Bridges in Mathematics

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A Talk with the Mailman

By Dr. Eugene Maier

I was out pruning the shrubs around the mailbox when the mailman arrived with Saturday's mail. As he handed it to me he asked, "Are you a doctor?"

"Not the medical kind," I replied.

"What kind, then?"

"A Ph.D."

"What area?"


"I'm impressed. Do you teach?"

"I did."

"I wished I could have more of a conversation with you but I don't know much about math."

And then he told me his version of a story I've heard many times. A story that starts "I did fine in math until..."

In my mailman's case it was percentages. He said it just didn't make sense to him when he was told he should divide to find out what percent 18 is of 39. It had seemed to him that one ought to be multiplying. I acknowledged that percentages in school could be confusing and, switching from gardener to teacher, I suggested there were ways of thinking about percentages that might make more sense to him than what he remembered from school. He didn't pick up on my suggestion but rather—as if to assure me that he wasn't a mathematical incompetent—told me that as an adult he had figured out percentages and, without giving me an opportunity to find out how that had come about, continued on his way.

I can only surmise what confused my mailman. His reference to multiplying reminded me of what a colleague had mentioned a couple of days earlier: How he'd been put off by a teacher who told him, "In mathematics, 'of' means 'multiply'" when he knew that to find something like 1/3 of 48, one divided 48 by 3. My colleague isn't the only schoolchild to get the "'of' means 'multiply'" message. It's one I got and, I'm sure, countless others have gotten. I could imagine my mailman getting this message and then being told that to find what percent 18 is of 39, one divides. And I could imagine his reaction: "What do you mean? 'Of' means 'multiply,' and now you use the word and tell me to divide? I'm confused!"

I was struck by how vivid my mailman's recollections were. He could tell me the exact point, with an example, when mathematics became confusing to him. I've noticed that with other adults who, finding out I'm a math teacher, have told me their stories. There's a particular incident or topic they can identify that marked the beginning of their difficulties with math-a point at which mathematics stopped making sense. A point at which insight and intuitive understanding was overwhelmed by dicta-by authoritative pronouncements of propositions and procedures.

Mathematics by fiat doesn't work. When math is cast as a bunch of dictatorial rules to be followed regardless of understanding, it ultimately becomes a morass of confused and contradictory half-memorized, half-manufactured messages.

There are other ways to teach math. One doesn't have to dictate procedures at all. In my mailman's case, if the teacher had made clear what a percent is-through pictures, diagrams, and words-and then set the students to work collectively on a set of problems that built on their understanding, the students would have come up with appropriate ways of doing things. And the future mailman wouldn't have divided unless it made sense to him.

Of course, that's supposition on my part. I would have liked to continue my conversation with the mailman to get a better sense of what he remembers of his schooling in mathematics and what remnants of it remained in his adult life. If we really want to know how effective we've been as a nation in our mathematics instruction, we should be talking to the mailman, and a lot of other adults, rather than testing students at the end of grades 3, 5, and 8, or whenever, to see what they've crammed into their short-term memories.