The effect of a Thompson-like cognitive model on beginning algebra students' success with coin problems
Eisenmann, Cynthia J.
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Coin problems are a difficult topic for beginning algebra students. A Thompson-like cognitive model was designed as a tool to investigate the relationship between students' conceptual understanding of variables (as measured by the Chelsea Diagnostic Mathematics Test) and their competence in quantitative reasoning (as indicated by their performance on beginning algebra coin problems). The model allowed students to show relationships between individual quantities and to focus on the relationship between the number of coins. This tool isolated students' difficulties in solving beginning algebra coin problems, and was used to investigate the effectiveness of a cognitively-based teaching strategy to alleviate students' conceptual errors in coin problems. Six students were selected at different levels of variable understanding. These students completed a pretest on coin problems, were given individualized instruction using the investigator-designed model, and then were given a post-test on coin problems. Students had the most difficulty in determining the relationship between quantities. Students with a lower level on conceptual understanding of variables were not successful with solving coin problems, indicating they are not sufficiently competent in quantitative reasoning to begin work on coin problems.