I don't know why I Googled on "Constructivism; math". I should know better at my age. But it did take me
here to an editorial written by Lee Stiff, president of NCTM from 2001-2002. In it, he talks about a familiar theme: Constructivism doesn't exist. Gee, where have I heard that before? Well, last time I heard it, Jay Mathews of the Washington Post was talking about it.
Lee Stiff says all the right buzzwords:
"Constructivist math is a term coined by critics of Standards-based mathematics who promote confusion about the relationships among content, pedagogy, and how students learn mathematics. It is how they label classes where they see students engaged and talking with one another, where teachers allow students to question and think about the mathematics and mathematical relationships. Critics see these behaviors and infer that the basics and other important mathematics are not being taught."
[Reform-minded teachers] "promote making connections to other ideas within mathematics and other disciplines. They ask students to furnish proof or explanations for their work. They use different representations of mathematical ideas to foster students' greater understanding. These teachers ask students to explain the mathematics. Their students are expected to solve problems, apply mathematics to real-world situations, and expand on what they already know. "
So, the Hay Baler problem in IMP expands on what students already know? Is that true?
So, asking a student the solution to 5 divided by 1/2 in the midst of a problem set of whole number division problems prior to students receiving instructions on fractional division (as Everyday Math does) expands on what students already know?
He prattles on about how working in groups allows "students help one another create richer meanings for new mathematical content." And "that students should be encouraged to create their own strategies for solving problem situations."
First of all, I don't know what a "problem situation" is. And I probably don't want to know. But I do know that when I see essays talking about how math should be taught so that students "make connections" between "concepts" and "real world" situations, I head for the Dolciani, Saxon and Singapore texts and even my old Arithmetic We Need texts from my grade school days. Somehow these "traditional" texts make connections.
I really don't think this 2001 essay is outdated, even with the Focal Points in place.