tutor for every scholar.

    Do you have a Plan B in mind?

  9. Many thanks to Chris for the thoughtful response.

    A quick note on the absence of Gee and Devlin. I’ve read both of them. For various reasons, they weren’t as helpful for my project as I’d hoped.

    Devlin has a grand vision of all of math class reconfigured as an immersive game like a MMORPG. That’s a different project than mine, which is merely to steal liberally from games. Wuzzits wuz fun, though. My cohort-mate at Stanford is studying the game and early efficacy tests are promising. Perhaps Devlin is onto something.

    Gee meanwhile is best known for his catalog of gaming features, but I thought he left enormous amounts of heavy lifting to classroom teachers. I spent my talk trying to help teachers with that lifting.

    Kenneth Tilton:

    You seem to think “commercial” is a dirty word.

    Actually, no. Some of my best friends are commercials. But that’s a separate issue from the criteria that gets someone’s comment iceboxed on my blog, which tends to require a pretty high insight/pitch ratio. (Off the charts there, Raj!)

    Anyway, how *are* you going to achieve game dynamics without automation?

    Don’t have time to rewind / replay our whole thing except to say a class that is as fun as a game may include automation. (Examples I’m proud of.) Your stance seems to be that a class that is as fun as a video game must include automation, which makes me want to set up a Kickstarter to “Send Kenneth To Some Classrooms That Actually Exist.”

  10. Great talk. Really liked that last bit on the gift of kids’ time that we’re given.

    Re: embedded visual instruction, Portal is a great example but you only pointed out the obvious bits. When you play through it a second time (or if you play Portal 2 and watch for this), it embeds a lot of visual clues to how to solve the puzzle into the levels themselves. If you’re not looking for it, they might even be subconscious hints – things drawing your attention to a particular spot that you can fire a portal, for example.

    The weird thing is, once I realized they were there in Portal 2, I started looking for the hints when I got stuck. Often it helped, but a few times it felt a bit like cheating. And as a teacher it reminded me of times when we give students problems that are all “scaffolded” with a similar visual structure, to the point where the kids only recognize to do that particular math-move when they see that visual cue.

    Applying that is tricky. Visual cues are great, but if kids only recognize the cue and not the meaning behind it, we’re not doing this right. (Game designers don’t have to care about this the same way, because as long as you feel good about passing the test then they’ve done their job.)

    (That said, oh man, play Portal 2 it’s so good.)

    Two small other things:
    – games don’t force you to progress before you’ve mastered the required basics

    – you might want to give this book a read: http://www.amazon.com/Art-Failure-Playing-Playful-Thinking/dp/0262019051/

  11. @Dan I think you missed one of my comments (and the Sal Khan video someone offered). The idea is to use blended learning to free up time for the cooler stuff you have in mind for the classroom.

    I keep thinking you would love automation for that reason.

    As for “fun”, I think we should both go on that Kickstarter tour so I can show you some hard-working inner city classrooms where even challenging students positively brag on how hard their teacher makes them work. They take pride in their achievement and strive even harder for it.

    The Dalai Lama said there is a difference between pleasure and happiness. My students had little fun but were happy because they learned a ton of math. As I said, kids love doing good work.

    I was happy to learn later how far they jumped on the standardized test, but my real reward was when a student approached me after I handed out report cards:

    “Thanks, Mr. Tilton,” Tony S said. “I haven’t gotten a B in a while.”

  12. @josh Word up on the danger of hints. I played computer bridge and used the hinting on bidding (a fundamental skill!) and never learned to bid. This is why I am concerned that Khan’s hints (like the bridge hints!) just tell the student what to do.

    It is also why my app does not try to guess what the student did wrong: too mush help! I want them to sweat!

    Speaking of suffering, that work by Juul looks cool. I do not know about this, though:

    “Humans may have a fundamental desire to succeed and feel competent, but game players choose to engage in an activity in which they are nearly certain to fail and feel incompetent. So why do we play video games even though they make us unhappy?”

    My experience failing the professional license in Gran Turismo for two weeks was not at all about unhappiness or frustration. Why? Because I saw steady improvement. I do not think Juul understands the gamer mindset. They *want* it to be hard because the endorphin rush comes from succeeding after a struggle. Indeed, the worst thing one can say about a game is that it is too easy to beat.

    But I do get a kick out of Juul’s “gaming as masochism” thesis. :)

  13. Kenneth: Juul is pretty aware that those playing a game don’t identify as “not having fun”. He’s a game designer and game studies professor who’s been making, studying, and playing games for quite a while. The book does bring up counter-points like the one you’re making.

  14. @josh Yeah, I read a little further and saw he got round to:

    “Yet games also motivate us to play more, in order to escape that inadequacy, and the feeling of escaping failure (often by improving skills) is a central enjoyment of games. ”

    I just got a kick out of the grim Bergmanesque tone he finds in gaming. I felt like I was being sucked into a depressive Scandinavian film. …*googling*…Ah. he is Danish. Bingo! :)

    Seriously, do you feel like mastering a game involves “escaping inadequacy”? If so, that does not augur well for the math educational setting where students have no problem throwing up their hands, embracing inadequacy (“I am not a math person”), and failing Algebra.

    I think the good news is that Juul is wrong: the “hook” in games is the steady flow of small successes, with a challenging foe (math) that they all know matters. I did not spend two weeks failing the GT pro license, I spent two weeks learning how to drive fast* (and I have the points on my license to prove it).

    * Not to worry, I got a truck so I can have my GT fantasies at the speed limit.

  15. You mentioned why you didn’t mention Gee and Devlin, but have you read Jane McGonigal? I heard her book Reality Is Broken earlier this year (and made several blog posts about it – http://rootsoftheequation.wordpress.com/tag/mcgonigal/).

    Though she doesn’t talk specifically about math education like Devlin, or even learning in general, like Gee, she does talk a lot about taking lessons from video games and applying them to other spheres of life.

  16. A video game talk by Dan Meyer?! Awesome! Thank you for sharing.

    I have tons of thoughts but figured I’d focus on what may be most relevant to learning, and that is Self-Determination Theory. As I understand it (and I may be wrong), SDT claims that motivation is driven by three main factors: autonomy, competence, and relatedness (citing Deci & Ryan 2000 here). You really nailed how video games provide autonomy and competence. Thank you! Autonomy, well, that’s the “open middle”. And competence is given by allowing redos and failure, rather than a “locked test” approach.

    But the element of relatedness, that is, a “desire to feel connected to others”, it’s there in your talk as well, but maybe not highlighted as much. Aren’t showing and fixing examples of student failures a way to produce relatedness in a classroom? Isn’t the coolest thing about Stickman Golf the way you can see your opponent’s ghost player as you try to beat them? And the big one of course is MMORPGs, the reason people get hooked on those is not just the way you can customize your character and skillset as you level up (autonomy & competence) but the guilds you can join and the relationships that develop online (relatedness).

    I don’t know if I have a point beyond this. Maybe it’s to not dismiss MMOs out of hand, and to try to hide the scoffing at badges / attempts to gamify learning. (I am referring to my own dismissals and scoffs, not implying them on the part of anyone else. I think that there’s something worthwhile in there, but haven’t seen it work yet.) Apologies if this sounds like a critique; you’ve put in hours to produce something that is five stars of amazing. Please consider this a “Yes, and…” rather than a “but you forgot…”

    Thanks!

    PS If you haven’t played the first few levels of Portal with the developer’s commentary turned on, you’re missing out. You used the example of how the game flashes directions at you. But did you also realize just how finely-tuned each of the opening levels are to teach the various skills that are needed for success later in the game? For example in Level 1 a mirror is intentionally situated so you can watch your character go through the portal.

  17. @Jeff “Maybe it’s to not dismiss MMOs out of hand, and to try to hide the scoffing at badges / attempts to gamify learning. (I am referring to my own dismissals and scoffs, not implying them on the part of anyone else. …”

    Don’t worrry, I scoff, too, even as I marvel at the ability of badges to engage us. I saw somewhere on a pedagogic checklist something (approximately) called “recognition”. The thing is, badges and gold stars and all that are not *just* icons: they come from somewhere, in the end a person who awarded the decal or one who set the level required.

    When we know we have done well, that is great. When someone else acknowledges it, that is doubly great.

    Am I aghast that the exalted human is so easily manipulated? Yes. Is the effect ineluctable? Yes. Am I going to milk that in my educational app? Guess. :)

  18. As one of those weird AP Lit and AP Calc teachers – and a gamer – I think “story” is key in video gaming. Psychologists (like Willingham) and sociologists talk about the “story bias” of the brain. Nearly all long video games have a heavy story element. You are a character embedded in a story, be it open-ended or scripted. So often when I’m frustrated with bad game design I’ll push through because I’m committed to the story. So often when I finish the “missions” I give up on the well-designed “side-quests” because the story has rushed out of the game and it’s just a task-garden again.

    I’ll play Angry Birds for a few minutes. I’ll play Temple Run till I beat my friend’s score. But I won’t put 20 hours into a game until I find a story I want to be invested in. (In the same breath, I’ll say that – in the sense of “story” that Willingham uses it – Angry Birds and Temple Run have their stories, too. Far more than many “story” problems in math books like to pretend that have.)

    Not sure how you get rich story into math. How to become characters whose adventures we become invested in, not the scripted Jane who is trying to maximize the area of his pasture or the open-ended John who is trying to find a good way to estimate the number of people in a photo.

    Anyway – the first lesson I learn from video games is: humans will spend hours on a good yarn.

  19. @Tim completely agree with ‘story’ element with ‘story’ being used liberally. It has to do with theming as well. Earlier comment on other genres also was sparked by observation of story being very important. Look at Telltale with their Walking Dead, Game of Thrones, Wolf Among us. Or Bioshock Infinite or the Mass Effect trilogy. All deep immersion with their stories.

  20. Watched last week when you posted to Vimeo. Some key points that really stuck out to me…

    “And then you challenge the kid, “can you make a bigger number?” and they keep on playing and eventually what emerges is a strategy, just like a game.”

    “Video games lower the cost of failure”

    That last one, especially, was a powerful statement. Students are much more likely to try a challenging video game, than try a challenging problem based off the idea of failure alone.

    Great talk Dan.

  21. I initially recoiled at the title of this post, but what you’re really talking about is making math class more like things students like, rather than making math more like things students like. It’s a fine distinction, but I think we ought to be doing the former, and not the latter.

  22. Your talk (in particular the open middle and the ability to undo errors) reminded me of my favorite math software – Green Globs. (http://greenglobs.net) The challenge is to take out 13 globs with the least number of functional blasts in order to get a high score. The undo last shot button is the key to learning from errors and improving one’s shot. I’ve held Green Globs contests with middle schoolers that was extremely popular. (http://dmcpress.org/gg/)

  23. I enjoyed your thoughts as I have a 9 year old who loves video games and math but would much rather play video games to doing his math homework!

    One take away I have noticed is video games master ENGAGEMENT! Mental, physical and visual engagement is mastered with captivating graphics, dynamic game play and intricate strategy.

    If we could only replicate this type of student engagement with mathematics we could see phenomenal results.

  24. Hey Dan –

    Logan, high school science teacher from Montana here. I’ve been a quiet follower of your blog posts for a few years. I watched your talk on video games vs math, thanks for an incredible presentation! However it left me with a question that I would love to pose to you and your blogging community.

    I think there is one important Video-game vs School difference that you didn’t talk about much. What about mastery? When students play video games, they master each level in order (usually). Students don’t have to take on level 20 when they haven’t mastered level 2. Nobody enjoys playing the hardest song on guitar hero on the first day. I think this is potentially a very important difference between school and games, but I don’t know how to tackle it in the classroom.

    I have, and i’m sure most teachers have, students showing up to their classes that haven’t passed a science (or math) class in 2-4 years. How can I get that “just right” challenge for the huge range of students in my classroom? One solution is to have students move at their own pace, but I’m not sure I can drink that cool aid. I’m not sure if it is possible for one teacher to do this for twenty-some students without losing the group discussion, interaction, and challenge that makes things like your 3 act tasks so engaging. You would almost have to automate it, and settle for Kahn academy lessons. However, I still think that the issue of mastery or lack there of is huge.

    Sometimes I wonder if this lack of mastery is a large part of the reason students become convinced that school is a joke, just hoops to be jumped through. I think it results in a lot of academic apathy.

    Again, I’d love to hear what you or others in your circle think about this one!

    Thanks,

    Logan Mannix

  25. Built in scaffolding, independently repeat levels to gain mastery, all accomplishments celebrated – often with music and lights, frequent encouragement and positive reinforcement built in and leveling up is cool! It’s no wonder kids respond to the video game format thus making them an effective way to reach students.

  26. @Dan, apologies, haven’t had time to watch the talk yet. But I was curious whether you plan to work on creating lessons more like this. My sense is that your prior work has low barriers to entry, get to the point quickly, and grow more interesting and complex as they unfold, but do not do a lot of embedding instruction within practice. Instead, I think you’ve tended toward very open middles followed by lecture to cap it off, in other words, instruction which was separated from the exploration or practice. Sorry if you addressed this in your talk–I do plan to watch it later.

  27. Dimitra Georganas

    December 17, 2014 - 9:32 pm -

    My children in 2nd, 1st and Pre-K were trying to figure out the Function Carnival by Desmos that you have posted on your blog. They were so immersed in the “Cannon Man” that I had to put a limit of 5 tries for each child so they could rotate. I couldn’t believe how interested they were in reading graphs from such a young age. We had great conversations about what a “flat line” means and how the steeper (or “more straight down”) a line gets, the faster the cannon guy goes… and then the parachute comes into the conversation. This just shows how important math conversation and an effective tool for learning really are. Thank you for offering these great posts and tools for us to grasp a solid understanding of what math really entails outside of the textbook. By the way, I had run into Function Carnival as I was researching meaningful ways to introduce functions to my 8th graders! I am hoping for a similar reaction to come from them as it did from my little ones at home! Keep the ideas coming! :)

  28. @Logan Mannix I never thought about it until recently, but now I cannot believe the way we teach math. “Ok, you got a C on that test. Now let’s all open our books to the next chapter.”

    Of course the problem is that the teacher has to keep moving and individualized instruction is quite hard (I tried and failed once — the fast kids swamped me in work assigning/grading new material, when what I needed was time to work with slow kids).

    The sad thing is Bloom identified mastery as the key thirty years ago: http://www.ascd.org/ASCD/pdf/journals/ed_lead/el_198405_bloom.pdf Yes, the individual tutoring was a win, but that is not feasible at scale. But having kids proceed according to mastery was as important.

    More recently, the DragonBox Challenges have given us a bunch of statistics on mastery. This article http://www.forbes.com/sites/jordanshapiro/2013/07/01/it-only-takes-about-42-minutes-to-learn-algebra-with-video-games/ quotes an unidentified soure: “of those students who played at least 1.5 hours, 92.9% achieved mastery. Of those students who played at least 1 hour, 83.8% achieved mastery. Of those students who played at least 45 minutes, 73.4% achieved mastery.”

    No, I do not consider D/Box to be Algebra, but it presents a similar intellectual challenge so I find those numbers quite encouraging: if we just let students work (hard!) at their own pace they can get there.

    What is really interesting is that, in playing twice as long to achieve mastery, students did not change their activity. So no monkeying around with approaches to learning, just let them have at it (like aided by their peers, and if so testimony to the social side of learning).

    *pulls out soapbox* People love to throw around the term research-based? Why has not math education seized on Bloom after thirty years? Instead we get Common Core worrying about the order and choice of topics to master, and how they are explained to students. None of which matters.

  29. One of the things that they did in Portal was developer commentary.

    The useful thing to me was just how much time they spent play testing and tweaking the learning process to keep it engaging, as well as the minutia they paid attention and developed learning experiences for.

    It feels like a luxury that we as teachers don’t have.

    Also, if flappy birds were like math, you’d get to play each level once all the way through the game (whether you beat it or not), and if you didn’t beat enough of the levels, you’d have to start over from the beginning and play them all through again.

  30. @Tim: Story is one element among many that hook players into games. It is a way of generating curiosity and fantasy / imagination, which are key elements of developing intrinsic motivation. But 1) a good story is not the only way of generating these hooks, and 2) intrinsic motivation also requires challenge & control (aka autonomy & competence). Therefore while story can be essential to hook some players, it’s not essential. See Tetris.

    What’s more interesting to me in an educational context is the meta-story, that is, the narrative that players make up about their actions in the game. Many of the great video games give your character at least some chance to make decisions that impact the outcome. For example, execute the evil criminal or turn them over to the authorities. So what stories do students believe about the “game of math” that they are playing? That’s the important one, regardless of whether or not the math they learn is presented in a game format or not.

    @Mr. K, I don’t know if developers always have the luxury of time. Triple A titles (e.g. Halo) have release dates linked to production & distribution that cannot be moved without consequences. And many big studios compartmentalize the various teams that work on one game, with the programmers separate from the artists. So once you get past a certain development point of the art / narrative / game mechanics you can’t make significant changes without having huge knock-on effects in the workload for other teams. Conversely if it’s a small design team, well yes they have time, but as there are fewer actual bodies working on a project, they don’t have that many hours per week.

  31. A little sorry to be nit-picky, but I think the units are wrong in your angry birds vs Panama Canal Comparison. I’m bothering to write this because I know you care about helping students understand what the numbers mean.

    My guess is that the 200mm AB minutes are actually 200mm AB person-minutes (1 AB person-minute = one person playing angry birds for one minute). That is roughly 381 person-years. However, since this was the measure for a single day and AB lasts forever, you could call this a flow: 381 person-years/day.

    To compare that with the Panama Canal construction effort, we need to know how many people were working on the canal over its life. A bit of an integration exercise, if you will.

    I couldn’t find clear data on the number of workers engaged in the construction of the Canal. Using data from Wikipedia (where else would a mathematician get history data?), I saw:
    1881 – 89: Active work on construction, cumulative death toll 20k workers. Death toll is considered “very high.”
    1889 – 1894 little/no activity
    1894 – 1903 maintenance only
    1904 – 1914 Active construction work, death toll in this period about 5600. Phrasing suggests death toll is considered “high/moderately high.”

    Subjectively, I’m going to translate a “very high” death toll to mean 25% of all workers died. I think the units require that the death frequency is dead workers/worker-year (more people who work, the more people died, the longer they work, the more people died). That means we just multiple the total dead by 4 to get total worker years: 80k worker-years.

    For the period 1889-1904, I’m going to assume 0 worker-years.

    For the last period, let’s say the rate was 10% dead workers/worker-year. Again, we just divide total dead by that 10% to get 56k worker-years.

    Adding the two active periods for 136k worker-years.

    So, to complete the comparison between AB and PC, we find that we would need 357 days for the effort (person-years) spent on angry birds to equal the effort spent to build the canal.

    to retain the joke, simply reformulate the punchline:
    “Though the analysis gets a little complicated, that means we’d need the world to play AB for a bit less than a year to equal the Panama Canal.”

  32. Ever played demon souls? That, and the sequel dark souls, make it clear that the cost of failure isn’t key. One reason I love those games, and why they are so popular, is because they are SO damn hard. Demon souls even gets harder the more you fail. Both games are intensely collaborative and forbiddingly difficult. But then, different games, as different teaching strategies, suit different people.

  33. One more thing. I don’t mean that we shouldn’t use gaming elements occasionally in teaching, but I really don’t think we should strive to somehow transform learning into gaming. The two activities are by their natures very different, not least in terms of the motivations that the person learning/gaming has to take part of that activity. Gaming is entertainment, while learning is a much broader enrichment of ones mind as well as the community. It can be entertaining, sure, but that’s not its main purpose.

  34. (a) @Julia One good thing about Algebra (for those who have failed it 4-5 times) is that “Too easy!” will never be a problem for us. :)

    (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. :)

  35. I disagree with both of your statements, Julia. I mention Demon’s Souls in this post specifically (http://rootsoftheequation.wordpress.com/2014/07/15/productive-failure/) as still having a lower cost of failure than most things. Yes, it is greater than most games, but you still get to retry – you aren’t barred from doing a level over ever again just because you failed it. And as you get better and see how your actions get you closer to victory, the failure itself feels good.

    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.

  36. James and Kenneth, regarding cost of failure, the point is not that demon souls has a high cost of failure (of course it’s not as high as not getting a high school diploma, for instance), the point is that part of the game’s charm and power to attract a huge fan base is that it has a high cost of failure compared to other games. Compare to Skyrim, which last I played had absolutely no cost of failure – and was therefore not challenging enough to be interesting to me. The challenge (and the amazing graphics, and story, etc) is what is motivating about games like demon and dark souls (the latter of which I never managed to finish, not because I didn’t want to but because it seems to require far greater skill than I have – I still see it as the greatest game I ever played though).
    I think a major obstacle to using cost of failure in videogames to inform teaching and learning in schools is that the kind of costs incurred in schools are usually very different in kind, not just in amount, to those incurred in video games.

    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.

  37. I’m not convinced that 3-Acts are really about storytelling. I know you can consider the student to be the protagonist and the student’s need-to-know to be the conflict. But I’m not sure the students see themselves as engaged in a story when they’re doing a 3-Act. And whether something is a story is, I think, purely subjective, so that the student’s experience is what matters. Do you think 3-Acts would be better if the set-up explicitly asked students to imagine themselves in the role of someone else who has a need to know, and if this other person’s character were developed a little bit to make them real and human? In other words, will students respond to the same 3-Act task better if they think THEY need to know, or if they imagine themselves in the role of someone else–a sympathetic character–who needs to know? Or will that make no difference?

    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.

  38. I’m not trying to make students literal heroes in a mathematical story any more than Tolkien attempts to make the reader a literal hero in The Hobbit. In similar ways that authors engross readers in their books, teachers can engross students in the work of doing math.

  39. @Dan, but The Hobbit does have a hero: Bilbo. A 3-Act doesn’t have a protagonist, unless you count the student.

    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.

  40. Good discussion. I’m trying to follow up on Evan’s Twine idea: http://evanweinberg.com/2014/12/24/using-twine-to-build-a-choose-your-own-adventure-lesson/. The only idea that is missing that I think a lot about is flow, in the Mihaly Csikszentmihalyi sense. http://www.ted.com/talks/mihaly_csikszentmihalyi_on_flow?language=en I also like Natasha Harrington’s blogpost about it. http://www.gatheringmagic.com/natasha-lewis-harrington-editorial-research-05302013-create-and-discover/ She’s talking about the connection between flow and the create/discover activity. (The article’s in the context of Magic, but with lots of real psychology research.)

  41. More mini-points:
    (1) David Radcliffe made a nice implementation of Shikaku here: http://bojagi-gotmath.rhcloud.com/
    In fact, I don’t think he knew about Shikaku when he made it. Three nice features: clearer link to the area model (which reduces counting squares and I think makes it a more fun puzzle), nice colors (it is very visually appealing), and a way to build your own puzzles.

    (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.