Bridges in Mathematics

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Math in the News

I ran across three mentions of school math in the news a few weeks ago. All incidental. All negative.

The first occurred in a story about Ira Glasser, who is retiring as executive director of the American Civil Liberties Union. The story said he "was an odd leader" for the ACLU in that he didn't have a background in law. Prior to his involvement with the ACLU, he was a mathematics professor. "It was good training," the story reports, "of all the audiences he has faced, he says, none have been so hostile as college students in required freshman calculus."

Then, in Friday's sports page, a story about the upcoming Oregon-Wisconsin football game concerned the uncertainty of who would be playing for Wisconsin because of the possibility of players fulfilling suspensions. The Oregon coach had given up trying to figure out what personnel his team would face. The paper reports him saying: "I'm not smart enough to figure out the scenarios... 11 players suspended for three games, 15 players for one. Ä It's like one of those math problems I hated in high school.... It's a waste of our energy to worry about it."

A couple of days later, a commentary on the Napster situation appeared in Sunday's business section. The author identifies the founder of Napster as "the sweet kid I suffered through high school calculus with."

I suspect most people breezed by these comments without pause. Perhaps a wry smile appeared as thoughts of their own less-than-pleasurable experiences in school math were triggered. A few, however, may have reacted as I did, identifying with the professor trying to teach calculus to defiant students who are there because it's required. I was reminded of all those pre-meds who, for the most part, didn't care a wit about calculus and yet wanted A's so they could get into med school. (I have a vivid memory of running into a former student. The first thing he said to me was, "You're the one who kept me from being a doctor." I had given him a D in calculus.)

Comments about hating math and references to hostile and struggling students in calculus classes are commonplace. But they attract little attention. The public doesn't fret about them as it does about the rank of U. S. students in international math assessments or the math scores on state-mandated tests. It should. If the goal of school math is math literate adults, then the reaction of adults to their school math experiences ought to be given as much attention as student scores on state and national tests.

Hatred and hostility are not hallmarks of literacy. And raising test scores isn't the cure. I suspect the current emphasis on high-stake tests and the accompanying move to stiffen math requirements--such as the "algebra for all" movement—will only intensify the ill will adults harbor against math.

The rationale for requirements warrants scrutiny. The prevalent attitude seems to be that school math ought to prepare one for every eventuality. If there is some chance, however remote, that someday one will encounter, say, a quadratic equation, then include it in the curriculum. Then there is the insidious practice of using math requirements to weed students out of programs, for example, requiring a full-blown calculus course for pre-meds—I never have understood what learning calculus has to do with practicing medicine.

Math in the News

By Dr. Eugene Maier

When I was chair of a small college math department, to the surprise of my colleagues in other departments, I fought against establishing a college-wide math requirement. I had two reasons. First of all, I didn't want students in math classes who didn't want to be there and, secondly, the math department had all the students it could handle. I had no control over what other departments and programs required, and if a student questioned me about why they had to take a certain course, I told them to go ask their advisor. As far as I was concerned, they were free to drop the course. If they didn't want to be there, I didn't want them there.

It's not that I discouraged students from taking mathematics, but I had little success motivating recalcitrant students by trying to convince them that learning the math at hand was critical for their future well-being.Wondering why, it occurred to me that I was lying to many of them. So I decided to tell the truth. I told them they may never have need of the particular mathematics being studied and, further, it was impossible to know what mathematics, if any, they might encounter in their lifetime.

Then I would tell them what I wanted for them: that they develop their mathematical aptitude and abilities so if, at any time in their lives, they had the need or desire to learn about a particular mathematical topic, they felt capable and confident of doing so. To accomplish this, to a large extent, it didn't matter what topics we studied as long as it furthered their mathematical development. Once I adopted this attitude, the hostile "what's this good for?" challenges largely disappeared.

It seems to me that we as a nation are gifted enough to be able to figure out an educational system in which hordes of students aren't forced to take courses that end up as negative experiences. As a start, we can adopt more modest goals for school math. Let's not attempt to determine and prepare students for any possible use they might make of mathematics in their adult lives. We're not that omniscient.

In elementary school, let's aim at developing number and spatial sense, building on the intuitive knowledge students bring to school. Beyond that, let math be an elective subject. Have it there for those who like it--which, if taught properly, will be a surprising number--and those who have decided it will be important for what they wish to accomplish. If certain math topics arise in the pursuit of another subject, let students start that subject, see for themselves how math is encountered and then learn what's needed. And let's not expect this to happen in the first fourteen years of a person's life. Rather than forcing ninth-graders into algebra classes, let's make it possible for any person at any time they are ready and willing to do so, to learn as much algebra as they want or need to know, Maybe this requires changing the way we deliver education, but why stick with something that doesn't work?

As long as we continue to force-feed mathematics to our students, the news about math will continue to teem with hostility and hatred. We're not going to change this by cramming even more math down our students' throats.