The discrepancy between students’ performance in hands-on and paper-and-pencil mathematics
摘要
Mathematical knowledge can be represented situationally or through abstract symbols. Theories typically treat the development of mathematical ability as a hierarchical structure from situation to symbols, and educational practice also follows the path. There has been empirical evidence showing that the two types of mathematical knowledge representation may follow relatively independent developmental paths. Thus, the advancement of symbolic mathematical ability does not necessarily lead to parallel growth in situational mathematical ability. The current study examines whether hands-on mathematics, a form of typical situational mathematics, displays better performance than paper-and-pencil symbolic mathematics. A total of 385 seventh-grade middle school students participated in the study. A hands-on cake-sharing task was used to assess students’ situational or hands-on fraction ability, and a corresponding paper-and-pencil fraction division arithmetic task was used to assess symbolic or paper-and-pencil fraction ability. The findings revealed that about 81.60% of students successfully solved the paper-and-pencil fraction problem, but only about 13.87% (Scoring A) and 32.27% (Scoring B) of the students successfully solved the hands-on fraction problem. This reveals a discrepancy between students’ performance in situational and symbolic mathematics, underscoring the need to reconsider instruction for situational mathematics in curricula and educational practice.