Tuesday, June 4, 2013

New Math Game: Change Your Rule

This post is in two parts: The first part outlines the basic flow and structure of a new game idea which, I think, has the potential to support the conceptualization of math concepts such as combinations, permutations, patterns, variables/attributes and reflection symmetry.

I know that's a tall order so in the second part of this post I briefly discuss my reasoning, pose a few lingering questions and then ask for feedback.

Part One: Basic Flow of the Game
The idea for this new game started with a picture:

 Photo via: http://www.fotomat.es/arte-combinatorio/
I immediately thought how cool it would be to have this kind of mathematical art/visual inspriation in a living or learning environment, something to hang out with that evokes noticing and wondering.  In this case, a real-life shelf with spheres and cubes just begs for interaction, something to play around with and ponder. I want one! In the process of thinking about how to get this kind of installation in my own house, a new game was born.  Here's the basic idea:

Make/build a rule.  Find a way to change it.

These are the game pieces. Set 1 includes two shapes, four colors.  Set 2 includes six shapes and six colors.

Rule Change #1: Make a rule/pattern. Using the same shapes/colors how can you make the next iteration different from the first.  Does order matter?  How many different combinations can you make?

Rule Change #2: Make a rule/pattern. Change one element of each shape to make a new pattern.  For example, orange turns into red, or square turns into circle.  For each new design change only one variable for each piece.  How many times can you change the rule? How many new rules/patterns can you make from your starter rule?  Can you ever get back to the original rule/pattern?

Rule Change #3: Build your pattern then reflect the design. What do you have to do differently when you build the reflected pattern?

But what happens if you only use one color and shape?

How many combinations can you make using three of one shape and one other shape?  Would it change things if each of those circles were different colors?

On another line of questioning, what larger design can you make by building your design line by line using the same shapes/colors in each line?

Part Two: Thoughts and Questions

Even though Part One seems like a lesson flow, it's really meant to be more of a general framework for exploration.  My intent was to provide a little structure, some basic 'rules' and a lot of room for inquiry.

I'm wondering if it really feels like a game, or is more of an activity?  If it's going to feel more game-like, does it need more structure?  A timer? Some 'change your rule' cards?  Or, maybe, some cards that say how many different attributes to use in the pattern?  How many different rules would be enough to create a sense of chance? What other 'change rules' would you include?

Based on trying this out with my own kid this morning, if you were to do this more as an activity/lesson perhaps it would be helpful to have some really easy starter examples, like all one color, or two different colors to get the ball rolling in a positive direction.  I asked my daughter to build a pattern with three pieces but then gave her the 'change rule'.  She didn't really like that and we left it there.  The game pieces and board are still out, though, hanging around.  I'll see if she wanders back over.

Questions I still have include: When combining or creating permutations, how much does the second attribute matter?  For example, this first design (two colors, one shape) looks like it combines in exactly the same way as the second design (two colors, two shapes):

Another one of my goals for this game/activity was to also explore the ideas of attributes/variables in design -- how well do you think it does that?  I intentionally did not use pattern blocks -- only one attribute/thing to change -- and instead made my own (Set 1). What would pull the attribute/variable idea out a little further?

I hope it's clear that I am hoping to dig into the brain trust that is my modest but wonderful readership.  That means you by the way, so please if you have any thoughts about all this, I'd love to hear your ideas.

Things I would love feedback on: key ideas about combinations/permutations at the elementary level, thoughts about the game structure, ideas for other 'rule changers' to add into the mix, and any other thoughts you may have.  Thank you!!

p.s. If you want to leave a comment but don't see the comment section below, please consider refreshing this post or closing the post altogether and come back.  This template has some bugs. If you don't see a green-lettered header and/or the page menu at the top, then chances are the template did not fully load.  Sorry for the hassle.

1. I'm going to enter a comment in hopes that will trigger this blog design/template to show comments! A couple people have let me know they weren't showing. :-)

2. Game/puzzle/activity... people argue about this all the time. This does feel more like an activity right now. Playful, though.

One game that I wonder how I never thought of is using the Quirkle pieces to play Eleusis Express. (Cf. http://www.logicmazes.com/games/eleusis/express.html or http://mathhombre.blogspot.com/p/games.html) That's one way to go with this.

Some thinking out loud:
-The whole reflecting or transforming patterns is a neat idea.
-To increase constraints (and force creativity) you need a limited supply of pieces. Like a hand, or your own scrabble tray, or pile. Random addition to this (like drawing from a bag or a face down pile) would help, too.
-To be more gamelike I think there could be a well defined set of moves. Like:
a) swap one block out for another from your pile. The line still needs to be a pattern that you can explain.
eg. square, square, circle, square, square, circle: you swap the first circle for a triangle, changing the pattern to square square different.
b) add three blocks to a line. Has to continue the pattern in a way you can explain.
c) transform a pattern. Create a new line that has a connection to an existing line. have to have at least 5 blocks in the new line. You have to be able to explain the connection.
eg. square square circle, square square circle: you add the new line triangle triangle square triangle triangle.
d) draw a new tile and discard one back to the source.

The lines should be restricted somehow. Like each player may start one. After that, new lines come from move (c) or finishing a line. (10 or 12 tiles to finish a line?)

To be competitive you could score for each tile played, or when you change a line you score the length of that line, or you keep the tiles from a finished line. Player with most tiles wins...

Definitely worth playing around with this.

3. I had thought about Eleusis too when Malke talked about 'rule changes'. Malke, your daughter may not be ready for Eleusis yet, but if you could play it with some adults or teens, it might inspire you.

This post also reminded me of Set and Quarto.

I don't have much of a feel for game design (yet). I am intrigued by your process.

John, maybe we could play with this when I come visit in the few weeks.

4. p.s. I love the photo at the top.

5. Thanks John! Those are GREAT ideas. We're not really game players around our house -- it's always been hard for me to get the hang of rules, funny enough. My kid, too, has little patience for learning rules. We'd both prefer to make them ourselves, which is why I'd love for this game/activity to have that idea embedded in it -- like a 'make your own rule' chance card thrown in there. But, the rules you suggest seem manageable to me. I'll continue to play around with the idea a little.

I do think that a "playful activity" as you say would be enough for the younger kids. A little chance, and a little structure in terms of how to build/change a rule, might be all it takes to make it challenging and interesting to the K-3s. I'm still thinking of how to formalize the design aspect -- I started with that and then got sidetracked by a peek into what combinations/permutations really are. The design element is something I don't want to get lost in the game design. Probably a good candidate for a collaborative game between two kids, or a solitaire design version? Whatever it ends up becoming, I'm enjoying the making process!

One other big question is how to keep the focus on working with multiple attributes.

And, Sue, if you guys have time to play around with the ideas I'm all for it! :-)

6. Oh, and there's been some interesting discussion on the game over at the Math in Your Feet FB page, too: https://www.facebook.com/photo.php?fbid=377782982327743&set=a.274450789327630.50665.273959679376741&type=1&theater

7. Interesting. It seems like an activity and I like it as an activity more than a game. I don't like having to follow rules, I guess : ). I like the activity of playing with the numbers, although it seems like you are ultimately teaching the concept of probability. There are great exploration here, but wonder if you could tie in numbers too. Best of luck with your ideas!
Kids Math Teacher

8. Malke, I played this with my son today. It definitely felt like an activity. He likes activities as long as there are stories behind them. In our case, it was an exercise from the series I called "The Wisdom of Yoda". It reminded me of the activities series in the Alexander Zvonkin's book "Math from three to seven". We will definitely revisit this activity quite a few times (duh, how come I didn't think about using Quirkle tiles?! they are perfect!) How to turn it into a game... One of the ideas I had (but I haven't yet tested it) is to throw in some randomness. I'm going to make two dice - one for the color change and the other one - for shape change. And start with a limited number of tiles like John suggested earlier. This would work for Rule Change 1. But I love-love-love the Rule Change 2 idea (reminds me of those word puzzles where you start with one word, change only one letter at a time and get the opposite word in the end). So I was thinking to make it more game-like, to have a different field layout. I've not tested it either, so I'm going to try it out myself this weekend, take pictures and post them to FB.