algebra

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subtitle:  What mathematics should the citizen know and when should he know it?

This post is in response to a couple of my friends who wondered what I thought of the article:
Is algebra necessary?

Preliminary note.  Algebra has a firm place in the educational system and will long remain there for those who need it for their program of study.  The subject of this article is whether the great majority of students should be required to take algebra in either high school or college.

Beginning in high school (or sometimes in the 8th grade) we begin to put our students into what is called elementary mathematics:  algebra I, geometry, algebra II, trigonometry, and perhaps precalculus.  Only those who are inclined toward the subject take trigonometry and precalculus and the rigor of Euclidean Geometry has, for some time now, been Gone With the Wind, replaced by something considerably more accommodating.  That leaves algebra.  

Once upon a time, we valued algebra as a discipline, a complete logical system that sharpened the student’s intellectual skills.  Many of my math colleagues were certain that it was good for their students’ souls to go through it. It was not just the math people, the whole academic community bought into this mene.  (As late as 1980 I heard this argument from a history professor friend.)

And God saw mid century American higher ed, wherein we placed about 10% of our students, and it was good.

Bye an’ bye that part of our students that went to college increased to 20% then 30%.  People started asking why are we doing this algebra thing?  The answer was quite clear: 1. the logical system argument, and 2. after Sputnik, we had to have more math, science, and engineering types to get to the moon.  If they didn’t know algebra, then they might get confused between the English system and the metric.  That would be expensive.

Bye an’ bye that part of our students that went to college increased to 40% - 50% - 60%.  Well, that is how many started.  By this time we are far enough down into the second and third tier (quartile = fourth) that a lot of them were being wiped out because of that algebra requirement and freshman English.  Those two were the gatekeepers. 

Some of us in higher education argued for and got a general education course that would meet the math requirement without algebra for those who did not need algebra in their program.  Our approach was to ask the question:  “Out of all of mathematics, broadly defined, which parts are the most important for every college student to know?”  We viewed this as pertaining to the part of education that goes to preparing one for citizenship in a democracy.  The answer did not include much algebra because we calculated as very small the probability that our students would ever, in their role as a citizen, come face to face with a quadratic equation.

In the eighties that type of course spread across the collegiate landscape like wildfire.

But what about learning the logical system?  Well, the weaker students never did understand that system anyway. They memorized enough facts to get through the course the second time or they dropped out of college.  But the question deserves a more extensive answer than that.  Teaching a logical system is a good thing and we should try to do that.  But why not find a logical system that is more pertinent to the world that all students will encounter?  Why not something that is pertinent to citizenship and regularly shows up the media?  The area of (very) elementary probability offers a logical system. In combination with percentages and statistics it is one that is much more relevant to the modern world.  In fact they are frequently essential to reading a newspaper.  This is offered as an illustration not a program of study.

At the university level we have resolved this question without algebra.  You might expect that the high schools would be following suit.  But the legislature has commanded that, in high school, we put almost ALL of our students through the sausage grinder that is called algebra.  Why?   In order to prepare that very small percentage that will actually have any reason to know algebra later. 

We live in a quite different world from 1945 and the mathematical community needs to be prodded into reviewing ,on a k-12 level, the question:  “Which part of mathematics is it really important for the citizen to know?”