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ERIC Number: EJ1051915
Record Type: Journal
Publication Date: 2015
Pages: 42
Abstractor: As Provided
ISSN: ISSN-0737-0008
From Number Lines to Graphs in the Coordinate Plane: Investigating Problem Solving across Mathematical Representations
Earnest, Darrell
Cognition and Instruction, v33 n1 p46-87 2015
This article reports on students' problem-solving approaches across three representations--number lines, coordinate planes, and function graphs--the axes of which conventional mathematics treats in terms of consistent geometric and numeric coordinations. I consider these representations to be a part of a "hierarchical representational narrative" (HRN), a discursive narrative around a set of representations that model conventional mathematics in structurally consistent ways. A paper-and-pencil assessment was administered to students in grades 5 and 8 along with videotaped interviews with a subset of students. Results revealed students' application of particular meta-rules, which reflect their attempts to find and make use of recurring patterns in mathematics discourse. One such meta-rule, consistent with the HRN, was characterized by students' coordination of geometric and numeric properties of an axis, whereas alternate meta-rules reflected coordinations inconsistent with conventional mathematics. Detailed analyses of problem-solving strategies are reported, and implications for theory, curriculum, and instruction are discussed.
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Publication Type: Journal Articles; Reports - Research
Education Level: Grade 5; Intermediate Grades; Middle Schools; Elementary Education; Junior High Schools; Secondary Education; Grade 8
Audience: N/A
Language: English
Sponsor: Institute of Education Sciences (ED); National Science Foundation
Authoring Institution: N/A
Identifiers - Location: California
IES Funded: Yes
Grant or Contract Numbers: R305B090026; ESI0119732