Constructive action in calculus education

What should we do when our students (on the whole) are learning mathematics badly?

The instinct is to try new ways of presenting things in the classroom, one hopes without lowering standards in the end. But if we consider that our problem with students is common to all instructors at all universities, one must conclude that something else must be done. We must tacitly take a stand on whether the problem exists because

. . . 1. Mathematicians are terrible teachers, with no contact with reality, or

. . . 2. Students are poor learners, for most of us mathematicians do have contact with reality.

What can be done in the classroom?

. . . 3. Lower the level of aspiration of learning.

. . . 4. Raise the level of aspiration of learning.

Why would the students buy option #4 above?

. . . 5. Because the individual instructor says so.

. . . 6. Because the Math Department says so.

. . . 7. Because JHU says so.

. . . 8. Because the united front of all universities (or at least all peer institutions) says so.

Based on my experience to date, I say #2, #4, #7.

I have seen beneficial consequences of doing a reasonable amount of #4. Though I would like to say #8 in place of #7, it is beyond reasonable expectation at this time; it would be a mistake to settle for #5, or even #6, because too many of the students will be simply concluding #1.

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Steven Zucker
July 19, 1999