Re: Meaningless problems in algebra texts

[John Clement <clement@HAL-PC.ORG>]

>         John doesn't really argue against my advocacy of "magic X",
> because I am not advocating sticking symbols into equations.

Actually I was thinking of the texts which say "X marks the spot" and then
proceed to use X almost exclusively as if it were THE variable.  In addition
most texts use X and Y almost exclusively with other variables thrown in
gratuitously and meaninglessly.

The problem of getting students to write equations is much more subtle and
requires much more that getting them to look at descriptions and then
generate equations.  Understanding the difference between variables, names,
meanings, units, and numbers is absolutely vital.  Math deals almost
exclusively with numbers and manipulation when it needs to deal much more
with meanings and should always use units.

Examples of these are legion.  For example students when asked for the
meaning of something will give either the name or the units.  A simple
example is displacement.  Name: Displacement, Meaning: how far you traveled,
Units: m or cm ...  Variable: delta X.

When math drops units out of all calculations they have dropped a very
important means for checking the answer.

Do the math books ever take an equation and then ask students to generate a
meaning for it????

Once you have grasped the meaning for a variable, it is often easy to write
the equation.  Essentially the problem is one of translating between a
description and an equation.  Often the student needs to generate in
intermediate step such as a graph.  Then there is the necessity of using
metacognition in the process.

One of the few texts that actually has students translate between all
representations is Minds on Physics from the U.Mass Amherst research group.
It actually has students write equations and also solve problems using
calculus ideas (area & slope) without the calculus formalism.  Much of the
text looks simple, but some of it is challenging to college students.

One of the activities out of MOP that I find interesting, but I am not sure
if it worked well in my hands, was translating graphs to physical
situations.  Students were given all kinds of crazy graphs and then were
required to us simple objects to reproduce the motion.

My objection to most math teaching is that it concentrates almost
exclusively on equations.  While graphing calculators can be helpful, having
the students graph and measure on paper or with real objects is just as
vital.

John M. Clement
Houston, TX