ERIC Number: EJ1037541
Record Type: Journal
Publication Date: 2014-Aug
Abstractor: As Provided
Reference Count: 34
Relationships between Fractional Knowledge and Algebraic Reasoning: The Case of Willa
Lee, Mi Yeon; Hackenberg, Amy J.
International Journal of Science and Mathematics Education, v12 n4 p975-1000 Aug 2014
To investigate relationships between students' quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. The students were interviewed twice, once to explore their quantitative reasoning with fractions and once to explore their solutions of problems that required explicit use of unknowns to write equations. As a part of the larger study, the first author conducted a case study of a seventh grade student, Willa. Willa's fractional knowledge--specifically her reversible iterative fraction scheme and use of fractions as multipliers--influenced how she wrote equations to represent multiplicative relationships between two unknown quantities. The finding indicates that implicit use of powerful fractional knowledge can lead to more explicit use of structures and relationships in algebraic situations. Curricular and instructional implications are explored.
Descriptors: Correlation, Logical Thinking, Thinking Skills, Mathematical Concepts, Algebra, Cognitive Processes, Interviews, Middle School Students, High School Students, Statistical Analysis, Equations (Mathematics), Case Studies, Grade 7, Knowledge Level, Multiplication
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Publication Type: Journal Articles; Reports - Research
Education Level: Middle Schools; Secondary Education; Junior High Schools; High Schools; Grade 7; Elementary Education
Authoring Institution: N/A