Mathematical
Physics for All, First or Last, is Realistic
Stewart E. Brekke
The advent of the cheap arithmetic and scientific calculator has made
the standard high school mathematical problem solving physics course,
Physics First or last, available to all students. The use of calculators,
both scientific and non-scientific, in a high school mathematical physics
for all, is essential (1). Many at-risk and even highly
motivated students are often weak in their basic arithmetic as well
as in their algebra. At one time in the past the standard mathematical
course for all, first or last, was not possible because the students
were in many cases unable to do long division, fractions and decimals
by hand. Solving physics problems was not possible very often. Even
though most students could understand how to do the problems, they
could not get the correct answer because they could not do fractions
and decimals properly. In the inner city, and probably elsewhere, physics
and chemistry courses often degenerated into reviews of basic arithmetic
skills instead of concentrating on the physics at hand (2).
Therefore, the qualitative course such as Conceptual Physics was invented.
Scientific notation was made easy by simply using a calculator
such as the TI-30, provided the students were shown how to enter
the quantities. I have found that using a cheap
arithmetic calculator to multiply and divide was sufficient for even
at-risk students if a review of adding and subtracting signed numbers
was done. Therefore, problems using E = mc2, converting the mass
of a proton into energy requiring scientific notation was easily
done by all students from those at risk to the most motivated. A
foundation in scientific notation must be made first however. Using
graphing calculators is mostly confusing to first year physics students
and a simple scientific calculator such as the TI-30 is much better
for all students taking physics for the first time.
Also, when the standard and most widely used high school physics text
was Holt, Rhinehart and Winston’s Modern Physics, many
students of all types faltered, especially when the physics teacher
provided little direct help and relied erroneously upon the thinking
capacity and ingenuity of the novice students. The old Modern Physics text
often had few examples of how to do the physics problems and there
were few drills and practices on each type of problem in the book.
Often high school teachers such as myself had to take one problem from
a set and make up a worksheet of 10 problems using one formula such
as I = V/R and giving three problems solving for each variable I, V
and R during the class period. This was followed up with possibly
6 more problems solving for all variables for homework.
That is why there was an almost immediate shift by many physics teachers
from the most widely used high school physics text book, Modern
Physics, authored at that time by Trinklein et al to the Murphy
and Smoot Physics: Principles
and Problems, published by Merrill, when it appeared about 15-20
years ago (3). This book had an example for each type
of physics problem and quite often 7-10 practice problems. Finally,
the long established principles of educational psychology, such as
drills and practices and examples for each problem type, were used
to enhance learning in the standard high school course. Physics teaching
was much easier since the teacher did not have to make up a set of
problems generating drills and practices using a particular formulas
and the students could use the example of how to solve each problem
if they needed to refer back to the text for help.
Many at-risk students I have found do not learn from examples in the
book or from examples on the board. They learn from the teacher going
around the room showing them how to do a particular problem and then
practicing on two or three more of the same type so that they get the
idea of how to do a particular physics problem. As time goes on the
students usually become more independent in their problem solving and
laboratory work. With this extra help, the many at-risk and less motivated
students become good physics problem solvers and even potential physics
majors. Many university physics researchers and teachers
would be surprised at the variety and kind of high school students
capable of doing the standard problem solving mathematical course.
With success in problem solving using calculators, all of the students
become interested in the course and look forward to coming to the course
each day. Also, we provide all the students with a true understanding
of physics and the capacity to go on in the sciences as well as enhancing
their rationality and organized thinking.
I have found that all students can do basic modeling of laboratory
data using simple models of curves and their formulas such as lines,
parabolas and hyperbolas. They identify the basic equation for the
curve such as y =kx, y =k/x or y =kxB2 after plotting the data if they
use an approximate best-fit approach. With repeated help at the beginning
of the course most students can find the approximate formula of any
phenomena they take data on. Again, the scientific or simple arithmetic
calculator has helped enormously in the calculation of various quantities
in the laboratory situation such as calculating the approximate height
of the school building using the stopwatch to time the descent of a
rock. The calculator has made the doing of physics, problem solving
and labs, much easier for all students, and allows them to concentrate
on the phenomena under study rather than on tedious calculations by
hand. This is especially true for at-risk type students. Cheap
stopwatches also have made many labs possible that were not available
students before such as finding the period of a simple pendulum and
even approximating the speed of sound.
Mathematical Physics First, second, or last, for all high school students,
is certainly possible and realistic in my opinion especially with the
text formats such as in Zitzewitz (4), the newer edition
of the old Murphy and Smoot, and the advent of the cheap arithmetic
and scientific calculator. Having worked with inner city students,
for many years, I have been repeatedly successful in this endeavor.
We can give the many students who are often at risk and weak in their
algebra and arithmetic, as well as higher level students, real physics,
not the smoke and mirrors of the qualitative course. My experience
in the inner city high schools of Chicago in providing the standard
mathematical course to all has shown me that there is a great untapped
pool of potential high school physics students who are capable of passing
a true problem solving physics course. We physics teachers have
not reached them and must do so. The mathematical course is needed
because it provides the students with the capability of going on in
the sciences, a true understanding of physics, and enhances rational
and organized thinking.
References
1. Brekke, S., "A Mathematical Physics For All Students," The
Physics Teacher (1999) vol. 37, p 557.
2. Brekke, S., untitled letter to the editor, Physics Today,
(Aug. 1986) vol. 39, no. 8, p.?
3. Murphy, J. T. and R.C. Smoot, Physics: Principles and Problems
(1982), Merrill & Co.
4. P. Zitzewitz & R. Neff, Merrill Physics: Principles and
Problems (1995), Glencoe/Mc Graw-Hill
Stewart E. Brekke is a retired physics and chemistry teacher in
the Chicago Public School System. email: sbrekk@cs.com, 100 W. Roosevelt
Ave, Bensenville, IL 60106, 630-521-9668
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