Advise on What Math to take

D23 is taking Honors Trig/Alg 2 and finished 1st semester with an A- and currently has an A. Last year she took Honors Geometry and finished the year with an A. Her HS allows students who qualify to take Honor Pre Calc over the summer and so long as they get an A in the summer class the student can then take AP Calc AB as a junior. My daughter wanted to take this path but she only got a 540 on the math portion of the PSAT so she was told she does not qualify.

Normally she does well on standardized testing so I don’t know why she didn’t on the PSAT. Would you push back the school a bit on this? I feel like the final test is doing well in the summer class so if she doesn’t then that would be it but I feel that it is unfair not to let her at least try especially based on the PSAT after such an odd year.

Imo it’s completely up to you. Ask your D how she feels about math because PSAT math is only alg1 and geometry. Honestly it’s not that great of an idea to do pre-calc in the summer and go to AB because pre-calc provides all of the foundation for calculus. Honestly I would say do pre-calc next year and go to BC if that’s an option for you. Ask your D how she feels about math right now and decide based on that. Hope this helps.

Agree on this. Pushing for an exception falls under penny-wise and pound-foolish IMO.

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Gonna agree with both the above and add an anecdote. Due to us immigrating my D “needed” to take a summer school one year in high school to get to calc by senior year. The school counselor was adamant that the only one she thought one should do that for was geometry, that algebra and precalc are too fundamental to rush through.

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Can you get a report showing what she got right and wrong on the PSAT? Or have her take an SAT practice test and see what she knows. I think that test is a great diagnostic tool, because it’s relevant and it’s not tied to a particular school curriculum. If she can do well on all of the SAT math, she’s probably ready to take AB calculus.

I don’t think I could possibly disagree with this more strongly. Almost nothing in Pre-Calculus is covered on the SAT.

My D scored 790 in 8th grade. In no way was she ready for AB Calculus

I recall the SAT requires the ability to work with exponentials and trig functions. That’s about all that’s needed to start calculus. Fluency with the typical algebraic expressions is typically developed within the calculus course, as long as the student has the tools as described going in. Did you try giving her some basic calculus?

Exponentials are Algebra 2. The trig on the SAT consists of SOHCAHTOA, about two days of class. I taught her all she needed in 30 minutes.

If you think the other 175 days of a PreCalc class is just a waste of time, we can just disagree.

(But good luck trying to understand why the derivative of csc(x) is -csc(x)cot(x) when you’ve never seen any of those terms)

If D23’s honors precalculus class covers most of the following topics, you should have her take the class during the school year and, if she does well, go directly to AP Calculus BC (if your school allows.

  • limits
  • continuity
  • derivatives - powers, product rule, quotient rule, chain rule, implicit differentiation
  • derivatives (cont’d) - trigonometric functions, inverse trig functions, exponentials, logarithms, etc.
  • Parametric eqns.

In answer to your question, pretty much yes if the student is really solid. It’s more efficient to learn and practice the skills in the context of an actual calculus course.

I think the reason we delay calculus based on multiple recommendations from the math teachers’ organization National Council of Teachers of Mathematics, which keeps throwing more stuff in before calculus, is because very few high school teachers can teach beyond the AP level. They just aren’t good enough at math to teach multivariable calc or linear algebra, and it’s not something fixable by taking one or two refresher classes.

In theory, high school math teachers were supposed to be math majors when they were in college, with additional teacher training course work etc… So they (or most of them) should be able to teach multivariable calculus or linear algebra.

However, there are other issues:

  • Multivariable calculus and linear algebra as high school courses (rather than college or dual enrollment courses) would not be accepted for advanced placement in college, since there are no AP exams, and the number of students for such AP exams is probably too small for AP exams to be made for those courses.
  • Not all students taking calculus BC in 11th grade will go on to a college major that requires multivariable calculus and/or linear algebra.

Math majors, as in completed courses in real analysis and abstract algebra? Thinking back, some of my high school math teachers may have had such a background. But I doubt there were any at my kids’ high school which is supposedly as good or better than mine was.

Here is a “mathematics, prep for teaching” major at a typical state university:
https://catalog.sjsu.edu/preview_program.php?catoid=1&poid=431

Note that the first courses in abstract algebra, linear algebra, and real analysis are required, and at least one of the second courses is required. Calculus-based probability and statistics is also required.