The biggest bluff in maths education
And why learning maths feels lifeless
If learning mathematics in school / high school looks like a lifeless, tedious enterprise, you are not alone.
A teacher or a maths book would try to answer two kinds of whys in a lively maths lesson. Firstly, why did humanity discover this mathematical idea in the first place? What problem were they trying to solve? The other is, what can you do with that idea now? Why is it still relevant? Maths education feels dry as you never get answers to both these questions. Do you know why you never get a response? The most prominent bluff in school teaching: school maths teachers rarely know the answer. It is tough to find teachers who know what to do with a mathematical idea beyond setting questions in the exam. If some teachers want to make an effort, they are held back by the sheer size of the syllabus. There is so much to teach that they don't have the time to go deep.
This is why, from primary school onward, we try to teach mathematics abstractly. There is a complete disregard for concrete examples. Sure, books (the NCERT ones) are becoming better every year. They do start by motivating one-off practical problems. For example, a Trigonometry lesson will begin with talking about measuring the height of some tower etc. But this practical introduction is very short-lived, like an awkward speech that teachers want to end quickly. Then books and syllabus promptly go to the dry part: abstract ideas, randomly introducing things without explaining why we need them.
The explanation given for this strange ritual, especially for later grades, is generality of maths. That maths is a general tool, so we must teach it in an abstract sense. So no more talking about specific examples, usage and motivation. For instance, all problems talk about general ABC triangles. Or polynomial equations and their coefficients are introduced without explaining what to do with them. Just a lot of ideas are crammed together in a syllabus.
Well, a screwdriver and nut bolts are also general-purpose tools. But we don't learn to use them with vapid explanations. Most children learn it with the help of construction kits and mechanic games. Pick up the tools and build something like a car or aeroplane or whatever you want. The constructions might look silly to adults, but that does not matter. In the book Lifelong Kindergarten, this idea is explained as learning through play, projects and passion. Because that is how human beings learn naturally: by creating something meaningful to them and playing with it. It also touches on the constructivist learning theories: the outcome of knowledge building and making something.
For example, interns working with me to build video games routinely use maths advanced for their age (like quaternions, trigonometry, and a bit of calculus). They do not learn Trigonometry as properties of some abstract triangle ABC revealed by scriptures. For example, they might get obsessed about rotating a character in their project game in a certain way. I find them instinctively reaching for arc tangents function and quaternions. They don't know the text of the impulse-momentum principle verbatim. Still, they routinely toy with that idea to make their characters follow a specific path in the game.
The recipe for unsuccessful maths education is to teach you a laundry list of disconnected ideas without telling you what to do with them. For a successful one, you would use maths to do something specific on a project that is meaningful to you. You'd play with the same idea repeatedly till it becomes a part of your muscle memory. Constructing such a learning experience is challenging. But until we attempt to face complex problems and question years-long dogma, maths education till high school will remain a failure. Students are not dumb. They just don't understand why they should care enough to work hard to learn maths.
If you have better ideas about how do we fix this sorry scheme of things, please get in touch. We can collaborate 😃 !