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Here's the actual story of why calculus is required. It is required because it really was very useful in the jobs of many high school graduates at the time the
by galdosdi 4y ago
Here's the actual story of why calculus is required. It is required because it really was very useful in the jobs of many high school graduates at the time the curriculum was formed[1]. Unfortunately times change but school curriculums have incredible inertia.
The concepts of calculus are incredibly useful. If you really think derivatives and integrals are so obvious (let alone, N'th derivatives and N'th integrals), sorry, you are wrong, you just have known these concepts so long you forgot how to think of them as nonobvious. This is a common effect. If you doubt this, talk to someone who definitely has never been exposed to these concepts.
BTW the valuable concepts of calculus go further than that. For example, the derivative of an exponential curve is always another exponential. This fact was at the top of my mind at the start of the covid pandemic as it was very relevant, as it means that if either of the "cases per day" or "total cases so far" graphs is an exponential, the other will be too. Similarly, the fact that the exponential is a solution to the differential equation y` = ky is very meaningful IRL. It means anytime the rate of growth of something is proportional to how much something there is -- such as reproducing life forms where their respective reproduction doesn't interfere with each other in some way -- you'll get an exponential.
I could go on and on.
So, we obviously should not stop teaching calculus. We just need to stop teaching the 80% of the curriculum that focuses on being able to do manual calculations that very few people will ever need to do. This actually allows more time to focus on more important concepts and should leave the rare student who does end up needing symbolic calculus very well prepared to quickly learn it on the fly.
Best of all, it allows time to add math that was not so relevant in 1910, but is very relevant today -- discrete math, the math of computers. Counting and basic combinatorics, basic boolean logic, basic graph theory, etc. All very applicable things. Literally every time I go to the grocery store and form a single line but all the other dullards form individual lines, because they don't know or care that a single line is proven to be more effecient, it becomes relevant. Also, more emphasis on probability and statistics.
[1] Nobody used to go to high school, essentially. In the early 20th century there was a movement to build a lot more high schools and get more people going to high school. High school graduates were more necessary because of the exploding industrial sector. And who designs the machines and factories and processes? Engineers. And the more you can apply fancy math, the better, more cost effective designs you can produce. And what kind of engineering is this? Mechanical and electrical, occasional chemistry. All uses calculus. And all calculus had to be computed by hand with paper and slide rule. So you had a need for a vastly increased population of people who could be comfortable sitting at a desk all day doing integrals, perhaps referring to a big fat tome with tables and tables of integrating tricks from time to time. It actually made sense at the time. Everything since then is just justification.