I teach at the college level but it is not uncommon for students in my
algebra-based physics course (which I have taught a lot, but not in the
last 3 years) to have knocked off their high school math requirement in
10th grade so that, by the time I see them as juniors in college, they
have not had a math course in over 4 years. My impression is that the
reason that they stopped taking mathematics courses after 10th grade was
that they thought that they were "not good at math." I have a set of 10
math tests. Each test is designed to take about 30-45 minute. In
practice, students take between 15 and 60 minutes. Students are
required to show their work. Each student "has" to score 100% on one of
the math tests by the end of the first month of classes (a firm date and
time is announced on the first day of classes.) I give a version of the
test during the 1st class session or the first recitation section and I
make the first couple of lab exercises short so that students have time
to take the math test at the end of a lab session, but other than that,
students take the test "on their own time." The lab supervisor or I
will administer the test, between 8:30 am and 5 pm virtually anytime a
student wants to take it (and if we are unavailable, other professors in
the department will administer it). After each test, we go over the
test, one-one-one with the student, as we grade it. This is often where
the student learns or relearns how to do the math. The students are
given the tests in an arbitrary order, but, if a student takes ten of
them, the eleventh will be a test that the student has already taken and
has a copy of for study purposes. Essentially every student "aces" the
test before the deadline. No student has ever taken the test more than
36 times. It is rare that any student comes close to that number. Most
students "ace" it before taking it more than 10 times. I use the policy
for both the algebra-based physics course and the calculus-based physics
course. Some students score 100% on the first test. When I say the
student "has" to score 100%: The policy is that if a student scores 100%
then the student's average physics test/hw/quiz/lab report weighted
average gets multiplied by 1. Otherwise it gets multiplied by .9 .
Nobody wants their physics course grade to be multiplied by .9 .
[I got this multiplicative grade idea from an article that I read. I
think it was in The Physics Teacher (but perhaps elsewhere) some time
between 1988 and 1993. I can't find the article. Information on it
would be appreciated. I'd like to credit the author.]
Regarding this math test policy:
Plusses:
1) Many students who thought that they could not do algebra (I think
this is because they were exposed to it too early for them, e.g. in 8th
grade) find out that they can do algebra. Not only that, but
21-year-old humans can learn algebra incredibly quickly. The occasion
of the "ace" is sometimes a joyous one. "This test is going on the
refrigerator!"
2) I spend a less time dealing with algebra issues during the rest of
the school year than I did before I instituted the math test policy.
This doesn't mean that no student ever again writes that 1/(1/a+1/b)=a+b
for arbitrary values of a and b, but that this kind of thing has been
less of an issue since I started the math test policy.
3) Students get some practice in checking their work. Occasionally in
life, more often in some occupations than others, we really "have" to
get it right. (Yes, some of my students do become surgeons.) We
teachers don't often demand that they actually get it 100% right. In
this case, I do.
4) Students who could do algebra at one time "knock the rust off" their
algebra skills early in the physics course.
5) On the average, the student who needs the most practice gets the most
practice. It doesn't work out every time. Sometimes a student who
could use more practice "gets lucky" on a math test and sometimes a
student who is pretty good at algebra/trig/geometry makes one lousy
minus sign error on 5 tests in a row, but, on the average, students who
need more practice get more practice.
Minuses:
1) This process is labor intensive for the laboratory supervisor and for
me.
2) The policy can be stressful for all involved. It doesn't feel good
to miss the 100% by one minus sign five times in a row. Sometimes it is
hard to hide your feelings.
Okay, now I finally get to the part where I address your question: I
provide the students with two math documents and a video to accompany
each document. The first document is an outline of the topics addressed
by the math test and the corresponding video is a chalk talk on those
topics. The second document is a set of problems. The set of problems
includes about 2 to 3 times the number of problems on any one of the
math tests and includes all the kinds of math skills/knowledge that the
students are tested on in the set of 10 math tests. The corresponding
video shows the solutions to the problems. I give my students a cd with
the documents and the movies but they are also available under Math
Skills Video and Math Problems Video at: http://www.anselm.edu/internet/physics/cbphysics/math.html
Some of my students find these resources useful. I do realize that you
were specifically asking about a text, but perhaps some of your students
will find these resources useful as well.
Jeff Schnick
-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu
[mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of adrian
sears
Sent: Friday, August 04, 2006 4:43 PM
To: phys-l@carnot.physics.buffalo.edu
Cc: karen krupnick
Subject: [Phys-l] the mathmatics of physics
My name is adrian sears i teach physics at bishop
union high school. My question is rather general in
nature but I would appreciate some feedback from other
teachers in the same predicament. I find myself each
year having to teach more math (basic alegbra,
exponents,quadratics etc.) then physics. Is there a
good text that simply deals with the most common math
encountered in intro physics. Hopefully a good
reference text would result in being able to teach
more physics than math.
Thanks in advance
Adrian Sears
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