Week 3 Post 2 (Boostrapping their Way to Mediocrity / Kitchen Table Math)

I did not so much respond to the blog entry as I did to some of the posts in the response thread. A constructivist mathematics program (IMP) had written some testimonials to its product. The teacher expressed approval at how students who were not inclined towards math could do algebra, trigonometry, etc. with the methods espoused by the program.

A poster remarked that in a college calculus class he was in, there was a huge difference in the quality of answers between students who had learned traditional mathematics and students who had learned reform mathematics. He said that even though reform math students could eventually arrive at an answer, they did so in 2 pages, with equations going in incoherent directions, and then going back, with diagrams, tables, arrows, etc. It took them 30 minutes to do what other students could do in 5 minutes on six lines. He said we are training students who can find answers, but who really can't do math.

He later likened it to a wonderful story written without any rules of grammar or spelling. It's great that a student could write a compelling story, but that student cannot be taken seriously in a vocation if he produced something riddled with spelling and grammar errors. He ultimately does not have any command of the written English language.

I echoed this poster's sentiment by suggesting that we no longer teach the "R's" in school these days - reading, writing, and arithmetic. The order of the day is inventive spelling, no grammar at all, and manipulative and calculator-based math, which have replaced essential arithmetic.

I recounted my own experience with Impact Mathematics, a program I described as constructivism on steroids. At no point does it give a step-by-step explanation for any mathematical procedure. It confuses and frustrates students, and ultimately I trashed it for a more traditional approach to math. It is a struggle, because I am constantly borrowing from other sources, and the students really do not have a reference for doing their homework aside from their notes. Then again, even if we used the textbook, they would have no reference for completing their homework.

Other posters later commented on how constructivism demeans students by not believing that they can learn the simple facts necessary for going on to higher planes in mathematics.