Our task today is to develop a curriculum which will address the problems of today's students.
What are the problems of today's students?
They can't do math.
Yes, but the deeper problem is that they find our courses too difficult, and 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?
Oh, little things, like homwork, 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.
We already have. The calculus sequence which used to be two semesters has been spread out to four.
That's a positive idea. We could similarly stretch out other courses.
That would force us to drop some courses, maybe even ones I teach!
Do your students really understand and master those courses?
Well, no, 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 will end up in jobs where computers do that work for them.
Ok, suppose we drop some of those lower enrollment advanced courses, and expand some of the lower level courses. What have we got left then?
Well, most students today have 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?
And the algebra course itself could be pruned of the more difficult topics. We could put them 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 percents and fractions to the advanced course.
What about those students who find math too theoretical? Those who can't prove theorems, for example?
An applied algebra course could be added to better serve them.
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.
Special sections of regular courses labeled "for teachers" is the traditional way to handle this problem. 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 courses '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.
Huh?
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 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 made an optional elective.
Then no one would 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 engaged in turf defense!
Still, we need to get 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 them?
Course titles make a big diference. How about "The Romance of Numbers"? Or "Having Fun With Figures"?
All right, people, we are digressing again. What realistic things can we do to make math more appealing to 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. And 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.