Early elementary students' fractional understanding : examination of cases from a multi-year longitudinal study.
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For more than three decades fractions have been considered critical and foundational, yet they represent a challenge for teaching and learning higher mathematics by students, teachers, and teacher educators. The purpose of the study was to investigate early elementary students' understanding of fractions and growth in thinking about fractional concepts over multiple years. This research study analyzed data from a larger longitudinal research study that was conducted from 2007 to 2013 with students from kindergarten to third grade. The study used purposeful criterion sampling to select student cases to gain insight into students' fractional understanding and thinking. This study employed an explanatory multiple case study design to examine ten early elementary students' fractional understanding after they had participated in the larger longitudinal research study for at least three years. Each student was examined as a separate case before cross-case analysis was conducted to reveal common themes and patterns. The study explored the relationship between early elementary students' understanding and the use of manipulatives to teach fractional concepts such as part-whole partitioning, fair share, unitizing, and equivalence over time. Findings of the study relate to what early elementary students know and understand about fractions such as understanding of one-half, interference of whole number knowledge, and difficulties with symbolic representation of fractions. The study also presents findings that relate to the relationship between use of manipulatives and students' fractional understanding in terms of selection and efficiency of various manipulatives. Results of the study also examined the growth in students' thinking about fractions over time. This research study aimed to provide an understanding of the relationship between students' fractional thinking and use of manipulatives to better focus classroom instruction for deeper impact. The researcher discusses the implications in relation to curriculum, use of manipulatives, and development of students' understanding of fractions.