>People shouldn't be taking physics before they take calculus.
In an ideal world, you're absolutely right. In practice, it's hard to arrange. Assuming a US high school student even takes calculus, it's going to be senior year. So, if physics is taught senior year (don't know what the norm is), at best you're teaching in parallel. To be sure, derivatives are taught fairly early-on in calculus and they're probably most relevant to physics at the high school level.
But, you're right, there's a lot of plug and chug in physics without calculus. On the other hand, physics also helps get students into other things like dimensional analysis etc.
Also, to be fair, the issue of prerequisites comes up a lot of places. There are often facts in intro classes that have to be taken on faith until the topic can be dealt with more deeply later on.
> College level science and engineering education doesn’t make sense without a understanding of at least basic calculus.
That doesn't actually mean that you need to cover calculus in high school. The calculus needed for the first year of college science and engineering can be easily taught early in the first year in the classes that need it.
That's how it worked at Caltech when I was a student (late '70s and early '80s). Around 75% of an incoming class had no calculus. It only took a lecture or two in Phys 1 to cover all the calculus that would be needed for the rest of first year science and engineering.
That calculus taught in Phys 1 wasn't rigorous and proof based, but high school calculus usually isn't either. By second year everyone had a year of Ma 1, which was rigorous and proof based calculus.
My high school only taught physics without calculus. In 12th grade when I took calculus separately I was sort of annoyed to realize how much easier physics would have been using calculus.
> "Yet we regularly teach smart high school students and first-year undergraduates calculus..."
High school students are taught plug-and-chug calculus where one uses rules and formulae without any real understanding of the underlying subtleties that make calculus work.
>Hard science, i.e. math and its applications, teach you how to think, reason, etc.
Although, especially in high school but to a more limited degree in intro level college courses as well, you still end up memorizing a lot of formulas in a course like physics--one issue being that you probably haven't taken the calculus yet that you need to derive those formulas. Of course, you often end up knowing formulas you use all the time off the top of your head anyway. But you presumably could derive a lot of them if you had to.
The author claimed that calculus is required to biology major in many colleges. I would argue the opposite, I thought at two different universities and talked to many people. They always find it strange that it is not required for most biology fields. There is even an American invention called algebra based physics. This for people in biology who never saw calculus and your try to teach them physics and mechanics without calculus (Good luck with that, that is at best lost opportunity to understand physics) I thought in algebra bases physics classes many times and it was always horrible experience for both sides. Also calculus is not mandatory in US pre-college.
In general, you don't understand physics without calculus, period.
I hated calculus until learning Physics. It was so abstract and seemed useless. I'd much rather be presented with a problem, like how far did this ball travel, then learn calculus as a tool to solve that problem.
I agree with you though that attempts to teach Physics without calculus are sorely misguided. It's ridiculous to force students to memorize kinematic equations that can be trivially derived from each other.
If you were allowed in a calculus based physics course (some schools offer non-calc versions for non-science/engineering students) without ever being asked if you had taken calculus, there was an issue here other then you not having taken calculus. Calculus is not part of the standard curriculum at many US high schools. I attended one of the top 10 engineering schools in the US, and it was not that unusual for students to need to take calc before taking their first physics course. This kind of basic prerequisite verification is something any major university should be doing.
>The other half of USA high schools? They don't even offer a Calculus course of any kind [1]
That's a bit misleading. There are many districts where one school serves as a magnet school where anyone interested in taking more advanced classes can go. So yes while it may be true that half of all schools don't offer calculus--far less than half of all students can't readily take calculus.
When I was taking high-school physics, we started without calculus, but we definitely needed geometry. Otherwise, one wouldn't be able to work on free body diagram, circular motion, optics, and etc, as all of them involves trigonometry and some basic geometry.
Calculus had this fearsome reputation in high school of being terribly difficult. When I finally learned the basics of it (in college) I thought "is that all?" Of course, it wasn't all at all, but the calculus needed for high school physics is pretty simple.
I took every honors class in high school. Everything they had. I was terribly, woefully underprepared for college. It took a year and a half before I had my legs back under me. It was a wonder I didn't flunk out.
But I had a great time in high school. I had little responsibilities, a little money, and lots of friends to hang with.
Does it though? For example, you simply cannot teach Newton's laws of motion without knowing what a derivative is.
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