An interview-based analysis of sixth graders' cognition of fractions in contexts of subdivision, comparison, and partitioning

The research questions prompting this study called for exploration of sixth grade participant's knowledge of fractions in terms of the meaning of fractions and fraction symbols, ordering and equivalence of fractions, and operations on fractions; investigation of their use of conceptual and procedural knowledge in operating on fractions; contrast of more successful and less successful math students' understanding of fractions and operations on fractions; and examination of students' cognition of fractions in contexts of comparing, subdividing and partitioning. Think-aloud protocols and clinical interviews with twelve participants were conducted and video-taped. Seven of the participants were identified as successful in their sixth grade math classes, and five were experiencing difficulty with math, while all had average or above verbal scores, thus permitting a contrast of cognition of fractions in high and low performing math students. Analysis of transcripts involved segmenting, episodes into statements, which were categorized utilizing the context of the interview episodes. Findings indicated that the sixth graders had developed a part-whole concept of fractions and that one-half was a relatively strong intuitive concept for all participants. Among the less proficient math students, a whole number interpretation of fraction symbols was common, and the reasoning behind errors revealed whole number interference. Successful students had more complete and well integrated concepts of fraction, and displayed greater conceptual knowledge than their counterparts. Students were not limited to procedural knowledge, but utilized physical referents to represent fractional situations, and produced high frequencies of conceptual knowledge statements in conjunction with verbally presented problems. Furthermore those students who generated the highest frequencies of conceptual knowledge and automaticity statements were also the students who produced the fewest errors. However, a dissociation between conceptual knowledge was suggested by differential reasoning in response to symbolically and verbally presented problems.