A Constructivist Approach to Second Grade Mathematics

Our overall objective in this paper is to share a few observations made and insights gained while conducting a recently completed teaching experiment. The experiment had a strong pragmatic emphasis in that we were responsible for the mathematics instruction of a second grade class (7 year-olds) for the entire school year. Thus, we had to accommodate a variety of institutionalized constraints. As an example, we agreed to address all of the school corporation’s objectives for second grade mathematics instruction. In addition, we were well aware that the school corporation administrators evaluated the project primarily in terms of mean gains on standardized achievement tests. Further, we had to be sensitive to parents’ concerns, particularly as their children’s participation in the project was entirely voluntary. Not surprising, these constraints profoundly influenced the ways in which we attempted to translate constructivism as a theory of knowing into practice. We were fortunate in that the classroom teacher, who had taught second grade mathematics “straight by the book” for the previous sixteen years, was a member of the project staff. Her practical wisdom and insights proved to be invaluable. It appears that we have had some success in satisfying the institutional constraints. The achievement test scores did rise satisfactorily, the parents were all universally supportive by the middle of the school year, and the administrators developed a positive opinion of what they saw. As a consequence, we are currently working with 18 teachers from the same school system. In general, we hope that our on-going work constitutes the beginnings of a response to Brophy’s (1986) challenge that “to demonstrate the relevance and practical value of this point of view for improving school mathematics instruction, they [constructivists] will need to undertake programmatic development and research – the development of specific instructional guidelines (and materials if necessary) for accomplishing specific instructional objectives in typical classroom settings” (p. 366). Thus, we concur with Carpenter’s (1983) observation that “If we are unable or unwilling to provide more direction for instruction, we are in danger of conceding the curriculum to those whose basic epistemology allows them to be more directive” (p. 109). Constructivism as an epistemology is, for us, a general way of interpreting and making sense of a variety of phenomena. It constitutes a framework within which to address situations of complexity, uniqueness, and uncertainty that Schon (1985) calls