Barr Garelick, via a kind email:

I believe strongly in how math should be taught, and even more strongly in how math should not be taught. Nevertheless, when I am involved in teaching it as I believe it should be taught, I feel vaguely guilty, as if I am doing something against the rules and perhaps even wrong. That’s how groupthink works. It is an acculturation process.

I am reminded of a job I had as a nighttime janitor at the University of Michigan Medical School the summer between my sophomore and junior years. The janitors put up with the college kids who worked with them, but they also could give us a hard time. On my first day, the supervisor told me to get a broom from the store room. This was an initiation rite. No matter which broom I laid a hand on, someone piped up “That’s mine!” In fact all the brooms had been claimed except one which belonged to someone who was not there. That one was off limits as well, but the supervisor finally said with an air of reluctance, “Well you may as well use that one. He probably won’t be coming back.” And true enough, he never did and the broom was mine. Several weeks later, another “new guy” joined the ranks and he was told to find a broom. Though I had found this initiation procedure ridiculous, when the new guy put a hand on my broom, to my horror I heard my voice booming “THAT’S MINE!”

My algebra classes used a book published by Holt (referred to as Holt Algebra). The team of authors include a math professor (Dr. Edward Berger) and a math reformer (Steven Leinwand). The book is fairly traditional, as evidenced by something the math department chair had said during the teacher workday I talked about earlier. Sally, the person from the District office had been telling us about the Common Core approach to teaching math—more open ended problems, more discussion, more working in groups, more problems that have multiple right answers. The math department chair brought up the point that it’s hard to do all this because the books they use just don’t have those types of problems in them. “Most of the problems can only be solved one way,” he lamented.

Nevertheless, the book does cater to some of the current groupthink trends in math education. When teaching the first unit for the first year Algebra 1 course, I wanted to focus on how to express certain English statements in algebraic symbols; for example, “4 less than a certain number” can be written as x – 4. While Holt Algebra does do this, it tends to focus more on the other way around—taking an algebraic expression such as 4/x and translating it into English. While most algebra books do this (as did mine from 50 years ago), the good ones tend to focus more on going from English to algebra. Holt Algebra spends more time going from algebra to English. In addition, it asks students to find two ways of expressing it, thus satisfying the “more than one way to solve a problem” motif that supposedly builds “deep understanding”.

“How are we supposed to find two ways to say this? What does this mean?” a girl named Elisa in my 6th period class asked me. She had told me on the first day that she was bad in math and requested to sit in front so she could see better and not be distracted.

“How would you say 4/x in words?” I asked. No answer. “What are you doing with the 4? Multiplying by x? Dividing by x?”

“Oh, dividing,” she said. “OK, so ‘4 divided by x’?”