Allen Esterson wrote:
This "traditional" approach to the teaching of mathematics in schools is
not only, I believe, more effective than the constructivist approach, it
is also far less time-consuming, enabling considerably more material to be
covered.
I had similar opinions until this summer when a colleague suggested I
read some of the work of Magdalene Lampert. I was convinced that if I
had her for an elementary math teacher I would have been far better
off. I recommend her article "Knowing, Doing, and Teaching
Multiplication," Cognition and Instruction, 1986, 3(4) 305-342, or book
Teaching Problems and the Problems of Teaching, (2001) Yale University
Press.
I'm not totally sure she considers herself a "constructivist"
teacher but I was impressed by how much deeper an understanding of math
processes her students got in comparison to the algorithms I was forced
to memorize as the "only true way" to do arithmetic. Reading her work
made math much more understandable and I could for the first time see
the link between the math I had in elementary and secondary education
and the proofs that my college instructors (and math colleagues) were so
fascinated with. Her work to get students to see math as a way of
thinking, explaining, checking, and proving your problem solving methods
seemed to be a serious advance on the math I was taught. I don't think
her students are any less proficient in using algorithms to solve simple
arithmetic problems but most of them also have more than one algorithm
to use because they understand the ideas behind their construction.
I am also not convinced that every elementary and secondary math
teacher in this country is as proficient a teacher as she seems to be
but reading her work convinced me that the new teaching goals in math
education are a valuable improvement on the older rote approach I
suffered through.
Bob Grossman
Kalamazoo College
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