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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?

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?”

On a recent shop project with the grand kids (ages 14-18) I wanted to attach a brace to a second frame member. The brace was longer (by design) that the frame member. I told the Grand Kids that I wanted an equal amount of the brace to stick out on each end and asked them to make the necessary calculation. One simply refused the challenge stating that he did not know how to do that. The other two collaborated to produce the wrong answer. They are smart kids and I thought it was very sad.

ReplyDeleteI would like the schools to teach enough math and logic to be able to solve the problem above

What's a frame member grandpa?

DeleteIn this case part of a workbench frame.

DeleteIs Algebra really that much of a stumbling block for most people??

ReplyDeleteYes.

DeleteSeems you're not alone.

ReplyDeletehttp://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html?_r=3&pagewanted=all

Looks like we're doin' fine.

ReplyDeletehttp://youtu.be/lhxsNXpoCZ8