[Gamification] Game Element #4: Coopetition


So, I feel like I just need to write something today because I haven’t written in a while.  And this is a game element that I am very interested in using in my class-as-a-game, so here goes.

Coopetition = cooperation + competition

On the cooperation side: I already work on finding or developing good group work tasks.  I look for tasks that have a low entry point, a well defined goal, and an “Open Middle”.  This way, I can get lots of buy in on the front end because it’s easy to get started, and I also get lots of different strategies for reaching the goal.  So the group work part comes easily. I have students who used different strategies share with each other and/or the whole class through short presentations.  What I need to improve is the collection of these strategies and presentations.  I want the students to bring everything together in a wiki or something, the same way gamers do when they share walkthroughs and tips.

On the competition side:  I really don’t do this at all yet.  I’ve never been good at creating a fun, competitive atmosphere, but I know it can be useful for motivation so I want it.  My first thought on competition is usually head-to-head games.  Like a “Quiz-up” competition, or a physics card game.  We played “Heads-up” with the iPads a few weeks ago and it went really well.  The kids love playing this game!  So I put some simple physics questions in and they played with just as much enthusiasm as they showed when playing the pop culture or celebrity categories.  This says to me that it’s the game play and the competition element that they are into, not necessarily the content.  If you haven’t seen your kids playing Heads Up, check out the game play here.

I also think this may be where my XP/Leaderboard system will be useful, as I will need to track completion of the “coopetition” activities.  With a good XP system set up, I can have different categories for leveling or prizes, and hopefully encourage the cooperation and competition aspects of the game.  For instance:

“Your team must attain 500XP to reach level 3 on this topic”

For this one, students would be relying on their teammates to acquire at least part of the XP needed to move to the next level.  So, if I can get students to want that next level, they’ll need to work together to get there.  And as long as I give XP for a variety of tasks, I can maintain the “choose your own adventure” feel to the class, while still leading students through a progression of topics.

“To receive this badge, you must complete 5 entries in the class wiki”

This is an example of an individual accomplishment, but one that requires a product that’s all about collaboration. Hopefully, students would want to complete the activity for a variety of reasons.  They might want the XP to move up the leaderboard, they might want their name to appear on the class wiki the most, they might want the badge to display on their binder, or they might want to “save the lost spaceship” before anyone else.  But whatever their reason for wanting to clear the obstacle, they’ll need to collaborate to make it happen.


Pizza Functions


At Twitter Math Camp this summer, I got the opportunity to work with a small group of amazing Algebra I teachers on planning a linear functions unit.  While the crazy of school has thwarted me from following through on all the plans, I still got in a thrown together version of one today.

So, the idea was to compare pizza companies and see who had the best deal.  But each company provides us with different info about their prices.  Check it:

To get things started, we all did Pizza Hut as a class.  We decided on the function c(t) because cost depends on toppings.  We wrote the equation c(t) = 10 + .85t.  We used the function to generate a table using the domain [0,5] because some people might want cheese pizza and 5 is a good max number of toppings.  Then we graphed y = c(t) using the same domain and we were done!  They did most of the work, I was just there to prod them along if they didn’t know what to do next.

Next, I told one half of the class they were to be my “Papa John’s Experts” and the other half they were my “Domino’s Experts”.  If someone had an issue figuring out one of the representations, they were to see an “expert” from the other side of the aisle.  It worked great most of the time; they found help on their own when they needed it.

I thought the best part was finding the cost per topping for Domino’s.  Since they were only given two points, it was really like asking them to find the slope of the line between (2 , 10.7) and (5 , 14).  But in context, it was not a scary math problem, just “well, there’s three more toppings there and it costs $3.30 more, so it’s $1.10 per topping”(their words).  Later I showed them (out of context) that they had done the good ol’ (y2-y1)/(x2-x1).  One kid even seemed mad that I had “tricked” him into calculating slope, as if he was proud of not being able to do it and I ruined all that for him.  Weird.

Note: It is fun being able to refer to the y-int as a cheese pizza all day! (Also, it was a great follow up to the 100×100 burger problem from Kaplinsky in which the y-int is a bun and dressings.)

Next class, we’ll choose a company and make whiteboards to defend the choice.  Is Domino’s really always the cheapest?  Is cost all we care about?  Tune in next time to find out.  🙂

Oh yeah, and I started class with a pizza themed counting circle!  We started at 10.5 and counted up by 1.25 at a time.  It was a good one, it went pretty fast.  And we did the “toss the ball and make a prediction” game, where I call “stop” and whoever has the ball tosses it across and we have to predict what that person will say.  I ❤ Counting Circle!

What I Learned at Camp


More specifically, Twitter Math Camp 2013!  Here’s what I got:

(note: these are just some highlights, I learned way too much to capture in one post)

First and foremost, I learned about how to teach math better.  That was definitely the focus of the conference.  And it wasn’t just obvious to us classroom teachers, see Eli’s take on it (from Team Desmos):


So, the “big picture” takeaway for me was definitely Max Ray’s “I notice, I wonder”.  I just love the wording of that!  It’s so inviting; everyone can notice something, and everyone wonders about things.   The basic idea is that when you present the students with the scenario you want them to analyze, first ask them what they notice, then what they wonder (and give credit to all ideas).  Simple, brilliant!  And when I really thought about it, I noticed that I had been trying to ask these questions of my students all along (in both my physics and algebra classes), but I had been fumbling the wording. 😦  I would say things like “so how does this work?” or “what’s going on here?”.  Duh, Mr. Owen, if they knew what was going on already, then they wouldn’t need the lesson.  In Max’s session, I noticed that after we had done a few minutes of noticing, some people started throwing out things that they wondered too.  I wonder if it’ll be that easy with students, I hope so.

I also learned about what makes for a good group work task and how to implement one.  Thanks to Anna (@Borschtwithanna) and Jessica (@algebrainiac1) for that one.  Main takeaway from their session was that to be a good group task, there need to be multiple obvious ways to solve it.  What a great way to get kids talking about math, have them solve the same problem and then debate who did it the “best” way!  That may not have been the main point of the session, but that’s what I got out of it.

While that session was on the topic of group dynamics, I also attended a great session on building a class community.  It was Sadie’s (@wahedahbug) session on Counting Circles.  A counting circle is a classroom routine that builds number sense.  It’s pretty much what you would think a counting circle is.  Sadie suggests chapter 4 of this book to get started (I have not had a chance to check it out yet, but will soon).  The book is for K-3, but the concept is totally scale-able.  It’s not just about counting!  For instance, let’s say we’re going around the circle counting up by 1/2s, then I stop and ask “what number will Suzie be?” (Suzie is 7 kids from where we stopped).  Some of my kids will go straight to a linear function to solve that, some won’t.  But that’s just it, the methods will all be on the table so we can share and learn.  But I think the biggest reason I’m gonna use it is for the confidence building.  As we started the counting circle with a group of math teachers, several of us commented that we were nervous.  Imagine how the kids will feel!  The thing is, we’re all in it together.  I felt like a part of a mini community in our session and that was after doing it once.  If I make this part of my class routine, my hope is that the kids will feel that same sense of community.  This should make them more confident and less afraid to share out, and that’s in addition to the numeracy skills we’re building.

It was also great having Team Mathalicious there.  I had already planned on utilizing some of their lessons, so having them explain their thought process really helped me out.  I feel that after attending their sessions, I’ll be not only better at implemented their lessons, but also better at writing my own real world lessons, based on my own and my students specific interests.  It didn’t hurt that Steve Leinwand  and Ann Lawrence were both in my lesson writing session, throwing out ideas and asking good questions.

I also learned way too much to type by just talking to people.  The importance of these face to face encounters cannot be overstated.  I think that was the best thing about the camp.  Every conversation I had was amazing!  Some were not math related (which is a good thing!), but a lot of them were.  And it was super obvious that everyone there has a passion for what they do.  Specifically though, I saw a passion for math (or maths for our British friends) in many of the attendees.  What I mean is that they were in one way or another involved in doing mathematics, not just teaching it.  In his Mathematicians Lament, Lockhart talks about how we don’t get music teachers that don’t play music.  The implication is that we do have math teachers that don’t “play math”.  And that has definitely been true of me.  It’s not that I don’t like math (especially to play with), but I haven’t been doing it, really.

So I had a few conversations with Edmund Harriss (@Gelada) and he totally convinced me that I need to.  Not because I’m a terrible teacher if I don’t play with math and constantly work at new problems, but rather because it is fun.  For example, he asked me if I had heard of the 3x+1 problem.  It goes: take a number, if even —> take half, if odd —> 3x+1 it, then repeat till you get to a loop.  Try it with 3:  3 – 10 – 5 – 16 – 8 – 4 – 2 – 5.  And bam! there’s the loop!  Now try 23.  Have fun!  But where it really gets interesting is in the mathematical art.  Check out some of Edmund’s stuff, amazing!  And after seeing the things he did with Desmos after only a few days of playing around with it, I’m convinced that I need to play around with math more.  Of course, kids like to play too, I just need to give them some toys!

So, there it is.  Teach math better, play with math more.

#MTBoS as a game: a n00b’s perspective


I have enjoyed “lurking” around the conversation about what the mathtwitterblogosphere is, where it could go, and how it can be more welcoming to newcomers. I really liked Sam’s post because he talks about how it’s different for everyone and you get out of it what you want or need. He’s great at welcoming newcomers and making them feel comfortable contributing.  I joined his new blogger initiation and that’s what moved me from lurker to contributor.  I also really liked Kate’s post on the culture of the MTBoS.  Her comparisons are spot on and very interesting, you should definitely check that one out if you haven’t already.  

Like most things I write here, I feel like someone (or lots of someones) already thought of this and wrote their own similar posts.  But then I write it anyways.  Because this is my blog and I write what helps me.  If I stopped every time I felt like my idea was unoriginal, I wouldn’t have written ANY posts this year.  So here goes:

I think the #MTBoS is like a game.

Ok, so I just got back from ISTE13 and one of the keynotes was by Jane McGonigal.  And I just started reading her book Reality is Broken.  Fifty pages in and it already blew my mind.  So that’s where the idea comes from obviously (or not obviously if you’ve never heard of her), but I think it’s a good comparison.  Here’s why:

1.) You tend to get out of it what you put in.  You can lurk around (like everyone does at first), but then you’re gonna stay at level one.  If you want to “level up” you’ve got to participate.  Joined a conversation: achievement unlocked! You earn two follows and one sweet lesson idea.  Wrote a good blog post: achievement unlocked! You earn two more follows and a worksheet on factoring.

2.) Participation is voluntary.  Why do we put in the extra time here?  To become better teachers?  I would think that would be the most common answer if I gave a survey, but does it really answer the question?  Why are we trying to become better teachers in this specific way?  Especially since…

3.) It can be really hard work.  I put in a lot of time (as I’m sure you do too if you’re reading my little blog) on Twitter and Feedly, trying to get everything I can out of them.  I am constantly checking my feeds on my phone, my iPad, and my computer, at home and at school.  Why so obsessive?  Well, I think it has to do with this:

“Strangers tell me at conferences how much the blogosphere has meant to their practice and their happiness.”  Dan Meyer said that earlier today in a comment on his blog.  That’s it!  Their practice AND their happiness.  Just like gamers wouldn’t keep challenging themselves if it didn’t make them happy, I think members of the MTBoS are putting in the extra hours because it makes them happy too!  Hence…

4.) Intrinsic rewards.  From Reality is Broken: “The scientific term for this kind of self-motivated, self-rewarding activity is autotelic (from the Greek words for “self” auto and “goal” telos“)”.

First, that quote made me think of this clip (a student talking about why he likes to play Minecraft) (Side note: that clip is from this video  by Douglas Kiang which is a wonderful breakdown on what gamer mindsets can teach us about education.)

Second, it made me think about what keeps me putting in the extra hours to keep up with the MTBoS.  Jane McGonigal describes the four intrinsic rewards that are most “essential to our happiness”.  I’ll just direct quote those bad boys here (emphasis hers):

“First and foremost, we crave satisfying work, every single day.  The exact nature of this “satisfying work” is different from person to person, but for everyone it means being immersed in clearly defined, demanding activities that allow us to see the direct impact of our efforts.”

“Second, we crave the experience, or at least the hope, of being successful.  We want to feel powerful in our own lives and show off to others what we’re good at.  We want to be optimistic about our own chances for success, to aspire to something, and to feel like like we’re getting better over time.”

“Third, we crave social connection.  Humans are extremely social creatures, and even the most introverted among us derive a large percentage of our happiness from spending time with the people we care about.  We want to share experiences and build bonds, and we most often accomplish that by doing things that matter together.”

“Fourth, and finally, we crave meaning, or the chance to be a part of something larger than ourselves.  We want to feel curiosity, awe, and wonder about things that unfold on epic scales.  And most importantly, we want to belong to and contribute to something that has lasting significance beyond our own individual lives.”

So, there she was describing what makes us happy, not exactly what about games makes us happy, just in general.  You might read that and think “Yes! And that’s why I am a teacher!!”  So where is the connection between games and the MTBoS?  I think it’s here, where she makes the connection between games and happiness:

“[Games] actively engage us in satisfying work that we have the chance to be successful at.  They give us a highly structured way to spend time and build bonds with people we like.  And if we play a game long enough, with a big enough network of players, we feel a part of something bigger than ourselves – part of an epic story, an important project, or a global community.  Good games help us experience the four things we crave most – and they do it safely, cheaply, and reliably.”

There it is!  Just replace gaming with “math nerd internet time” and she makes a great case for how the MTBoS makes me happy and keeps me coming back for more.

Collaboration is Key


I do not consider myself a master teacher. But I feel like I have brought myself closer to that goal this year than in my previous 5 years combined. And collaboration has been the key. My advice to all teachers who care to listen:

Get on Twitter and find some like minded people there.

Here’s just a few examples of how my Twitterings have helped me and my students this year (there are like a bajillion of these too!).

Example 1:


I follow Danny (college physics) and he posed the question “What is a model?”. You can see my reply and explanation there in the pic. What’s awesome is that this collaboration went from the classroom to twitter, then back again. Literally the next day in class, I used the analogy of a model being like a tool. We were in a circle holding up our whiteboards to show what we had learned from a lab. I told students to think about digging a hole. What would they do first? (Get a shovel) Then I said “the board you are holding is your shovel!”. Some of them were holding spoons we decided, and since it’s pretty hard to dig a hole with a spoon, we better figure out how to make those boards better.

Example 2:



Then this:


Example 3:

I think it is very important that HS teachers begin talking more with college professors so that we can figure out where there may be gaps in kids’ knowledge between our classrooms. And so we can share ideas on best practices in teaching and learning. Guess where we all are?


Example 4:

The best idea in collaboration since the mathtwitterblogosphere: the CCSSM Draft! Last night, a small group of teachers decided to NFL-style draft their two favorite common core standards from grade 8, along with one math practice standard, and then create a lesson with them. Here’s the story of how the whole thing shaped up over the course of a few hours on a Friday night (it’s a little long, but give it a chance!).

What I especially love about this is that it feels like our version of Genius Hour (a sort of free for all learning time). I would love, love, love for my students to have Genius Hour in my class next year and so the chance to model what it looks like and what you can get out of it is awesome! Bonus: the link I provided up there for Genius Hour also shows how powerful Twitter can be as a collaboration tool.

Man, do I feel like the major underdog on that list for the CCSS Draft! I better bring my A game. 😉 And that’s the point, right? Give kids some time to work on something they care about, and they’ll bring their A game too.