George K. Brown: Ideas for more effective math instruction
Once again Washington state is changing math standards and end-of-course exams. Fifteen years of such changes have produced nothing. I teach mathematics courses at Lewis and Clark High School. Since 1987, I have taught Business Math, Applied Math, Algebra I and II, Geometry, Trigonometry and Pre-calculus. I’m not the best, but I am pretty good at what I do. I still love teaching mathematics to children.
For 10 years or more, the pass rate on Washington state tests of mathematics has been unacceptable. The number of kids requiring private tutoring for high school math classes and remedial mathematics classes in college is also unacceptable. This is a national problem and it has been written about extensively for years. On international tests of mathematics, the United States ranks near the bottom of industrialized nations, and this is without dispute.
Most of my current students are extremely poor in basic arithmetic skills. They cannot add, subtract, multiply or divide with any accuracy or confidence without the use of a calculator. They have virtually no competence or fluency with fractions, decimals or percents. This deficiency has been worsening over the past eight to 10 years. In 2008, Washington State Standards required such proficiency. I have yet to see it. If a student is not fluent in arithmetic, then algebra will represent a serious hurdle. If a student is not fluent in algebra, then a firm grasp of calculus will be impossible. College-level mathematics is out of reach for many, if not most, of my students.
In my opinion, we need to implement some common sense changes. Here’s a list of starters:
1) Children should arrive at high school fluent in basic arithmetic and some simple algebra. For this to happen they must be taught to add, subtract, multiply and divide whole numbers, and to compute with fractions, decimals and percents. Proficiency must be developed through much practice.
2) Eliminate the use of calculators for kids learning arithmetic and algebra. It is neither necessary nor helpful. Calculators have their place, but not in the mastering of basic skills.
3) Enforce a strong attendance policy. It is not uncommon for a student to miss 10, 20 or even 30 class periods of instruction. What good are standards when we don’t require attendance? A student must know that excessive absences (more than 10 percent) will result in loss of credit. This is, after all, compulsory education.
4) Stop placing students in math classes for which they are not qualified. For example, students who fail algebra must repeat algebra. They should not be placed in geometry. This practice is not only counterintuitive, it is counterproductive.
5) Establish a rigorous and challenging applied math track at high school that teaches mathematics for business, construction, electricity, plumbing, mechanics and other trades. We desperately need an alternative to college prep math that counts toward graduation.
6) Establish a rigorous and challenging college prep math track, including algebra with some geometry, advanced algebra with trigonometry, pre-calculus and calculus. The geometry course we currently teach is nonessential to the study of advanced algebra and calculus. Remove it.
7) Don’t raise the math requirements for high school graduation. Student interest cannot be mandated and without it little or no learning takes place. This practice has not produced better-prepared math students. Higher-level analytical mathematics classes should be available as electives for those who choose them and who are academically qualified to participate in them.
8) Allow teachers to use district-purchased textbooks as written, without interference from folks who confuse having data with knowing students.
9) End state and federal meddling in local schools. The ever-changing obstacle course of requirements, regulations and testing is destroying the education of our children.
I expect that with the arrival of a new set of standards and new state end-of-course exams, we will fight anew the battles of curriculum and methodology and continue to ignore the need for attendance, interest and competency on the part of the learner. While the children are poorly prepared for postsecondary education, we continue to fight to the death over which book to use or how to use the books we have.
This is a shame and a tragedy. At the end of the day, the children are the real casualties.
George K. Brown is a math instructor at Lewis and Clark High School.