When math problems have no notion of how to use an equation to get the outcome you want, it's no wonder people struggle to apply math to their own problems.

Of Good and Evil Parameters In Math Problems

Of Good and Evil Parameters In Math Problems


January 19, 2021

Author: Victoria

Semantincally Meaningless

Much of the joy and utility of math depends on understanding the equations and their statements about the relations of the parameters they speak of. When a student solves an equation with no thought to the outcome, it’s like reading a sentence without meaning. It’s syntactically correct, but semantically meaningless. Noam Chomsky gives us a helpful example in ‘Colorless green ideas sleep furiously’ (1). This lack of meaning could be the culprit behind why so few students are able to translate textbook math to their own problems. If the information has to be useful to be utilized, then the reason for executing an equation is as important as the execution itself.

To back this idea up, the National Council of Teachers of Mathematics recommended that we ‘deemphasize traditional “word problems” where formulas and tables provide formulaic solutions. Instead they recommend a well-developed “operational sense” for deciding which procedures should be applied for practical problem solving’ (2) 4

Morality and Strategy

Theoretically, giving the parameters of an equation some emotional impact might tempt the brain into considering their implications a little more closely. Take a typical loan repayment equation. Eyes glaze over at the mere thought of it. However, if you were in the shoes of a banker, and your loan parameters determined both your and your clients likelihood of bankruptcy, these values now have a purpose. There are objectives and risks involved. Some parameter combinations are good, whether that be morally or strategically, and some are evil...whether that be morally or strategically!

The Good and Evil Minded

The particularly evil among us, might delight in combinations where:

P*r > M

or put another way, the principal multiplied by the monthly interest rate exceeds the monthly repayment rate, trapping the client in perpetual debt forever! <evil cackle> The more saintly might prefer to minimize interest, and then find themselves filing for their own bankruptcy after one too many failed loans <shakes head>.

On a cognitive level, creating a larger possibility space where riches or bankruptcy are both possible, causes a deeper levels of analysis to be conducted. Now it’s not just right or wrong execution, it’s good or evil morality and better or worse long term strategy. I don’t know what parts of the brain those activities involve, but there’s a brain network for every distinct capability we have. More differentiated thoughts leads to more interconnected information.

Cognitive Overload

A risk in adding semantic meaning to math problems, is cognitive overload and seductive attractors. Cognitive overload occurs when there is too much to focus on. Will the student be so concerned with the plight of clients, that they’ll stop focusing on how to balance an equation correctly? Possibly. Will they find the seductive details like clients business fitness so interesting that they stop caring if they’ve summed their geometric progression correctly? Maybe.

Even If semantics actually do help students apply maths to their own lives, it may be a mistake to make every math problem meaningful. Perhaps a balance of rote execution exercises, mixed with the odd semantic simulation is the best math diet for the brain.

Too Much Talking, Not Enough Doing

Theorizing for a thousand years won’t answer these questions. If you’d like to try your hand at this banking simulation with clients, risks and rewards, you can play it here. Feel free to @ me on twitter and let me know what you think!

Bibliography

1: Chomsky, Noam (1957). Syntactic Structures

2: Brook, Ellen (May 2014), Investigating the Adult Learners Experience When Solving Mathematical Word Probelms