Reply #61: My experiences with math instruction over the decades

[Lydia Leftcoast]

I went through most of grade school during the 1950s, when we still had to memorize the multiplication tables and do long division. The teachers made games out of learning the multiplication tables. We'd have flashcard competitions, which worked sort of like spelling bees: the teacher would hold up a flashcard, and the first of two students to answer it correctly got to face another challenger. We also had timed tests with different random multiplication problems (2 x 3, 9 x 7, 8 x 5... ), and on each occasion, we were supposed to try to come in under our previous completion time.

At that time, I found math tedious, especially long division, and the "story problems" always struck me as stupid. However, I did all right, and in sixth grade, I was even admitted to a special math group of students who were allowed to move ahead at their own speed. Some of my classmates even finished the sixth grade book and got a good start on seventh grade math.

However, I moved to a new school system and was placed in the so-called "enriched track" for all subjects. We used a series called Modern Math for Junior High Schools, which I liked pretty well as we learned things like percentages and a bit of probability and set theory. Ninth grade was a different matter, though. The Modern Math series approach to algebra just didn't work for me for reasons I no longer remember clearly, and I was placed in non-enriched math for tenth grade geometry.

I liked geometry a lot, since it seemed more like art than like math.

Algebra II was a shock. Again, I was in the regular program along with students who had not taken the Modern Math Algebra I. However, they seemed to have received much more explicit instruction in how to solve problems than I had. For one thing, they all knew how to do this mysterious operation known as "factoring." (If we had ever been explicitly taught how to factor in Modern Math, I missed it.) Anyway, the review period for Algebra II was where I finally learned Algebra I. I struggled through Algebra II, and what saved me was meeting with a Japanese exchange student every morning to compare answers and to rework any problems where our answers differed. (I later learned that she would have had all this material in ninth grade, so it was a sluff course for her.)

That was it for high school math, and it got me through my Physics for Non-Majors course in college.

After coming out of graduate school with no job, I considered for the first time the idea of becoming a translator. People told me that all the best jobs were in technical areas, so I decided to take a bit of math at the University of Minnesota. (At the time, the early 1980s, taking even one extension course at the U made me eligible for student health insurance, so there was an added bonus.)

Based on the results of the placement test, I was sent back to Algebra II, which came back to me quickly, and I received my first A in math since sixth grade. A further factor in my new-found success was that studying linguistic theory in grad school had taught me that you can't study technical stuff as if it were a humanities subject. The techniques I had learned for passing courses in linguistic theory helped me re-master algebra.

Feeling confident, I went on to College Algebra and received another A. Woohoo! I was feeling primed for Trig and Solid. Here I fell down a bit because in preparing for the first midterm, I didn't really believe the instructor when he said that we would have to memorize the basic ratios. I quickly remedied that after getting a D on the test, and with the ratios firmly implanted in my mind, I easily managed the rest of the course.

But Calculus turned into a brick wall. The instructor was incoherent, possibly because he was teaching full-time at a local private college AND moonlighting at the U four nights a week. He didn't collect homework, because the department didn't give him a T.A. I ended up back in C- land and bailed out after one term. From then on, I took language courses to maintain my health insurance.

Ten years after that, ready to work as a translator for real, I started math again at Portland State University. They had a self-placement policy, and because I didn't want to take Algebra 2 a third time, I signed up for Trigonometry. The instructor was a grad student who looked as if he had walked out of a heavy metal band, but he was one of the best math instructors I've ever had. He explained every new concept from at least two, sometimes three approaches, and if you didn't get the explanation the first time, you sure did the second or third time. Later, when I met the math department chair socially, I made a point of praising that young man's teaching ability.

Next on the schedule was another try at College Algebra, and while I zoomed through that, the instructor, another grad student, was abysmal. He was obviously unprepared, and he never monitored the class to see whether anyone understood. He did not even realize that some of the self-placed students were struggling with basic arithmetic. ("How do you divide fractions?" one fellow student asked me.) Of the students who were taking College Algebra for the first time, the only ones who did well were the ones who hired private tutors.

I started Calculus again the following term. The instructor was coherent, and I kept up the first three weeks of the class just fine. However, as sometimes happens in the life of a free-lancer, I landed a huge job with a short deadline and was unable to keep up with the homework, so I reluctantly dropped the class. I have not taken math since.

My next encounter with math instruction, however, came when I was tutoring street kids in a Salvation Army program that included help with G.E.D. preparation. I found that their average level of math competence was what I thought of as fourth or fifth grade. I asked them why this was so, and the most common answer was that this was where math became "hard" and that class sizes were so large that teachers couldn't deal with all the students who had problems. (Most of them had parents who were alcoholic, drug-addicted, mentally ill, abusive, incarcerated or any combination of the above, so there was nothing like the support I received at home when I had problems with long division.)

Some of the kids just needed a little coaching to work through the self-instruction books, but some of them didn't want to work that hard. "Why should I learn this stuff when I have a calculator?" one boy asked me. "What if you don't have your calculator with you?" I asked back. "I just always carry it," he replied smugly.

Lack of parental support and society's anti-intellectualism are closely linked to another factor in poor school performance, namely, local control. If a child lives in a school district where the parents are concerned and involved and insist on good schools (consider the typical college town), the child will get good math instruction. If the parents are anti-intellectual or overwhelmed with their own problems or unaware of their own power to influence local governments, then the child will get poor math instruction.

So that's one person's long-term view of math instruction in the U.S.