Abstract
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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