Re: question for math teachers

From: Herman Rubin (hrubin_at_odds.stat.purdue.edu)
Date: 11/23/04 

Date: 23 Nov 2004 12:28:15 -0500

In article <-9Cdneped6eP8j7cRVn-oQ@comcast.com>,
k wallace <wallace.k@engr.orst.edNOSPAMu> wrote:
>Herman Rubin wrote:
>> In article <20041122033559.06111.00000577@mb-m23.news.cs.com>,
>> Chergarj <chergarj@cs.comhaho> wrote:

>>>rphenry@home.com comments on the sequence of jr.hi and hischool math courses:

>>>>The way geometry is taught, you need to know some algebra.

>> This is a bad idea. Euclid's students knew no algebra; it
>> had not yet been invented.

>I have to disagree- I worked with my daughter (and several of her
>friends) through last year's geometry class. Other than a few "solve for
>x" problems involving the Pythagorean Theorem (light pole this tall,
>shadow this long, how tall is the man casting the shadow sort of stuff)
>there was no "algebra". There were, however, a lot of theorems, but
>really understanding *why* was not (to my mind) adequately taught.
>That's what I spent a lot of time with these girls on. As a result, I
>believe, they all scored directly at the top of the class. (as a result
>of course of their understanding, not just my tutoring and help).

I see no disagreement that algebra is needed to understand
geometry. Euclid's students would have been able to do
those problems.

The key part of algebra is the use of variables; this belongs
early, as "mathematical language", not as a mechanical means
to solving problems.

>>>>The way algebra 2 is taught, you need to know some geometry.

>>>>Etc.

>while currently this is true, there is no reason I can think of that it
>needs to be.
>As for the forgetting of things over the intervening year- I disagree
>that it doesn't mean that they never understood it in the first place.

Details may be forgotten, but concepts not. However, the
current emphasis on "objective" testing makes it difficult,
and in some cases impossible, to evaluate the learning of
concepts. However, details can be looked up, but not
concepts.

                        I
>am talking about kids who, unlike me and several other nerds of
>then-high-school-age, do not spend their summers and/or free time on
>science and math; they spend it on basketball and socializing and camp.

So what?

>The fact that my daughter forgot how to exactly use exponent rules, how
>to simplify alebraic fractions, etc- as soon as she did a few examples,
>she recalled the way things work, yes. But I can bet that next year,
>when she starts trig, she'll have forgotten the sine-cosine relations,
>the rules for angles, etc- because she's not using them this year at all.

So what? The details are easy to relearn, if the concepts
are there. You are making my point for me.

>For example- I do a lot of math in my school and work life. However,
>yesterday I had to derive an expression for a general form of
>deformation of columns and beams, and in integrating ended up with a ODE
> , second order, nonhomogeneous. I had to think for *quite a while* to
>recall the part about setting my particular equation equal to Ax + B,
>before solving it became simple again. Not because I didn't understand
>Diff Eq's the years ago when I took that class-but because I hadn't
>*used* that skill in a while. I think that happens to most people.

Again, so what? You could also have gone to Mathematica or
Maple or Matlab or Maxima, and not knowing the trick to solving
that particular equation is not of great importance. Knowing
how to use the concepts to derive the equations is important,
but knowing the tricks of solving is not, even for most mathematicians. 

-- 
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu         Phone: (765)494-6054   FAX: (765)494-0558

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