Defending Math Teachers Against Experimentation
To the Editor (Of Education Week):
I rise to defend math teachers against "Yours is not to Reason Why" (Commentary, Sept. 6, 2000). Between 1964 and 1996, I spent 20 years teaching math classes in Los Angeles' public and private secondary schools. Students entered my pre-algebra classes in grade 7or 8, bringing a variety of skills, concepts, and work ethics. My goal for the course prior to algebra was to build a solid foundation for their future success. Since I also taught algebra, I knew how important that foundation was.
Partnerships, publishers, and pundits do not teach math to children; classroom teachers perform that challenging role. Rarely does a middle school math teacher find that all her entering students are at the same starting line. Rather, she must set her ideal finish line, then go full speed ahead to arrive there without leaving students behind. The student in your Commentary knew how to plug in numbers when given formulas for the area of simple polygons. How much geometry should he have known? America's 6th grade math courses vary greatly.
My geometry unit for pre-algebra classes began with vocabulary. Students memorized and were tested on terminology, from angles and adjacent to perpendicular and polygon, to quadrilateral and equilateral. How else would they know what we were talking about? They learned about various polygons, circles, and composite figures and computed perimeter and circumference. To study area, we used graph paper to create area formulas, from triangles to trapezoids. I demonstrated how the area of a circle is slightly less than four times the radius squared, so they would understand why A = x r2.p x r2.
Eventually, students memorized the formulas. My tests required that they name the figure, write the proper formula, and calculate and label the answer. I always included word/story problems about gardens or carpeting or fences in which students had to figure out whether it was an area or perimeter problem, then solve it. Knowing their formulas was an advantage, as they understood. We were not only learning how to find the area of geometric figures, but how to use data for problem-solving.
As students went forward into algebra and more-advanced math and sciences courses, they would rely on data stored in their heads. Pythagorean theorem, the PEMDAS device for order of operations, perfect square numbers beyond 100, formulas for volume of various prisms or slope of a line or interest on a loan, quadratic formula; imagine if one had to constantly figure each out, rather than having it mentally stored.
My textbook did not determine my expectations. My colleagues and I developed them, then selected textbooks that best suited our goals. When California rejected real math in the 1990s, making it impossible to purchase appropriate pre-algebra and algebra books, we teachers held on to our existing books until California came to its senses. Teaching math effectively had never been a greater challenge; teachers were determined that our students not be victimized by educrats' experiments.
In many school districts across America, that experimentation continues. Why are states using math programs already proven not effective? Why are publishers of computerized materials taking so much scarce school money? Why are elementary teachers who never teach algebra designing the math course prior to high school algebra? I recently advised my Ohio school district on the benefits of Saxon Math to develop mastery and understanding of concepts and skills. May it be as successful here as it is nationwide. I salute teachers whose students can reason why and be able to multiply as they go forward in mathematics.
Betty Raskoff Kazmin
Retired Los Angeles Math Teacher
Member, Board of Education
Willard School District
Willard, Ohio