Saturday, May 19, 2012

Math Evolve

Math Evolve - a basic operations fluency game for iOS. Free Lite version to try out, full version $1.99.

Somehow Math Evolve came across my radar again this week; it's an iOS app for elementary math. I'm always willing to give those things a try. Tired, frustrated with other stuff, I tweet:

And didn't think any more about it.

The next day, Adam tweets back, very politely. Immediately I feel like a heel. If I was speaking to someone in person, I wouldn't express myself that way. So I want to apologize to Adam here.

I had high expectations because the app store page has the following:
★ Winner of BEST EDUCATIONAL GAME OF 2011 (2nd Place) in the Best App Ever Awards.
★ “The holy grail of edutainment math apps.” Editors Choice, 5/5 Score -Best Apps for Kids 
In Math Evolve you are an alien organism, completing number sentences on a quest to grow and return to your people. At the beginning of a level you fill in the first blank, then the second blank after the operation, then finally the result. Later you pick the first blank and the computer provides the second. (I always get the first one of those wrong as I don't notice when the switch occurs.)  All the while you are dodging combatants and trying to shoot them out of the way. You control your position on the screen by moving your character with a touch. Finally the boss appears and asks you to compute particulars.

Another part of why I expected/hoped for more is that it is slick. Trying to develop ParabolaX (or rather, watch while Alejo and Kevin program ParabolaX) has given me an appreciation for the work that goes into slickness in iOS.  Is there a role for a practice app? I think so, but I don't value it anywhere nearly as highly as one that helps students learn. After all, if they need practice, typically there's room for greater understanding.

I'd love a practice game that gave more for students to notice. Like asking 7+3, 6+4, 5+5, ... or 4x5, 5x5, 6x5... or 5x6, 6x6, 6x7... Noticing and generalizing are things that I value more about math.

Given the context, the practice mode could have meaning of the operation.  Gathering or eliminating to add or subtract, repeated groups for multiplication... lots of possibilities. I do like how at first you're gathering all the equation elements, then the game fills in the second spot, then the boss poses a computation. The incorrect answers are not particularly problematic, and the boss doesn't seem to use missed problems to pose problems. Maybe at higher levels? Ways for added difficulty could be including choices that are not computable, such as choices between 3, 6 and 7 when you have 21÷___.  I did only play the Lite version, so possibly some of these things come later.

Boss level.
I love how open and interested Adam is in improving the game, the context and game mechanics are well developed and suitable, and the game is fun enough that students will be happy to play. And he is obviously a far better internet citizen than I am, but hopefully he's taught me to watch my oafish responses.

As I think about evaluating math games and apps
Objective: facts practice, four operations, including negative numbers.
Gameplay: fun enough. Think Galaga/shoot 'em up.
Aesthetic: great. Cute characters, good effects.
Pedagogy: beyond difficulty selection, no visible fact strategies or support for learning. Minimal math practices.

I'd love to hear what you think of the app, and what do you feel like would make for a good facts learning game.

Thursday, May 10, 2012

Guess My Rule

Some activities seem ageless. They work in elementary, middle and beyond. Guess my rule I have played with very young students, and this week I got to try it with my summer intermediate algebra course.
Guess My Rule
Any number of players

A rulekeeper makes up a rule that gives a number output for a number input. (It should be a function.) Players take turns giving an input, and the rulekeeper tells them the output. If a player wants to guess the rule, they tell an input and what the output would be. If they're right, they guess the rule. Then that player makes the next rule.
I don't know who originated this game; it feels ancient and right, so kudos to whomever developed it. I let rulekeepers use a calculator, and I usually start out with a few rules until the guesser feels comfortable making up a rule.

Today I started with the number times two minus three.  (Highlight to see it, or guess from the table.) Inputs came from all over. 12,  5, 10, 1... some shock at a negative answer. I encourage the students to record the results, hoping that it will lead to some ideas about what inputs to suggest. Organizing data is not a natural tendency. At one point they started asking 30, 40, 50...

Oooh! That's a pattern. It goes up 20 when the input goes up 10. So they could predict the answer for multiples of ten. Thinking about that, they suggested a rule that worked. We looked at the rule to see from where the up by 20 pattern came.

The solver was not comfortable coming up with his own rule, so I chose another: eight minus the number
\(7 \to 1 \) then \(1 \to 7\) drew an audible gasp/hmm. There was one student who loved asking for 12. The third multiple of 10 got the rule again. Subtract eight and then take the opposite of your answer. One of the reasons I love this game is that it always brings up equivalent expressions. I shared my original rule and we talked out the equivalence.

Now they were ready to suggest a few rules. A couple like my rules, then input times 5 divided by 2, which got a nice check of "oh, that is the same as the number plus half of it," and "I had the number times one and a half." Then one student came up with a stumper. When guesses were not focusing, I started taking notes on the board.

I also asked for what patterns they noticed. Some good stuff.  We got to the idea of asking inputs in a pattern, and I asked them to predict the output from 2 before Edras gave us the actual. (There's some really nice research on the power of prediction in math, some by my colleague Lisa Kasmer.) We spent some time on different expressions of the rule, like ___ x ___ + \(\frac{1}{2}\) ___ x ___, (___)^2 + ( ___)^2/2 and \( 1.5 x^2\).

For a last question, I asked them to find what input would give 100, and got unexpected riches. Students really worked hard, consulting group members. Several tried to solve symbolically, but didn't know what to do with the \( x^2 \). One student had an excellent guess and check. We spent some time discussing that, including what an excellent problem solving method it is, and how when I use it, using numbers gives me a much better feel of what's going on. Maybe they've been discouraged to use it by previous teachers, but it's a great strategy. We did discuss how to make our guess more accurate and efficient. Like was 8 or 9 closer to 100 in output?

Another then shared a traditional symbolic solution. One student asked, "why did you divide by 1.5 before you took the square root?"

"Because you have to."
"It has something to do with the order of operations..."
"Doesn't PEMDAS tell you what to do?"
"But you have to reverse it maybe..."

"Let's try it." (OK that was me.) They told me the steps and I wrote it down. Amazed to find the same answer. A good moment to point out to them that are almost always multiple methods in math. Teachers may have told them that there is only one way to do things in the past, but that is bullsh*t.

I should not swear in class. (In response to my usual 'jot down one thing you want to remember' there were many repetitions of that statement. In my defense, it is a college class. And the comedic potential was ripe.)

The next activity is adapted from Pam Wells' adaptation of an activity from the excellent Mathscape curriculum.

(Here's the Word file if you want to edit - it wasn't appearing correctly in the embed.)

It dovetailed very well into the Guess My Rule, allowing us time and grist to find many connections amongst tabular, symbolic and visual representations, reiterating the equivalent expressions and multiple solutions themes, and giving us a launching point for a definition. Using the Y pattern rule, I made a table for S=1, 4, 7 and 11. The changes in output were 9, 9 and 12... what went wrong? They found that the difference in the inputs was not constant, and when we changed 10 to 11, the output pattern worked. To me, that's the moment for the generalization.

We went on to launch Linear War, which gave me a chance to share why we use the term linear and some of what this stuff has to do with lines. Next class, we play!

All in all, it was a fun class. I was impressed with their willingness to try non-traditional problems, and they're gaining rapidly in ability to work cooperatively and make conjectures. The meta-messages about mathematics seem to be gaining some traction, too.