High School Physics - “First” or “Last” - Must and Can Be Mathematical
An argument for making any physics course, mathematical
by Stewart E Brekke, MS in Ed, MA
August 1, 2008
Placing physics first in the high school science curriculum is supposedly done to provide a solid scientific foundation for the understanding of high school chemistry and biology since physics is the subject upon which all sciences are based. Often, in a course called “conceptual physics,” given in many instances, very little or no mathematics is used.
One real reason conceptual physics does not utilize much mathematics is that most high school students in the United States take basic algebra, the mathematics needed for the standard basic high school physics course, in the first year usually at the same time they are taking physics first, usually depriving the ninth grade physics student of sufficient mathematical background to do the standard basic high school course. Also, many students, from above average to average, especially in the inner cities of our country, are weak in arithmetic, fractions, decimals and long division and for many years were given non-mathematical science courses. Because of this weakness in arithmetic and algebra and lack of insight, many high school physics instructors simply gave up on these otherwise bright and capable students and offered them a non-mathematical physics or physical science course.
“Conceptual Physics” emerged about 20 years ago and is widely used today. Dr Paul Hewett, a physicist, created this new way of teaching high school physics, emphasizing the ideas of physics and de-emphasizing the problem-solving method of teaching physics. This combination of “weakness in math,” a math deficit of many high school students - majority and minority - provided the niche for various forms of Paul Hewett’s conceptual physics, physics with little or no mathematics.
Dr. Hewett stated that undue emphasis had been placed upon the mathematical aspect of physics with little understanding of the concepts involved in the subject. He has stated that over-emphasis had been placed upon using the tools the of physics, the mathematical techniques to solve problems, rather than have the students deal with the underlying principles of physics.
Dr. Hewett has also acknowledged that conceptual physics, emphasizing the concepts of physics with problem solving secondary, is used mainly in physics for non-science students courses. Very often, conceptual physics has meant physics without math at all, especially for all minority and at risk students in the inner cities who constitute substantial numbers of our country’s high school student population. However, as a physics and chemistry teacher from the Chicago Public Schools for many years, I have discovered that all kinds of students, from minority to majority, from average to honors, can do at least a basic mathematical course in high school physics, if not more.
I have found that these intelligent students, among them gang bangers, football players and pregnant teen mothers, can even do more complicated problems in physics if the student is shown how to do the problem and then allowed to drill and practice on the problem type, thereby not only mastering the problem type, but also developing skills needed to solve other mathematical physics problems.
Even Dr Hewett has recognized the need for more mathematics in the conceptual physics course. He has written a problem-solving manual to accompany his Conceptual Physics text and has pointed out that, in his opinion we need both the quantitative and qualitative aspects of the introductory physics course.
Physics teachers in high school and higher education should realize that for many years, basic algebra and trigonometry have been taught in the elementary school in 7th and 8th grade. Also, I have found that by taking a period to teach or recall some basic trigonometry to high school physics students or to teach the basic trigonometry as the physics course progresses to at risk students, is entirely feasible and pays dividends in higher level physics learning through mathematical problem solving.
In teaching at risk inner city students, average to honors, I have found that many students, even learning disabled students with math problems, can overcome the arithmetic barrier using basic inexpensive pocket calculators, virtually eliminating the fraction, decimal and division problems encountered in a basic physics or chemistry course. Furthermore, even if the student has not had formal algebra in elementary school, basic use of formulas is done all through the elementary student’s mathematical education… such as using the formulas for the areas of various geometrical figures like squares and triangles. Even the most at risk students can substitute a value for a variable with a little help from the instructor and then use his pocket calculator to produce a correct answer.
If the physics teacher, concentrating on one problem type, puts an example problem on the board showing the students how to substitute, and also goes around the room helping individual students use their formulas with drills and practices, substitution behavior will be mastered by many students. My experience has shown that if this learning method, using a single problem type, and going around the room helping individual students, with drills and practices on that single problem type, is done for the first few months in the first part of the mathematical physics course, most students average to honors, at risk to not at risk, will be able to master a basic algebra-trigonometry physics problem solving course in high school, physics first or last.
The single concept approach, dealing with one type of physics problem each day and then drilling and practicing on it in class and for homework, will produce many mathematically literate physics problem solvers even among the most at risk students, provided the physics teacher helps the students individually especially at first. This approach, using the single problem type with an example on how to do the problem, with drills and practices on that single problem type, was used in some earlier editions of Physics: Principles and Problems authored by at first Murphy and Smoot and later authored by Zitzewitz et al, and made the editions of the text the most widely used high school physics text in the country. I found inner city “at risk” students could easily do the mathematical high school course with a basic calculator using this text with help from the physics teacher when needed.
Unfortunately, with the problem example and single concept approach, with drills and practices, the high school course was abandoned by the publisher of the new “Physics: Principles and Problems” and its market share took a recent 10% decline. I contend that this shows that high school physics teachers need to have a sound educational approach to the first course with examples as well as drills and practices in a single concept format to reach the vast majority of students. This approach makes it easier for the high school physics teacher to reach all the students in his classes, not the just the few that can afford tutors or have a college educated relative who can show the average student how to solve his physics problems. We must remember that the great physicists such Bohr, Planck and Rydberg, all had tutors to help them pass their physics exams and solve their physics problems.
As the earlier editions of the text Physics: Principles and Problems has often stated, the language of physics is mathematics, and the most effective manner of teaching physics is through mathematical problem solving. Unless the physics first course is mathematical it cannot provide the solid foundation for a student to understand high school physics. Formulas are concept organizers and their use and manipulation is an essential part of knowing the subject of physics, chemistry or the chemical aspect of biology.
Just like physics much of the language of chemistry is mathematics, and the high school student must know how to use formulas, scientific notation and units in chemistry to understand the foundations of chemistry such as the mole concept, the gas laws, reaction rates and concentration. One of the foundations of biology is chemistry and therefore, one cannot have a good understanding of some of biology unless he knows the fundamentals of chemistry. In fact, it is one of the great endeavors at this time to make as much of biology as mathematical, chemical and physical as possible.
The physics first teacher, in my opinion, must teach the basic algebra and trigonometry himself as the physics first course progresses through the year and not wait for the students’ algebra teacher. This takes valuable physics time, especially at the beginning of the school year, but pays great dividends as the physics course continues through the year. In reality physics time is not very valuable unless it has a solid mathematical foundation. Furthermore, many more students will take ninth grade physics first and later skip a final mathematical physics course in his/her senior year. If we do not provide a solidly mathematical physics first course, we are not only depriving the student of a true experience in physics, but also giving that student a misconception of what physical sciences are, possibly setting the students up for failure or disaster when they take a mathematically based physics or chemistry course in higher education.
One reason we must give the mathematical course is that the mathematical course enhances logical thinking and reasoning which transfers to all aspects of life. Literacy in science, especially in the physical sciences is not memorizing definitions of words and concepts; rather it is the capability of doing physics by problem solving manipulating formulas and taking data and analyzing it mathematically. The language of physics is mathematics and if we do not give the student the mathematical course, physics first or physics last, we are deluding that student with the misinformation making him/her think that they know a subject when they really do not. Certainly, knowing concepts and ideas of physics is essential, but also doing the mathematical portion of physics is a fundamental aspect of the subject.
The object of a mathematical physics course, the standard basic high school course generally given to about 30% of a high school student body, is not just physics literacy. It is also, perhaps more importantly, equality of opportunity. The well paying careers in medicine, technology, engineering and the sciences, are virtually unattainable unless the student has the mathematical physics course - first or last. To become a nurse or medical doctor, engineer, chemist or biologist, the student must be able to solve a physics or chemistry problem.
We therefore cannot leave an optional mathematical physics course for the senior year of high school. If the student takes the nonmathematical physics first course and later does not take the mathematical algebra trigonometry physics course in his/her last year, he probably will be locked into a lower paying career since he/she will not be able to master the standard mathematically based college physics and chemistry course.
This is especially true for minority students who are often given a non-mathematical physics and/or chemistry course in high school depriving them of the chance to improve their economic status. Many of these minority and majority students try to take a real physics and/or chemistry course in college only to find themselves totally lost and far behind the other students who have had the mathematical course in high school. Often, these intelligent minority and majority students have the mental ability to do a standard mathematically based physics course, but do not have the knowledge base of the mathematical problem solving skills to master a basic quantitative type physics course, thereby thwarting their upward mobility in society through good paying scientific, technical or medical careers.
In summary: In my experience with teaching physics and chemistry to at risk students in the inner city of Chicago, I have found that there are many students, not just the upper 30%, in the average high school - majority and minority - capable of doing the mathematical problem solving physics, provided the teacher makes an above average effort to teach scientific notation, units, the single concept approach per class session with drills and practices, and algebra and trigonometry when needed. With the mathematical physics course, first or last, the lives of our students will be enhanced. We cannot short change them with a qualitative conceptual physics course which does not really provide a solid foundation for any science, chemistry or biology specifically, nor prepare them for any worthwhile career, let alone life in an increasingly technological world.