This study explored how prospective elementary teachers (n= 106, 29 groups) enrolled concurrently in elementary science and elementary mathematics methods courses used algebraic reasoning to construct and describe relationships among and between variables in the context of solving a problem involving the action of Class 1 levers. Group members collected data and tried to develop a mathematical formula that would allow them to predict where a weight of given size could be placed on one side of the lever to balance a specified weight at a specified distance from the fulcrum on the opposite side. Data sources for the study included journal entries, transcripts, and documents produced by students. Four categories encompassing the most general groupings of students' representations based on both the rule and formula were constructed. Eighteen out of the 29 groups were able to solve the problem. Specific weaknesses characterized by the solutions presented were (a) a confusion in the meaning of mathematical concepts connected with ratio and proportion; (b) a lack of mathematical language skills and/or understanding of how to symbolically represent relationships among variables in formulae; and (c) a lack of understanding of the generalizability characteristic of variables in mathematics and science.

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This study reports our understanding of the views on problem-solving developed by prospective elementary teachers as a result ofexperiencing problem centered learning in an integrated math-science methods course. The course was designed to assist the prospective teachers to develop their problem solving skills in mathematics and science contexts and to develop problem-solving activities that integrate mathematics and science to use in their classrooms. Small group activities, where students had multiple opportunities to interact with concrete materials and to discuss their ideas, were emphasized. Data sources included audio taped interviews, field notes, and documents such as portfolios and lesson plans students produced during problem solving activities. Four assertions related to students' attitudes toward problem solving, their knowledge ofproblem solving and problem solving processes, and the role ofproblem solving in elementary classrooms are discussed. Implications for planning and implementing integrated mathematics and science problem solving activities in methods courses and for continued research are presented. 66

A light fare to whet your mathematical appetite.

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