How automating calculations in a math problem might help people struggling with math see a new side of math here-to-fore hidden from them.

No Number Math Problems

No Number Math Problems

January 11, 2021

Author: Victoria

Through a series of experiments on my unfortunate friends and family, I’ve come to suspect most time in a math problem is spent dwelling on basic questions like:

  • Did I add those numbers together right?
  • Did I read the numbers right?
  • How do you do division again?

If this was all one had thought on the topic of math, it’s quite understandable why the subject is frequently considered boring and useless. Math becomes useful when the focus shifts from calculation to questions of variables and their relationships:

  • Do these variables make sense?
  • Is the answer good enough for my purposes?
  • Which formula gets me more gems/money/gold/whatever?

To find out if simple calculations are indeed obstructing awareness of the more creative questions in math, I’m coding a computer assisted math problem. In having the calculation parts of the game automated, it frees the player to focus on aspects of math they may otherwise be too preoccupied to notice. Would this help develop the players skills, or dare to dream, their interest in math? Maybe. Probably. I am not sure myself, but what’s the harm in asking?

Is Math Like Running or Reading?

If we consider the warning of ‘running before walking’, this approach seems doomed to failure. This metaphor however, compares a complex skill with several sets of intertwined skills, with a linear mastery of the body. Walking and running both require incrementally skilled use of the same leg muscles. Math however, requires numeric and geometric comprehension, calculation and comparison. Math is actually a lot more similar to a language. Is it appropriate to speak before learning your letters? Yes it is, in fact, it’s recommended. Designing problems where the computer handles some of the prohibitively boring stumbling blocks for struggling mathematicians, may allow them to wrestle with new, hopefully more interesting aspects of maths, that were here-to-fore unknown to them.

From Calculation To Solving

Here’s an example. This game puts the player in the shoes of a small-town banker. The player creates financial loans for simulated customers. These loans may be simple interest, compound interest, or annuities, depending on what the player wishes to study. Instead of plugging the equations and variables into a calculator, the challenge now comes from selecting the right formula for the problem, and solving the equation in terms of important loan variables, like the interest rate (r).

What happens if the player selects the wrong formula?

The game can tell the player they were wrong, but thanks to open-source Javascript math libraries like Nerdamer, the computer can carry on with whatever errors the player makes. Showing, rather than telling, what happens to the goal numbers when a formula is wrong. Experimenting with equations and different variable values in power, multiplication or division positions, seeing the changes in the resulting profit, something that can take the calculation shy a lot of time and effort, gives a new perspective on the utility of math. Now the player determines what they think the best equation and inputs are for their own purposes.

Experiment 1

Selecting the desired profit, the financial formula, and solving it in terms of interest rate and time.

This focuses the players attention on selecting either the technically correct formula, or a formula that will make more money (and probably bankrupt the client, but eh, details). The game then solves for the interest rate (r) and years (t), and generates a set of distractor equations for multiple choice questions. Regardless of whether to player solves their chosen formula correctly or not, the game will proceed with solving the equation for the desired profit.

One problem here is the limitation on the goal variable, profit. This is necessary to make solving for r and t relevant. It does however prevent the player from asking, which equation-variable combination is most beneficial to them.

Experiment 2:

Selecting the financial formula, and controlling all variable values to maximize profit

This allows the player to see how raising or lowering different variable values changes the goal, depending on their relationship in the equation. Making a divisor bigger results in less overall profit for the player. An equation with powers has be significantly more profitable than one with multiplication. This requires comprehending what the equations say about the variables.

However, this approach does not exercise the players skills in manipulating or solving equations.

It takes a lot more players than my games currently have to query whether partially automated math problems are helpful to struggling mathematicians. Do they enable players to see a utility in math they have been unable to appreciated when mired in calculations? Does having a goal and characters change the meaning in the equations and numbers? Or does it simply create more points of confusion? Is the player better off learning how to read music before learning how to play music?

We’ll find out, eventually. Probably.