Brown Bag Teaching/Learning Seminar #1
Calculus Reform?

A couple of months ago the Chronicle of Higher Education ran an article on the Reform Calculus Disaster. At the time I just glanced at it and said "Harumph". Recently, though, I looked at it again and decided there were some pretty cogent points on both sides. So I propose that we discuss it this Thursday.

On the other hand, I suspect that even people who read it more conscientiously than I have forgotten a few details, so I plan make copies available and start off with a Silent Reading Period. Then we'll cut loose and bat the ideas around.

We will meet at noon in the Math Lounge.


The Brown Bag has just expanded (a dangerous concept!) Chris Hillman has been having a highly pertinent correspondence on the subject of Mathematica's Calculus Wiz. I will append portions of it below as well as bringing hard copy to the Brown Bag (along with the article I originally promised you.) Chris will also be at the Brown Bag. His correspondent offered to come, too, but since he thought we were in St. Louis that didn't quite pan out.

What hasn't changed is that the Brown Bag will be on Thursday, April 11, at noon in the math lounge.

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The correspondence:

Chris launched it with a letter to Tom Brooks at Wolfram, of which the major part was:

On the other hand, someone in our department recently posted on the common room bulletin board a glossy ad for a package called "Calculus Wiz" (a product of Wolfram Media Educational Products developed by Keith Stroyan) which I and a number of other people found extremely disturbing. The first line of the ad reads "Don't toil over tedious calculus homework assignments when you can solve problems instantly with CALCULUS WIZ". Two sentences later it continues "Calculus Wiz practically does your homework for you".

The difficulty I have here is that--- as almost every mathematics graduate student or faculty member would unhesitatingly agree--- "toiling" over homework problems is ultimately the ONLY way to learn mathematics of any kind.

Many of us involved in mathematics education feel that one of principle challenges we face with modern students is their impatience with the concept of doing outside work. I for one feel that an ad such as the one in question tends to reinforce this attitude problem by suggesting that it is indeed possible to master the calculus (and get a good grade, probably an even more important goal for many students) without putting in long hours of toil.

In fact, I and many of my colleagues feel that routine drill problems are an essential tool for elaborating, reinforcing, and illustrating points made in lecture, and that students who are never exposed to a large number of such problems are often cheated of any real opportunity to develop their skills before they are faced with an exam--- which they will in all likelihood flunk, if they have done all their homework using a tool such as CALCULUS WIZ or by looking up the answers in the back of the book.

In short, a certain amount of toil--- even of tedium--- may be an essential part of learning mathematics, and if so, it is in my opinion irresponsible to suggest otherwise to our students.

To which he got a reply from Keith Stronyon at the University of Iowa, which started off

We are in the final stages of finishing the Calculus Wiz and when you see it I think you will agree with the advertising. It really does do almost all the student's homework in the traditional Calc 1 & 2 courses - solves the problems in detail and typesets the solution, ready to hand in.

Mathematica can do the template activities that so much of calculus instruction has been reduced to. You are right to be interested. This changes things in the traditional approach to calculus.

The solution is NOT to be disturbed, however, but to embrace the technology and view it as a way to make a major advance in the goals of mathematics education. For example, I am also writing a second edition to my book "Calculus Using Mathematica" that will be published in time for fall classes (it will be called "Calculus: The Language of Change 2nd Ed", Academic Press, Inc.). I would be delighted to have all my students have the Calculus Wiz. The sooner they get over the little template activities, the sooner we can entertain serious questions like: "Why did we eradicate polio by vaccination, but not measles?" This and many other student projects are possible with some technology (and are part of my book.)

...

Template solution activities do NOT encourage thinking, but reduce a partial thought to a skill. Not a worthless skill, but one that can now be mastered an order of magnitude faster. Calculus can be a rich and deep intellecutal activity - it doesn't have to be the infinite list of oversimplified memorized templates it often becomes. The Calculus Wiz can do templates and free students from tedious details. It is up to teachers to take advantage of this and elevate the course. The potential advance is great.

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There's more, but you get the general picture. Definitely food for lots of good conversation. So come converse!


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