A bad maths curriculum

How to kill the joy of mathematics.

Jan 28, 2024

A few weeks back, my kid & I were discussing his school maths exam. The topic he'd strugged with was tax calculations, which was, interestingly, a topic under the chapter Comparing Quantities. "Papa, I keep getting confused if the denominator is cost price or sales price.", he said to me. It appeared he'd memorised the "rules", and as with any such approach to learning, a mistake was bound to happen.

I had a discussion with him then about what constitutes mathematics vs what doesn't, and why he shouldn't feel too bad about being confused. This post captures some of my thoughts on the topic.

So what is maths?

If you think about any subject/topic, educating oneself on it should largely involve getting the essence of that topic. So what's the essence of mathematics? Paul Lockhart in his provocative essay A Mathematician's Lament defines mathematics as the music of reason (the book extends the online essay with a Part II, titled Exultation).

While you'll find mathematicians (professional & amateur) be at different points in the spectrum about Abstract vs Concrete, the notions of "reasoning", "pattern/structure" and "deduction" stand undisputed.

Because you're dealing with the method of reasoning, it isn't required to limit the object of study to something physical. It's here that the tension starts, as one starts getting into topics more advanced that basic arithmetic. How does one teach kids a method of reasoning, when they've been taught the rules without questioning ("minus times minus is plus")?

We don't learn how to do maths, we learn about maths, to borrow David Perkin's excellent expression "aboutitis" (and "elementitis") from his book Making Learning Whole. And in mathematics, the more rules you learn, the lesser you're doing maths.

Is commerce maths?

With that background, let's assess if taxation makes for good maths. When calculating taxes, the essence is about the flow of money, of commercial value addition, and taxation as a form of revenue generation for the government. Without any of that context, the rules of taxation are arbitrary - there's no deduction, no reasoning, only blind application of something you've learned about. You either know it, or you don't - you cannot deduce it.

Rules are always going to feel arbitrary, and arbitrariness kills the joy of mathematics! And therein lies the reason why kids end up memorising x=-b±b2-4ac2a, or that trick to some proof. They were never taught how to think for themselves. They're learning someone else's mathematics (to borrow Paul's words).

"Practical Applications"

"But without practical applications, won't kids not understand the value of maths?". Paul, in his essay, responds to this in a much better way, so I'll just refer the reader to his essay. But in the immediate context, it's simpler to just ask the following questions:

  1. By not studying taxation under mathematics, would the kid be deprived of tax calculation ability later in life?
  2. By studying taxation under mathematics, are they able to calculate taxes any better as against say those who studied it under commerce/economics?

If the answer to both the questions is no, what exactly did the kid learn? And if you think the answer to #2 is yes, are you sure you aren't conflating calculation with mathematics (is producing a sound the same as music)?

To be clear, I think it's perfectly ok to use applications to motivate a problem. My issue is when we start conflating that with doing maths.

The price we pay as society

It's no wonder that we come across a plethora of "I'm not a maths person". Our society is built of folks suffering PTSD from having been "taught" mathematics, who then inflict the same upon their kids, confusing speed for intelligence, and arithmetic for maths ("let's do some math!" - I heard the McKinsey guy exclaim).

I learnt to enjoy maths not because of my school but despite it.

I don't have answers that scale. I get to enjoy my conversations whenever my kid brings up interesting questions, often ones that make me revisit my own rules. Paul Lockhart gets into some possible answers, and so does Perkins, but the nature of those changes at scale are non-trivial without large societal support. So for now, I'd restrict myself to just point the issue, and encourage others to rethink what education means.