## Achieving Mathematical Physics for All High School Students

By Stewart Brekke

Around 1983, I was assigned to teach physics and math to every student, except slow learners, at Paul Robeson High School in Chicago.

The school was so completely isolated in the black neighborhood of Englewood, the students could not be effectively bused to white neighborhoods in accordance with integration practices.

Therefore, the school was required as a compromise to offer four years of mathematics and science to every student. Being assigned to this school was a very fortunate experience for me, because I found that, contrary to common assumptions, all students, average and above, could do the standard mathematical physics course normally reserved for only the upper 25% or so of each American high school.

The mistakes many texts make in high school and college is that there are usually three or four different types of problems, each one uniquely solved with no examples provided. This format was disastrous for the ordinary student with little capacity to get outside help, *e.g.* from a cousin in engineering or physics in college.

However, I found that most students, from the average to the most intelligent, from the most motivated to the most at risk, can do physics problem solving if they are given individual help at least at first in the course, gradually being provided with less assistance as the school year progresses. They learn to solve physics problems because the teacher shows them how to do the first problem and then lets the students solve a few more of the same type.

In my experience, it takes almost an entire semester for most students to get the hang of how to use a formula and scientific notation successfully to solve a problem on their own. But even at-risk students can do more complicated problems involving the solving for two or more variables in different steps, if an example is shown on an individual basis and the student is then required to solve three more similar problems. It's a method that has been used by the mathematics community for years.

There are some drawbacks to teaching average and at-risk students. Their lack of facility with decimals, fractions, long division and algebra must be offset with a ready supply of cheap arithmetic calculators and/or scientific calculators such as the TI-30. As the course progresses, the students become more proficient with their algebra and remember how to use exponents, solve for different variables, use square roots and trigonometric functions. This also helps prepare them for real science in higher education.

In addition, labs in the inner city and high level magnet schools were of the "string and sticky-tape" variety. The students always took data, often graphed the data, and modeled it if we had time. To complete a physics lab in the allotted 50-minute time frame is difficult, so often I would help the students set up the apparatus after they copied down a skeleton format from the board, and helped them start taking data. For years, students were stymied on setting up apparatus and often incomplete data was taken. With assistance given to them in the early stages to save time, the students were able to get a better idea of what the lab work was all about.

By making the mathematical high school physics course "user friendly," yet substantive, with good quality problem solving and labs, I passed more students that other teachers at the high school, some of whom failed as many as 90% of their students. Many teachers had given up on these students, gave them a watered-down qualitative course which virtually wasted their time, and did not enhance their potential for well-paid, satisfying careers in science or science-related fields.

However, I found that adolescent girls with two children, gang-member boys and girls, athletes, hair dressers and carpentry majors, to name a few, could do the same mathematical course given to the top students, if direct instruction were given with drills and practices, and an emphasis on developing skills rather than theory.

I believe that the physics departments in higher education must use the principles of educational psychology to enhance learning in high school physics as well as at the university, and not simply require more physics competence of candidate teachers. And high school physics teachers must be prepared to put in a good deal of time and sometimes money to enhance the user friendliness of their physics courses to reach average and at-risk students.

There is solid physics potential in the inner cities, but we have to go out of our way to reach these students. Almost every night for the entire school year I put in between two to four hours of lesson preparation, and many professors do the same. But I can say I walked out of the inner city high schools of Chicago with my head held high because I did not "sell out" my students with a watered-down qualitative course.

*Stewart Brekke is a former teacher of physics and chemistry with the Chicago Public Schools, now retired.*

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