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 in India) 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.
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 in India) 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.
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