Publication 2110

Steffe L. P. & Thompson P. W. (2000) Teaching experiment methodology: Underlying principles and essential elements. In: Lesh R. & Kelly A. E. (eds.) Research design in mathematics and science education. Lawrence Erlbaum, Hillsdale NJ: 267–307. Fulltext at https://cepa.info/2110
A primary purpose for using teaching experiment methodology is for researchers to experience, firsthand, students’2 mathematical learning and reasoning. Without the experiences afforded by teaching, there would be no basis for coming to understand the powerful mathematical concepts and operations students construct or even for suspecting that these concepts and operations may be distinctly different from those of researchers. The constraints that researchers experience in teaching constitute a basis for understanding students’ mathematical constructions. As we, the authors, use it, “constraint” has a dual meaning. Researchers’ imputations to students of mathematical understandings and operations are constrained by the language and actions they are able to bring forth in students. They also are constrained by students’ mistakes, especially those mistakes that are essential; that is, mistakes that persist despite researchers’ best efforts to eliminate them. Sources of essential mistakes reside in students’ current mathematical knowledge. To experience constraints in these two senses is our primary reason for doing teaching experiments. The first type of constraint serves in building up a “mathematics of students” and the second type serves in circumscribing such a mathematics within conceptual boundaries.

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