Adapting the mathematics curriculum to the needs of today's students.This is a transcript of a recording made with a hidden microphone during a university mathematics department's meeting on curriculum development.
Our task today is to develop a curriculum that will better address the problems of today's students.
What are the problems of today's students?
They can't do mathematics.
Yes, but the deeper problem is that they find our courses too difficult, and therefore we are getting fewer and fewer math majors. So we can't expand our faculty, and are even in danger of having our staff size reduced.
Now that's serious!
So what makes math so difficult for students?
Oh, little things, like homework, exams, standards.
We've already cut back on homework and lowered standards.
Some still find the pace too demanding. All these things get in the way of what they really came to college for: socializing, sports and sex. The three s's.
We could slow the pace of courses.
We already have. The calculus sequence that used to be two semesters long has been spread out to four.
That's a positive idea. We could similarly stretch out other courses.
But that would force us to drop some courses, maybe even courses I teach!
Do your students really understand and master those courses?
Of course not, but at least we are exposing students to that material. Surely that has some value.
We all have to make sacrifices. Besides, who really needs advanced mathematics these days? Most students end up in jobs where computers do that work for them.
Ok, suppose we drop some of the lower enrollment advanced courses, and expand some of the lower level courses. What have we got left then?
Well, most students today will need to take algebra, or they should. They don't seem to have learned it in high school.
Even algebra is tough for some.
How about offering a pre-algebra course to ease them into it gradually?
The algebra course itself could be pruned of the more difficult topics. We could put those topics into an advanced algebra course.
But we just proposed dropping those advanced courses!
Which topics could we leave out of algebra?
Well, we could limit equations to those with the x on the left of the equals sign, and move difficult things like fractions and percents to the advanced course.
What about those students who find math too theoretical? Those who can't do derivations and prove theorems, for example?
If we leave out the proofs, mathematics becomes only a collection of unfounded assertions. That's a dilemma.
Students certainly can't handle anything with more than one lemma.
An applied algebra course could be added to better serve those who can't think abstractly.
You mean, the concrete thinkers? Most students prefer their abstractions cast in concrete.
Well, now this is shaping into a more user-friendly math curriculum. But still, I fear, it is too demanding for those students with more modest goals, those who want to be teachers of mathematics. You know that they are always at the bottom of the curve in every math class.
The traditional way to handle this problem is to offer special sections of regular courses "for teachers". It wouldn't be difficult to develop such courses, for they are just watered down versions of the regular courses.
But we are already watering down the regular courses! Soon the content will be so dilute that we can call the curriculum "homeopathic".
Remember the needs of "our customers". We can't be too elitist about these things.
No, that would be politically incorrect.
We must be sensitive to cultural differences.
Well there are two cultures, those who can think abstractly and quantitatively, and those who can't.
Could we possibly find a way to teach absolutely anyone to think like mathematicians?
All right, let's cut out the absurd impractical comments and come back down to the real world and get to the task at hand.
What was that?
Ensuring our survival as a department.
Students today live in the real world, so it seems that we could better serve them by limiting math to only real numbers.
Are you suggesting my complex variables course isn't necessary?
It could be an optional elective.
Then no one would elect to take it! I could equally well suggest that your course in group theory be dropped.
I'm already intending to rename it "Group Dynamics" to draw in more customers. So don't think I'm not willing to adapt to changing times.
We'll get nowhere if everyone engages in turf defense!
Still, we need to attract more students, to make our department's productivity index look better.
What about the general-education crowd? Can we tailor some offerings to be attractive to non-math majors?
Course titles make a big difference. How about "The Romance of Numbers"? Or "Fun With Figures"?
Students like courses with a mystical or occult tone. Perhaps "The Eternal Triangle" or "Transcendental Equations".
All right, people, we are digressing again. Realisticaly, what can we do to make math more appealling to all students?
Well, I hate to mention this, but textbooks do strike students as a bit formidable. They bristle with unfriendly looking equations, graphs, and diagrams. Often these are in black and white. Students want more colorful books. Look at the books in the sciences: four-color printing, lots of photographs, color-keyed symbols in the equations, etc. Our math books are drab by comparison.
Now we are getting somewhere. And couldn't we reduce the number of equations? Surely not all of them are necessary. You don't honestly believe that students read all of them, do you?
Heck, some students don't even purchase the required textbook.
At this point the tape ran out.