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) = 62.4x2y
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.