Program so accelerated that 8th-graders take AP Calculus.
Will that work?
Schools usually see parent ideas as poison, but this one is blossoming
by Jay Mathews
Washington Post
October 16, 2022 at 6:00 a.m. EDT
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Doing calculus early in school is a great idea. My son did it a few years ago and it has greatly deepened his understanding and application of physics, for which he is currently taking his final school exams. All of which will stand him in good stead for R & D engineering.

I think it is a great idea for kids that take to math. But wondering about what happens in college? My daughter got credit for AP Calc and is taking 2nd year engineering calc in her first year. What do these kids take? Are they taking the courses at a university or college that gives them credit? That would be great in some ways. But if you then go into engineering, what do you take in for the math portion? I have mentioned before about the boy at Hunter, years ago, who did his math and physics degree at Columbia, while he did the liberal arts kind of courses at Hunter high school. Graduated Columbia before he got his high school diploma a week later.

I expect that there are plenty of courses for them to take in college. My older two each had at least one kid in their HS class who had exhausted all of the HS math offerings by end of 8th grade (so they completed multivariable and linear algebra).

We are fortunate to be in an area with a lot of four-year colleges; there are six four-year colleges within three miles of our house. These kids attended math courses at a well known college within a mile of the HS. I know that the one kid went to MIT and started taking graduate level math courses freshman year.

Engineering really doesn't involve that many mandatory math courses, or it didn't when I went to college. Three semesters of calculus, linear algebra and differential equations - that was all I took. If you already took these courses at a college, you might not need to retake.

My middle kid, who took linear algebra senior year of HS, got a degree in applied math (as well as a humanities degree). There was plenty of math to take, and she took linear algebra again in college, except the college course was far more proof heavy.

I’m not an engineer, but I think it’s always possible and appropriate to go beyond any curriculum to aim to be a world class leader. For my son’s high school physics practical assignment, the class was told to ignore friction in their experiments. DS first completed the assignment as prescribed and then added a much longer section where he examined all the variables he could consider, including surface friction and air friction, applying very complicated calculus to show how all the other variables accounted for the gap between the expected and measured outcomes. His physics teacher commented honestly in his feedback that he lacked the ability to follow DS’s calculus calculations, but he was impressed with how well DS accounted for the gap between the theoretical and experimental data. In twenty years of teaching physics, no other student of his has ever attempted to go beyond the curriculum this way.

You are right, it is always possible to go above and beyond, and your son surely benefited from taking the physics assignment to the next level. Once he gets to college, however, there should be plenty of opportunities to go to the next level, especially if the institution has both undergrad and graduate programs. I don't know how things work in Australia, but in the US, you can take graduate courses as an undergrad and get involved in research.

While it does depend on which sort of engineer you are, in general, engineers don't use a lot of math day to day. I very rarely use anything beyond elementary school arithmetic. This doesn't mean that the math courses are worthless - I think they are valuable, especially because they require critical thinking skills.

I also realize from your story that my kids were lucky to take HS physics from teachers with PhDs in physics. I expect that is a bit unusual, though for high schools that offer AP Physics C, the teachers would need to have a good understanding of calculus.

Thank you. There are many engineers in our extended family (civil, mechanical, materials & software) and we have already gotten the sense that maths doesn’t play a big part in their work. DS is aiming to study R & D engineering, an undergrad course which incorporates aspects of several other undergrad engineering courses and includes participation in a research project (as an extra course load) from the beginning of first year. He intends to choose from amongst the renewables technology projects on offer at the time he commences.

I do worry about his prospects in Australia since it is a small economy with leaders still very invested in the fossil fuel industry but, at some point, I suspect the population will turn fairly rapidly to renewables and it would be great if DS is highly skilled up at the point when demand & investment escalate.

The basic concept underlying the calculus is very simple and can be understood by most kids even as part of a pre-algebra program. The problem is that calculus historically developed associated with advanced or complex math applications, so most educators see it only that way.