We don’t need no stinkin’ PreCalculus

February 16, 2006

Calculus books are supposed to start with a review of PreCalculus. I think that’s a Lemma or something.

Here’s the problem with starting with PreCalculus – the people that need it don’t pay attention to it because they don’t know they need it yet. For instance – if you have this fraction:

6 x + 84
----------
      2

You know you can’t just cancel the 6 and the 2. Well, maybe you don’t know it – but you certainly don’t have the patience in a Calculus class to write out:

2( 3 x + 42)
---------------   = 3 x + 42
        2

You think you know what you’re doing and then you get to the quotient rule and you substitute in for the appropriate things in the formula

(f/g)' = f'g-g'f
           -------
             g^2

and you go ahead and end up canceling the g’s. Anyone who has graded calc homework or exams has seen that a bunch of times.

Most of what trips people up in Calculus is not the Calc but the PreCalc. But they aren’t ready to listen to the PreCalc the first week of Calculus because they think they know it already. After all, they’re in a Calculus class. They wouldn’t be in a calc class if they needed precalc.

So my preference is JIT PreCalc (Java programmers recognize that as “Just in Time”). When I’ve got your attention because you perceive a need, you will be ready for me to review the PreCalculus in place and not in this separate module that you’ll tune out.

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4 Responses to “We don’t need no stinkin’ PreCalculus”

  1. Chris Adamson Says:

    @OffTopic: While Java programmers are probably most familiar with the “just in time” concept, it really comes from manufacturing – it’s the idea of getting parts to the plant “just in time” for them to be assembled into final products. According to wikipedia – http://en.wikipedia.org/wiki/Just_in_time – Henry Ford first publicized the idea, though it was the Japanese car companies, with little warehouse capacity, who really perfected it.

    So, going back to the original metaphor, you’re getting the necessary pre-calc to the students right when they need it, and not before.

  2. malcolm davis Says:

    Using wikipedia as the source of ‘just in time’ is kind of funny. 🙂

    Just in time is a very old concept. but I like ‘d’ use of the term, JIT in computers is a different concept that just in time with manufacturing.


  3. “You think you know what you’re doing and then you get to the quotient rule and you substitute in for the appropriate things in the formula”

    It all made sense until this point. I’m already looking forward to your book because I would love to understand maths well enough to get what happened there.

    Chris


  4. I quit teaching the precalc chapter several years ago because it seemed totally ineffective and, worse, soul-killing. (Its a bright brand new semester, people are as enthusiastic as they will ever be, and we want to sink our teeth into those derivatives!) Instead, I seek out problems for lecture where the common algebra or calculator mistakes show up. Its easy enough, while moving toward a solution, to point out the spots where the algebraically-challenged are likely to crash and burn.

    By the way, I am thrilled you are doing HF Calculus and would like to lend help and support as a reviewer.


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