Are High School Students – And Their Parents – Misled About Their Math Knowledge? Probably.

I just read an online discussion by high school students.  They were wondering how today’s math courses compare to the ones in the 60’s.

I attended high school in the sixties and took the most advanced course that my East Texas town of 35,000 had to offer; and, of course, I grew up with people from that era, so I have some idea of what math was generally like then.

I know the other side of the coin, too.  I have taught college freshmen for longer than I like to think.  And, starting in the 90’s, I taught second year calculus to exceptional high school students who had completed AP calculus and wanted to take more math.  I did that for over a decade.

Here are my thoughts about how students and parents are misled.

Let’s start with what they think is true.  Many think that they learn calculus in high school.   They think that they are doing “advanced” math.  So do their parents.  Their parents might think something like “I didn’t do that until I was in college, wow.”  Or, “I can’t do that, and I’m a college graduate.”  That’s what they think.

(By the way, there are things I can’t do anymore either if I don’t sit down and think about them, or even relearn them.  Does anybody out there who learned trig twenty years ago, want to take a test on trig identities?)

Now, let’s compare yesterday’s math courses with today’s courses.

I’ve already mentioned that my high school offered “Advanced Math”.  About 6-8 of us took the course.  That number in itself says something.  It could lead one to think that our school wasn’t good.  That would be wrong. I will explain why at the end.

Here is a non-technical idea of what we learned in that course.

We learned some calculus.  Some of what we learned was what many people call “theoretical”, though not learning it just means that the students aren’t getting much better in their quantitative thinking, and aren’t getting the math tools that are really useful.  Those topics and problems on them were removed from the AP exams in the early 70’s.  I give my explanation for that here.

(I will get technical for those who know.  Here is a problem I remembered from the course.  We had to use the formal definition to show particular limits existed.   That is, show how to find delta in terms of epsilon. This is the type of problem that was removed from the AP exam.)

So, one comparison is that we actually learned calculus in a meaningful way.  Since many people of my generation didn’t learn calculus in high school, they see their kids taking faux-calculus and think, “wow”.  (See here  (again) for why I say “faux”; and see this post  for how AP courses, in general, get dumbed down.)

Another difference is that, because we spent more time in courses below the level of calculus, we learned some fundamental ideas of math that, from my experience, kids are no longer learning.  Two examples are the binomial theorem and induction.  That becomes a problem later on.

Another problem is that, when you tell someone they are “learning calculus” when they aren’t learning it in much depth, it is hard to get them and their parents to accept this, and have to take calculus in college.  (To see an example that indicates how little good AP courses are, look here.)

I wrote above that it would be wrong to think that, because so few of my classmates took Adv. Math, our school wasn’t good.  Here is why that would be a mistake.  As we have seen, those who took Adv. Math learned more than students who take AP Math today learn.  Furthermore, even those who didn’t take Adv Math learned more. For example, they learned how to do proofs in geometry.  They learned things like the binomial theorem and induction.  They learned a lot.