It’s not exactly a secret that I don’t like how mathematics is done in secondary four and five. I feel like the mathematics course for those not pursuing a career in STEM isn’t exactly the best use of a student’s time, because the curriculum doesn’t give students the full picture.
I just want to talk about one particular concept that drives me nuts: the parabola function. In secondary four and five, I studied them in essentially their full glory, looking at how a parabola is constructed (using a directrix), as well as the full equation (given by $f(x) = ax^2 + bx + c$). In the “science” flavour of mathematics for secondary four and five, you look at all of that. It’s more or less all you need to know about the function.
However, when you’re in the regular flavour of mathematics in secondary four, you still look at the parabola function, but it has been castrated. I’m not kidding when I say students literally look at the function as only this: $f(x) = ax^2$. Said differently, while I studied any kind of parabola on the Cartesian plane, those in the other mathematics class look solely at the parabolas with their vertex at the origin.
The only question I can think of is, “What’s the point?” If they aren’t even going to look at parabolas in general and confine them to the origin, is there any real use to showing them? I mean, you literally cannot make a physical example of throwing an object because the parabola at the origin won’t describe that sort of motion! The classic use case of the parabola isn’t even applicable to these students.
I think it’s a shame that these kinds of topics are in the regular secondary mathematics. In my mind, they are just filler for the year, because there’s no further explanation of them when there is so much more they could look at (without too a lot of added difficulty, either). I just don’t get how concepts like these can be shown in the form that they are now.