In my experience, there was no review of alg2 or trig, by the way in my 80s HS in precalc. We were expected to know that from year before. Functions and analyt were not easy and had more of an adult expectation (nominally senior classes).

The tricky thing is not having a year of pre-calc and going directly to calc. I think this is possible as I was itching to do more calc when we did the baby stuff. But then again, I think it would be a train wreck for most students and would overload the calc course. Even though I thought all the theory fluff about functions was kind of a waste, it was probably good to have it solid. I don’t think I ever used that stuff about inequalities later though. That was just out of nowhere and went nowhere in future.

]]>I went to a good school in the 80s. We had a course called “functions” first semester that hit inequalities, limits and basic derivatives, and then second semester course that was “analytic geometry” which contained the classic stuff: conics, translation/rotation of coordinates, as well as polar coordinates and graphing rational functions (that was cool).

If anything it is kind of a strange year. Alg 2/trig makes a lot of sense. Calc made a lot of sense. Even analytic geometry made sense. But functions seemed a bit like we didn’t need a full semester for it and definitely not if you cut out the baby calculus.

]]>“What else would they do with a year between alg2/trig and BC?”

Lots of stuff that they used to do until the 80s or so: Logic, sequences and series, lots of vectors including a vector treatment of analytic geometry, and proofs. Many proofs.

Precalculus today is more of a rushed mishmash review of algebra 2 (plus limits and basic derivatives), or a straight-on calculus course that gets repeated next year in calculus (as this blog pointed out).

The textbooks are designed around content on a high stakes test, not around challenging the kids to actually solve difficult problems. The university STEM profs complain about students not being able to work outside a script, and the focus on test content over problem solving is one reason why.

]]>We might be digging too deep into the population. I wonder how some of these kids would do on a test from the early 80s. No graphing calculator crap.

]]>I think you can drill kids on the understanding too (Socractic questions, tricks, quizzes). That’s great. Just don’t assume they can’t do ANY procedures until learning some fundamentals perfect first. The mind doesn’t work like that. It actually puts a big unmotivated cognitive hurdle if you teach like that. Give them a basis intro conception that covers fundamentals (but don’t kill it for 3 weeks like some of your stuff please) and then move into procedures and just check and emphasize fundamentals as things go on.

]]>I’m not convinced that current algebra 2 courses cover material in sufficient depth to prepare students for calculus.

As just one example, I compared trigonometry coverage in 2 common Algebra 2 books: Prentice Hall Algebra 2 (first author Bellman) and Holt Algebra 2 (Larson) with one older precalc book (Brown).

Larson has 2 chapters of trig (13 sections); Bellman has 15 sections. Brown has 5 chapters of trig with 24 sections. Brown has lots of proofs as exercises. The other two have very few. Brown has a couple sections on polar coordinates; Bellman and Larson have nothing. Bellman and Larson present ideas in an odd order, like sandwiching complex numbers between two sections on quadratic equations and completing the square. Huh? Larson is an outline book: it’s light explanations and heavy on examples. All or most Larson books seem to be organized that way.

A lot of stuff in modern textbooks is out of order and presented to be memorized and regurgitated. It’s no wonder that students end up not understanding basic principles when they just aren’t taught them.

]]>I’m thinking more of an overall approach. Zombies, in my experience, are always zombies. That is, someone who says “Look, I’m just faking it. I am following the rules but I’m not sure how it works. I’d like to.” is very different from someone who has been frantically following algorithm rules and forgetting everything not immediately relevant to a test for 6 years.

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