Colleagues: Reuben Hersh, author of What is Mathematics, Really? and (with Philip Davis) The Mathematical Experience, shared the article below with me last month. Yesterday, I asked that Jimmy Kilpatrick post it on his site (www.EducationNews.org/), and he was kind enough to do so (he would be interested in posting any articles that you might send him as well). Hersh's full paper is available at http://www.EducationNews.org/classroom_encounter.htm
The Classroom Encounter by Reuben Hersh
As every newspaper reader knows, many people are trying to reform math education. The NSF, NCTM, MAA, and AMS are helping. Meetings are held. Grants are awarded. Textbooks are written and rewritten. "Technology" (use of calculators and computers) is introduced and expanded.
Has this activity made significant improvement?
"Too soon to tell."
When will be the right time to tell?
I hope this work succeeds, but I'm not optimistic. Why not? Because the reforms concentrate on curriculum and teaching strategy. The encounter between teacher and student is underestimated.
In the AMS Notices (1) Hyman Bass wrote: "Mathematical scientists typically address educational issues exclusively in terms of subject matter content and technical skill, with the `solution' taking the form of new curriculum materials. Curriculum is, indeed, a crucial aspect of the problem and one to which mathematically trained professionals have a great deal of value to offer. But, taken alone, it can and often does ignore issues of cognition and learning."
Of course the classroom is a place where information is transferred, but before that, it's a place where humans encounter each other--student with student, teacher with student. The successful teacher relishes that human encounter. He/she knows that teaching isn't just copying information from one abstract intelligence to another. "Covering the material" doesn't necessarily mean teaching the students. In fact, research and experience have found that a key ingredient in successful teaching is the relationship between teacher and students--sometimes called the "affective" aspect. Of course lectures should be correct, comprehensible, and interesting. But it also matters whether the student sees the teacher caring about her/him, as a human being. Human feelings and needs affect academic performance.