Today we find common agreement that effective mathematics instruction in the elementary grades incorporates liberal use of concrete materials. Articles in the Arithmetic Teacher no longer exhort us to use concrete materials, nor does the Professional Standards for Teaching Mathematics (NCTM 1991) include a standard on the use of concrete materials. The use of concrete materials seems to be assumed unquestioningly.
Three years ago, the mathematics teachers from grades 4-12 in our school met for two weeks during the summer for an in-service program related to assessment and decided to begin using portfolios with our students in the fall. I was enthusiastic, although I had no idea at that time how drastically my approach to assessment—and to teaching in general—would change a a result of the portfolio decision.
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