Annotated Bibliography of Resources for Educational Reform, Coherent Teaching Practice, and Improved Student Learning

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• Pirie, S., & Kieren, T. (1992). Creating constructivist environments and constructing creative mathematics. Educational Studies in Mathematics, 23, 505-528.

The authors suggest that the original notion of constructivism is in danger of being distorted and simplified by users who wish to be seen as doing the "right thing" in their teaching or research. Constructivism is more than having students use manipulatives and engage in group discussions. Many educators would like to have a list of behaviors that they could perform that would label them as "constructivist teachers." The authors note that there is no constructivist teaching model "out there" waiting to be implemented, but rather, that teachers can and do create environments based on constructivist beliefs in action. Four tenets of belief are seen as critical for the creation of a constructivist environment: (1) there is no mathematical understanding "out there" waiting to be acquired or achieved by students; (2) students develop their own unique understanding; (3) there are different pathways to similar mathematical understanding; and (4) there are different levels of understanding exhibited by different students. The authors report on a study of mathematics classrooms in which the teachers' intentions are to create environments based on constructivist beliefs. Seven episodes are presented of students learning fractions. The episodes validated the four tenets, showing that students do show individual understandings of the mathematics being taught and that the student's response to a situation creates the student's pathway to understanding.

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