ERIC Number: EJ1051915
Record Type: Journal
Publication Date: 2015
Pages: 42
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-0737-0008
EISSN: N/A
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.
Descriptors: Problem Solving, Mathematics Instruction, Graphs, Numbers, Number Concepts, Geometric Concepts, Grade 5, Grade 8, Video Technology, Interviews, Mathematics Skills, Metacognition, Qualitative Research, Statistical Analysis, Elementary School Students, Middle School Students, Student Evaluation
Routledge. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals
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