Interactive E-Mail Assessment: attached to the published paper gold02-08-98.pdf

E-mail Meets Vector Calculus: This is a program to help students succeed in vector calculus – a required, sophomore, course for physics and engineering majors. The program works by opening up lines of electronic communication between students and their instructors. Without technology those interactions would have inundated any instructor. So efficient e-mail and archiving tools were part of the development package.

The program received a two-year $30,000 Sloan Foundation Grant. The grant was used to improve an acknowledged problem: The nearly 100% wipeout of minority students from Vector Calculus. For example, of 51 black students who had taken the first quarter of vector calculus in a 10 year period, all but one had dropped out. Dennis Galligani was a system-wide UC administrator with whom I was friendly. When I told him this information, one day walking on the UCI campus, he said, "Well, who was the student who got through."

This was an enlightened adminstrator, and I knew he would ask. My answer, "Howard Thompson." Dennis repeated that, "Howard Thompson. He was the only black student who got through the first quarter of vector calculus?"

You see everyone in the whole system knew who Howard Thompson was. To them Howard Thompson was the UC equivalent to Jesse Owens running in the 1936 Olympics. He wasn't just a black kid, he was Howard Thompson (who went on to get his PhD in mathematics from UC Berkeley). Later a committee set up at Berkeley apprised Dennis further that it wasn't just black kids who had trouble with Vector Calculus. Even the best and brightest had trouble with it, for it requires 3-dimensional thinking in quantitative terms. You can't do science without it, and you can't find courses that take students from 1st year calculus in reasonable steps to it.

The programs I developed and put into practice included tools that did the following:

IQs were the sexiest part of the package. The question rubric of IQs differs from typical calculus book questions. Their main goal is to guide students to  many-step-thinking. The paper starts with an example IQ question. Typically an IQ has at least three, and usually four, parts. The paper then proceeds to the topic that makes IQs an educational research tool, polling student interaction portfolios.

These portfolies weren't depositories of multi-media presentations by students. They were records – one portfolio for each student – of the many interactions I had with students over the quarter. They included the students' individual IQ results. They also archived various responses of that student to the P(roblem) O(f the) D(ay). These daily e-mail interactions gave me more contact with students in one course than I'd  had in 20 years of teaching.

The mathematics department's usual dropout rate for this course was 25-40%. Using this new method, one of my classes started with 56 students and ended with 55. Retention was achieved. Further, final exams on which I could expect the highest scores of 100 out of 200 total points – achieved by maybe one or two students in the largest of those classes, about 85 – now had a 3rd of the class easily exceeding that mark. 

Instead of 33%, why not 100%?:  Answer: it is Vector Calculus, an intellectual human watershed to which a trail of genuses (Newton, Euler, Lagrange, Gauss, Jacobi, Riemann, Maxwell) had major contributions over a 250 year period. A summary of the course: Outputs of functions with two or more variable inputs.  I simplify only a little when I say the main methods turn the analysis of such functions back to 1st year calculus – outputs dependent on just one input.

Why were most administrators not concerned with the difficulties in this course? Answer: Many more students have trouble with 1st year calculus. Administrators wrongly conclude that doing well there means they can move readily to 2nd year calculus. A further intellectual difficulty: Engineers, Mathematicians, Physicists, Chemists can all teach 1st year calculus (assuming they can speak coherently at a steady, reasonable pace).

Not only are many people in such departments not appropriate to teach 2nd year calculus, but from those in Physics and Mathematics most highly qualified, it takes a special open-mindedness to see that the Physics and Mathematics version are really the same. It is not the complication of the material that causes this. It is that Physics and Mathematics use variables and equations differently, and (excluded the most enlightened of teachers) each is certain the others' approach is wrong. With no further explanation, note just two points.


In the math and science curriculum E&M and Vector Calculus are the two hardest undergraduate courses. It's much harder if it's really one course, and you end up taking it twice and never recognize it.