The reason they drill it in to the extent that they do is so that you have a foundational understanding of the underlying math on which to build new knowledge. If you show up in calc 1 in college without remembering even the basic concepts you were previously taught in things like trig…that can really bite you in the ass. My teacher LOVED pulling out classic substitutions for Secant, Cosecant, and cotangent (No, i didnt outright remember them from Trig, but I had seen them, and that made refreshing much easier). Also these concepts then form the basis of many other fields such as physics (electricity/magnetism, kinetic motion, optics, etc.), chemistry (quantum, MO theory, and things relating to the physics side of why chemistry occurs), and many of the graphing concepts used in engineering/stem only make sense if you have the foundational understanding of what integration/derivation are. Those stem from understanding how to graph complex functions by hand (like we did in trig) so that when you are doing it later with assistance, you still GRASP what is going on.
Yes its not perfect, and yes for people who never need that later in life it can suck. However, I would make the argument it is better to have more of your population educated to a higher standard than what is needed in daily life, than to only give that to those who are aware enough at a young age to actively seek said education
Personally once you got to the Cos Sin Tan and Log part of math in grade 11 and 12 no amount of practice ever improved my understanding of the underlying principles. Once most of the work gets done in the calculator or computer I just lost sense of what was happening in the background. It’s just turned into put number in calculator and get answer. But that’s probably just a failing of the local school systems methods or the individual teachers maybe.
There will be those that do and dont get the “nitty gritty” of the theory side of the math. Those people sometimes become math majors. Normal people (joking, dont be mad math majors), need more than simply the theory side of the math and actually need to see/perform the application side of things. I never once “understood” the lesson in math class when we go over the equations with variables only. I only truly began to learn the material and be able to use it once we got to the example problems. We would do multiple in class and then I would understand how to literally go through the problem and perform the math that was expected of me on the homework, and subsequently the test. There is tons of stuff i know how to use in math, but by no means understand WHY it came to be, or HOW its works for the realm of mathematics. I wanna know how this math can help me solve real life problems, problems I will face in industry, or even just a cool way to apply math in the real world. Not how it will be used in research to find new types of math we wont be able to apply for 70 years.
It was pretty funny being in calculus in college. I was in a class with mostly engineers who were also taking the exact same weed out courses, and nearly every day after the professor would finish showing us the theory side of the lesson, hands would shoot up and the question of, “What application does this have in real life or engineering? Like, how will I actually use this?” always got asked. So not “loving” the theory is by no means uncommon (we all wished for an application focused version of the class to exist, for people like stem students who are not into the math theory lol), but I still see the value in having it presented so that you can have a more foundational understanding instead simply going through the motions
The reason they drill it in to the extent that they do is so that you have a foundational understanding of the underlying math on which to build new knowledge. If you show up in calc 1 in college without remembering even the basic concepts you were previously taught in things like trig…that can really bite you in the ass. My teacher LOVED pulling out classic substitutions for Secant, Cosecant, and cotangent (No, i didnt outright remember them from Trig, but I had seen them, and that made refreshing much easier). Also these concepts then form the basis of many other fields such as physics (electricity/magnetism, kinetic motion, optics, etc.), chemistry (quantum, MO theory, and things relating to the physics side of why chemistry occurs), and many of the graphing concepts used in engineering/stem only make sense if you have the foundational understanding of what integration/derivation are. Those stem from understanding how to graph complex functions by hand (like we did in trig) so that when you are doing it later with assistance, you still GRASP what is going on.
Yes its not perfect, and yes for people who never need that later in life it can suck. However, I would make the argument it is better to have more of your population educated to a higher standard than what is needed in daily life, than to only give that to those who are aware enough at a young age to actively seek said education
Personally once you got to the Cos Sin Tan and Log part of math in grade 11 and 12 no amount of practice ever improved my understanding of the underlying principles. Once most of the work gets done in the calculator or computer I just lost sense of what was happening in the background. It’s just turned into put number in calculator and get answer. But that’s probably just a failing of the local school systems methods or the individual teachers maybe.
That’s where math starts getting spicy though!
You gain a new appreciation for logarithms when you do statistics.
There will be those that do and dont get the “nitty gritty” of the theory side of the math. Those people sometimes become math majors. Normal people (joking, dont be mad math majors), need more than simply the theory side of the math and actually need to see/perform the application side of things. I never once “understood” the lesson in math class when we go over the equations with variables only. I only truly began to learn the material and be able to use it once we got to the example problems. We would do multiple in class and then I would understand how to literally go through the problem and perform the math that was expected of me on the homework, and subsequently the test. There is tons of stuff i know how to use in math, but by no means understand WHY it came to be, or HOW its works for the realm of mathematics. I wanna know how this math can help me solve real life problems, problems I will face in industry, or even just a cool way to apply math in the real world. Not how it will be used in research to find new types of math we wont be able to apply for 70 years.
It was pretty funny being in calculus in college. I was in a class with mostly engineers who were also taking the exact same weed out courses, and nearly every day after the professor would finish showing us the theory side of the lesson, hands would shoot up and the question of, “What application does this have in real life or engineering? Like, how will I actually use this?” always got asked. So not “loving” the theory is by no means uncommon (we all wished for an application focused version of the class to exist, for people like stem students who are not into the math theory lol), but I still see the value in having it presented so that you can have a more foundational understanding instead simply going through the motions