Word Problems in Maths

In The Joy of x, Steven Strogatz talks of something all of us have struggled with in maths: word problems. Translating them into maths equations is quite a challenge for many. Ironic, isn’t it, that kids and parents complain that academics has no connection to the “real world”, but that’s what word problems are…

 

The root cause of why many struggle with word problems in maths is:

“(They involve) thinking not just about numbers, but about relationships between numbers… (and of course) relationships are much more abstract than numbers.”

But they still need to be understood, if not mastered:

“(Relationships) are also much more powerful. They express the inner logic of the world around us. Cause and effect, supply and demand, input and output, dose and response - all involve pairs of numbers and the relationships between them.”

 

Calvin, on the other hand, raises a different issue with word problems:

 

Jokes aside, Calvin’s point is the same as what Keith Delvin raised in an essay titled, “The Problem with Word Problems”:

“These problems typically assume you understand the rules of the game and agree to play by them, even though they’re often artificial, sometimes absurdly so.”

You know what he means: assumptions like people are equally efficient, or work continuously without breaks… and yes, Calvin, we assume that that vehicles move at the same speed throughout, and that there’s no traffic.

 

As a maths professor, Strogatz has an answer for Calvin’s charges:

“Those of us who teach maths should try to turn this bug into a feature. We should be up front about the fact that word problems force us to make simplifying assumptions.”

That sounded just like an acknowledgment, but how’s that a “feature”?

“That’s a valuable skill – it’s called mathematical modelling. Scientists do it all the time when they apply maths to the real world.”

I couldn’t agree more – that’s a valuable skill indeed, and not just in the sciences.