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
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
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
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
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
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.
- Gathered information from each student through Interactive
- Automated creation of portfolios on each student
- Organized weekly comment files for reinforcement and feedback to
These portfolies weren't depositories of multi-media presentations by
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
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
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.
- If I'm right, pitty the poor student we goes from this math
course to a physics course dependent on it.
- Further, almost no student sees – in the face of this – that the
Physics course electricity and magetism is just vector calculus with
the names of the variables changed.
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.