# Formulas as "Rewards" in Thermodynamics

The ESL game I encountered two weeks ago at a conference has got me thinking. Can we use the simple "beat the system" technique for something besides homework? The engineering course I'm developing includes (not surprisingly) a lot of formulas. Pages and pages of them in fact.

As an instructional designer attempting to think like a student, I kept wondering - what are they all for? It wasn't until I started working through some sample problems in the course that I began to understand their function (and began to realize which ones were actually time saving tricks).

If you're given a list of formulas, it's really very overwhelming. They are essentially pieces of random text you have to memorize, with weird symbols at that. Even though this class is designed for engineers, it has to still be a little confusing to wonder which formulas are the most important and when to use them.

But what if the formulas were presented sequentially as "rewards" for successful problem solving at the early level? First you're asked to solve problems (review perhaps) based on math you already know, but as you are required to solve more different or more complex problems, you might be given new formulas to unlock.

### An Arithmetic Scenario

I thought I would write an arithmetic scenario to capture what I mean. Suppose you have learned to add and you solve a few addition problems like "What is the cost of one apple plus one orange plus two grapes." At some point a student might encounter a problem like "What is the cost of 6 apples" which is actually more quickly solved by multiplication.

Maybe at this point, the game could whisper "Hey kid, want a secret tool called multiplication?" This would open a mini lesson on multiplication with a secret reference source called a...multiplication table. Would this turn a multiplication table from a torture device to a secret weapon? Maybe, if the right real-world scenario were given.

### Moving On

Math in particular seems like a field in which "gaming levels" really apply. For instance, you need addition to do multiplication which leads to exponentiation then logarithms (not to mention basic algebra). Math is taught in a sequence because skills often build on each other (although it can be hard to see the payoff in high school).

I think there are K-12 math activities like this, but can we extend this to high school and college? I've seen "capstone" activities (e.g. design a survey in statistics) where you put what you learn into practice, but it still seems like we present math as an abstract tool you will use at some later date.

The statistics / romance manga is moving in the right direction in terms of adding a plot line, but I'm wondering if a game element can add more of a reward system to with the real world context. I suspect the original mathematicians thought the current formulas were a gift in comparison to the "old way." Can we share that same "gift" with our students?

### Post Script - Mar 26, 2009

I just read post on the Kapp Notes blog about using a "survival" game to explore engineering formulas. It'll be interesting to see how it works out.

I like the idea a lot. I'm not sure if it, based on your example, makes something like multiplication "fun", but teaches the concepts in such a way that they become useful ways to make your life easier instead of just being another arbitrary thing to learn.

My only worry would be, does it hold up as things get more complex? Multiplication might be addition made faster, but I remember physics equations that were not based on a simpler, more fundamental concept that was easy to grasp. They just existed and you had to learn them or fail. That could be bad instruction, or it could be the complexity of the subject matter - I'm not sure.

Regardless I'd love to see how "rewarding with equations" works in something like Thermodynamics. Very cool idea!

Thanks for your comments.

1) Maybe the multiplication example wasn't fun enough. Perhaps instead of buying fruit, you're selling fruit and you want know how much money you made.

2) I really do think you could expand these engineering equations further because they are designed to solve real problems. For instance thermodynamics basically developed as a way to maintain and build better steam engines (including making sure they didn't explode).

Suppose you had to steam generated power plant that was acting up and you had to get measurements based on incomplete data. There are a series of equations you can use depending on what you know. You could start with a basic one (e.g. if we know pressure, temperature, volume, then how much gas is in that tank), then work towards the more specialized ones (e.g. we know this system hasn't changed temperature in 24 hours and the pressure but pressure is building - what is it now?).

Rewards could be tables you use so you don't have to calculate everything or those to get initial estimates.

I could also see something where if you were rewarded, you bought a pass for a period of time until the next crisis. But a failure could be a red alert or a big explosion.

It seems like we could be taking advantage of the original problem solving concept more.

This is a cool idea. It's really just scaffolding tied to a reward structure - something that games do really well.

We should capture ideas like this somehow! Maybe a game idea Wiki?