Understanding fractional equivalence and the differentiated effects on operations with fractions

This study compared two representations for teaching fraction equivalence. It traced the implications of both representations on the student?s comprehension of fractions as well as their ability to perform operations with fractions. The participants in the study included 65 sixth grade students in three extant classrooms. Two classes were instructed using the textbook representation while the third class received instruction using a representation presented by Van de Walle and recommended by the National Council for Teaching Mathematics. Data were collected from pre-tests, post-tests, student work samples, field notes and a semi-structured interview. Qualitative analyses were used to analyze the data. Items were coded for procedural and conceptual understanding and categorized into levels of proficiency. Additionally, items involving operations with fractions were coded for error patterns. Conclusions were drawn about how the different representations affected student comprehension and faculty with fractions.