When seeing isn't believing: Influences of prior conceptions and misconceptions

Abstract

Instruction often employs visual representations to support deep understanding. However, students’ prior misconceptions may override the meaning in these scaffolds. We investigate fraction bars, a common representation intended to promote sense-making. Our prior work found that students often did not use the fraction bars effectively. This difficulty factors assessment compares four scaffold types: pictures only, two forms of pictures with numbers, and numbers only, to assess which interpretation steps were difficult. On equivalence items, students performed equally well with all scaffolds that included pictures, but worse with the numbers-only scaffold, indicating that fraction bars improved scores for equivalence. However, including numbers with the pictures decreased performance for fraction addition. Although students demonstrated competence with fraction bars in fraction equivalence, they did not transfer this knowledge to addition. These results suggest caution in designing and teaching representations for sense-making.


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