To return to mathematics (my post of July 29), my disagreement with Mr. Hacker’s “Is Algebra Necessary” article in in that day's New York Times, is simply that Algebra is the gate to proceed past the simple arithmetic taught up until that point. For the first time, students work with abstract symbols rather than fixed quantities, and to quote Wikipedia, study the rules of operations and relations and the concepts arising from them. It is the entry to what I consider mathematics to be. If you would like a more outspoken disagreement, see the following one in response to a similar article in the Washington Post six years ago. bit.ly/P4wOis
Unfortunately, learning mathematics is hard work. But as time goes on, the cost of not being comfortable with it increases. As life and industrial products increase in sophistication and complexity, it becomes less and less possible to be involved in the process without mathematics. And although mathematics comes more easily to some (I was lucky in that aspect), to many it is indeed the most difficult of their subjects.
But mathematics is more than the ability to “get answers”. It recommends an approach to problem solving that is both beautiful and immensely powerful. To be uncomfortable with mathematics is to approach life with an incomplete tool kit and the inability to participate in increasingly many activities. Algebra is the commonly accepted entry.
Many people criticize the way mathematics is taught. ( I am a critic of the content of traditional calculus courses, although not of calculus). And it is possible to approach it in different ways. Some time ago I was involved in a major Sloan Foundation program entitled The New Liberal Arts, which was intended to help liberal art colleges better handle mathematics, science, and technology. As part of that, we received some money at Stanford to put together a year-long sequence for our own “liberal arts” majors that could be used to fill the requirements in these areas in lieu of the traditional courses, and which would be more consistent with their backgrounds and future plans. I talked a mathematician and physicist friend into doing this with me, and after a large amount of thinking and preparation, we taught it for five years. All three of us were considered outstanding teachers, we were all respected in our fields, we all had administrative experience in the university, and we were eager to do this.
The results exceeded our expectations. We even converted a few math-haters to math majors. But we team-taught the course with all three of us attending all sessions, used a large number of projects, gave a great deal of individual attention to the students, and in particular, in order to avoid presenting dumbed-down material, we focused on material that the majors in the field would not see until their later years — such things as quantum mechanics, cosmology, topology, and designing and building hardware. And yes we counted upon algebra.
We had planned on returning to our usual work after five years and at that time were getting a large amount of pressure to return to our more main-line activities.
But even though we looked hard, we could not find faculty members who seemed to have the right set of characteristics and were willing to give up what they were doing to devote the necessary time to the sequence
Three years later, another group of faculty set forth with a different approach, but this too, fell apart after a few years for lack of the right type of teachers willing to spend the necessary time.
During the period we taught the course, we had a Sloan-sponsored meeting of some 50 people who were doing similar things in different universities. It was a wonderful gathering, but each person was handling the problem in their own way, and much to the disappointment of the Sloan foundation,we concluded that if we tried to standardize the approach to handling the material in a way that was more effective to individual students, it would compromise what they were doing.
My conclusion is that the educational system is not set up to teach mathematics on the more individual level needed to appeal to all students at the university level. This is probably even more true at the K-12 level. So, Mr. Hacker, I believe algebra is necessary, and I challenge you to put together and teach material which accomplishes the goal of algebra in a better way that is consistent with the resources in the educational system. The world needs it. As motivation, re-watch Stand and Deliver, the film starring James Olmos, the true story of Jaime Escalante teaching Calculus in a very challenging school in Los Angeles. It can be done, but not by most teachers. Contact your local school and take a run at it.
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