## Wednesday, April 11, 2012

### Why I am Writing an Algebra Textbook

The Village Elliot is teaching College Algebra this semester.  I am so mad at the textbook we are using that I have decided to write my own text.  The thing that infuriates me is that the students (mostly college freshmen) are not able to perform tasks like calculating a mortgage payment based on the interest rate and loan; calculate the current drawn in a simple electric circuit or balance a chemical reaction.  On the other hand I've taught them to handle logarithms in Base 7 even though I have never in my 30 years of engineering had a problem that needed a logarithm in Base 7, and they can factor 3rd degree polynomial equations.  But what has really gotten my gall is the so-called applied problems like the following (I'm not making this up; I swear this is verbatim, courtesy of Educosoft):

Suppose that for a fish tank with a square base of side x, the force F on the base of the tank varies jointly as the surface area of the base and depth y of the water.  If it is know that a force of 200 lbs is exerterd (misspelling courtesy of Educosoft) on the square base of the tank whose base side is 5 foot (bad grammar also courtesy of Educosoft) and water level is 2 ft above the base, then write the general expression for the force function:

F(x,y) = 4x2y

Argh!  Those of you who weren't permanently tramautized by bad math books like this one will recognize that the tank has 5 ft * 5 ft * 2 ft = 50 cubic feet of water.  Now water has a density of 62.4 pounds per cubic foot, hence said force equation must be

F(x,y) = 62.4x2

It can not be anything else!  Not unless you do the problem on the moon or something so that there could be a lower gravitational force.

Worse, the book compounds the error by proposing a companion problem...a different fish tank with a different density of water (this time it is 22 pounds per cubic foot). And yet another problem with still another density for water.   This is horrible.  In effect, the book is teaching that the density of water for different fish tanks.  Ridiculous!

Just to show it is not a fluke, the text provides this brilliant gem:

Suppose the mass density r at a point P(x,y) of the vertical section of a water reservoir varies inversely as the square of the distance from the x-axis.  Suppose the density at (7,3) is 66 lb/ft3.  Write a complete statement for the density function:

r (x,y) = 594/y2

First of all the P doesn’t belong in this problem at all, and perhaps this is just a typo.  But in the real world water is an incompressible fluid, and density certainly does not vary according to the distance from the x-axis as the problem stipulates.  I thought that perhaps they were imagining bubbles or something in the water.  But notice that close to the x-axis (that is, y = 0), the density goes to infinity.  That just doesn’t make any sense. This is not real.

Just because this is math class and not physics doesn’t mean that educators should consider themselves at liberty to distort physical laws.  It is unprofessional to teach young people fake equations.  For example, relativity is E= mC2. That means energy is equal to mass times the square of the speed of light.  It’s not E = mC nor is it E =mC3.

Similarly, on earth the density of water is 62.4 pounds per cubic foot, with small corrections for temperature and pressure. You can not set it to some screwy function to satisfy some mathematical whim.  PhD Richard Feynman went on a rant about textbooks in his book Surely You're Joking Mr Feyman, after serving on a state commission to evaluate physics texts.  Though I am not in his league by a longshot, I can appreciate his frustration at silly problems, and in particular texts that tried  to take the average temperature of stars, and failing to realize that there is no such thing as "green hot" stars even though there is such a thing as "red hot."  Well, a mathematician might be forgiven for being ignorant about "green hot" or the lack thereof, but there is no excuse for allowing the density of water to approach infinity in an aquarium.  I mean, really!

I fear we are educating students who can not balance a checkbook, can not calculate interest rates on a mortgage, can not understand the meaning of the national debt, can not determine the load limits of a wallplug circuit, can not determine the relative value of differently sized cereal boxes at the grocery; can not estimate the operating cost of a home air conditioner, can not calculate the miles per gallon achieved by their cars or any one of a thousand practical tasks.  But they can calculate the value of a base seven logarithm, by jingo!

I am sure that some purist is going to argue with me that pure math is some exotic art form and need not be constrained by practicality.  Well, I will allow that there is a place for this sort of philosophy, but those who are going to think about such things probably nver take College Algebra, because they completed the math sequence through Calculus in high school.
The people who are taking College Algebra ought to be given skills that benefit their daily lives and make them more valuable to an employer.  If the idea of preparing students for jobs seems beneath you, you need to join the real world.

Make no mistake, the guys who write awful math texts like the one I am trying to teach from may be great at solving paper problems.  But I doubt whether they can function in the real world at all.  They probably can’t match their socks when they get dressed in the morning.

Hence the Village Elliot has promised to write a textbook on College Algebra.  It will be grounded in real world applications.  And there will be no problems where the density of water in a tank varies by some arbitrary function.

1. Best idea I've heard in a long time. In fact I volunteer as one of the proofreaders.

1. Hi End3rooo, thanks very much. Also, please send is for people to send me algebra problems from different fields.

2. I know how these problems are written. The writers collect click and clack's puzzlers (from NPR's car talk) on a weekly basis. Then, using Babelfish, the editors translate the puzzler from English to Chinese back to English again.

See my example below:

A teenage boy smitten with a teenage girl in his high school freshman class, made his feelings known. Overjoyed at finding them reciprocated, he took pen knife to a young hard wood in the vicinity and carved their initials within a heart, five feet up the tree's trunk.

Now, here's the puzzler. If the tree had added 35% to its height in the first 15 years of his absence, 10% in the following in the five years and 2.5% in the ensuing eight years, how far up the trunk did they have to look to find the carving with their initials?

Using Babelfish to translate from English to Chinese back to English: http://babelfish.yahoo.com/translate_txt

Several year-old boys hit hard with his high school newborn class's several year-old girls, makes his known feeling. In discovered wild with joy they are exchanged, he has adopted the pen knife in neighbor to the young hard wood, and has carved them in heart's initial, tree' Five feet; s bough. Now, here' s difficult problem. If the fruit tree added 35% to arrive at it highly in previous 15 year his absence, 10% in below in five years and 2.5% in eight years which then came, the bough they far must look at the discovery carving and their initial?

1. Problem of interest, out loud laugh making funny. Probably algebra is correctly the same methodologicalness.

PS The answer is probably about five feet, since real trees grow mainly at their extrema and do not stretch uniformly.

3. By co-incidence while you were posting this I was reading Thinking, Fast and Slow ... Chapter 23 which is highly relevant, albeit somewhat discouraging, to your endeavor. Despite that, from what I know of you, you will persevere. I encourage you to do what you best, think outside the box.

If I was doing this I would be making an app, with paths through the problem space that tried to match up with the different ways students learn.

Without defending the textbook in question and speaking for myself, problems that are physically unrealizable can be intriguing.

Also nobody I know under the age of 70 balances a checkbook anymore. The skill may be useful but is going to be a tough sell as relevant.
Do as Will Roger's always said: Seek modern isomorphisms

Good luck!

1. Hi Chick, well you are one of the brightest people I have ever known. People like you never take college algebra in college, because you were ready for differential equations when you reached Berkeley. I would definitely prepare something different for your purposes. Cellege Algebra students are not aiming at the same level.

As far as the checkbook problem is concerned, you are right. It is better to understand how this problem and others like it could be done in Excel. I suspect that prospective authors are chicken to use Excel for fear it will be out of date in a few years. And so it will be. I think then, that the modern textbook will have to be updated every five years or so. Much of what we teach should be to help use Excel or MATLAB.

4. algebra also include in mathematics. It is very complicated part of mathematics. It used different formulas according to the expressions and values.