Second grade students' interpretations of various representations depicting part-part-whole relationships
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[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] Through a cross-case analysis this study characterizes second-grade students' interpretations of mathematical representations (i.e., contextual situations, equations, part-part-whole diagrams, and open number lines) that depict part-part-whole relationships, and relates students' interpretations to their level of strategy development as indicated by a problem solving assessment. Data were collected from 10 students in a single second-grade classroom. Three main clusters of students' interpretations were identified: (a) viewing representations as final solutions (e.g., representations with missing values were unacceptable), (b) focusing interpretations of representations on location, sequence, or the meaning of operations (e.g., match the order of numbers or direct action of problem), and (c) interpreting representations using fact families or mathematical properties (e.g., applying commutativity or inverse relationships). For the 10 students in this study, a student's strategy development did not correspond to the students' cluster assignments. These data provide significant implications for all levels of teacher development, curriculum design, and assessment.
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