At meeting after meeting, I make the argument that poor student performance is in a large part due to our traditional school structures and approaches to education. Some people are skeptical and want more evidence that alternatives work better. The problem is that since there are few examples of different structures and approaches, the evidence is still thin.
A new and exciting piece of evidence can be found in an article in the May, 1988, issue of the Maryland Federation Teacher by Professor Jerome Dancis, who teaches math at the University of Maryland. Dancis describes how it came to be that black students taking freshman Calculus for Engineers at the University of California, Berkeley, did far better than the white students in the course. Here is Dancis' story:
" ... the average grade in Calculus for Engineers was 1. 9 for white students and I .4 for black students on the usual scale of 2. O=C and 3. O=B. .. Students need to understand calculus on an A or B level in order to be comfortable with the calculus aspects of later math, physics and engineering courses; C is not sufficient. So, while the white students' average was still not good enough, the I .4 average for black students represented a 'wipe-out.' Various remedial programs were tried without success.
"Enter mathematician Uri Treisman. Against all odds, he devised a program which resulted in the black students far exceeding the achievement levels of the white students.
"How did Treisman devise his winning strategy when a wide range of traditional, remedial programs had failed to help non-achievers succeed? He did so, first of all, by living in a black student dorm and observing black students for a month. He found that all the stereotypes were wrong. These black students were smart, high motivated, not lazy, and very hard-working, even when they did poorly. He was the first white person to visit many of their homes; in doing so, he found that each of them was getting strong support from at least one parent.
"Since these characteristics presuppose success, why were they flunking instead of doing very well? He discovered, in essence, that they had good study habits but poor learning strategies ...
"The black students studied like this: if they couldn't do a problem, they would turn a few pages back in their texts in search of sample problems - a practice which had worked wonderfully well for them with the skills-oriented high school texts. But this strategy only half works for calculus texts, with their moderate emphasis on understanding. When the black students still couldn't do the problems, they became frustrated. Despite their increasing frustration, they continued to work hard, but did not ask for help.
"Treisman also spent a month living in the dorm with oriental students, and thus could compare their behavior patterns with those of both black and white students. The oriental students used a different strategy: they regularly spent two to three hours studying by themselves, but would then come together in groups to criticize each other's work and to work on difficult problems. They felt no shame in asking a teacher or older student for help when a tern of four could not solve a problem.
"Treisman then suggested to the black students that they form study groups, but they felt it wasn't right somehow, or 'manly.' When he invited them for remedial sessions, many did not come until too late, because they had done well in high school math and didn't see themselves as remedial students.
"Then Treisman had a brilliant idea: he invited all the black students at risk of flunking to join the Black Honors Calculus Society. As is natural in an honor society, he gave these potentially flunking students problems which were as hard and harder than those given to the rest of the students. No easy problems. The students were asked to solve individually as many problems as possible. But when a student got stuck, instead of sitting there frustrated, he or she was to join with one, two or three other students to work on the harder problems. When this team could not solve the problem, they would then request help from the faculty member supervising the workshop.
"The result was that the average grade for black students rose to 2.6, and the calculus professors often referred to the black students as the smart ones in their classes. Then the white students demanded to be admitted to the Black Honors Calculus Society!
"It took the ruse of the Black Calculus Honors Society to get the black students to do math together, as their oriental peers did regularly on an informal basis. Their assumption was that 'one is supposed to make it on his own.' Once they changed their learning strategy, in a setting which presumed excellence, they did very well, and not only in calculus, but also in later courses.
"Uri Treisman summed up the basic premise underlying the workshop: 'through the regular practice of testing their ideas on others, students will develop the skills of self-criticism essential not only for the development of mathematical sophistication, but for all intellectual growth."'
There's much to learn from the Berkeley story. First: Treisman tried many other approaches before he succeeded. Moral: It's not easy to make major breakthroughs and we need to keep experimenting until we succeed. Second: Treisman challenged a widespread educational myth that students who are behind should be given easier, simpler tasks with lots of practice and drudgery. Moral: Students are more likely to work on their weaknesses and overcome them if they're challenged with high goals and are actively engaged in their own learning.
On one hand, we have small pieces of evidence like the Berkeley story that different approaches to education work. On the other hand, there's a mountain of evidence that traditional approached aren't working for the majority of our students. The choice is clear: we can stick with proven failure - or take a risk on something new.