ERIC Number: EJ1191847
Record Type: Journal
Publication Date: 2018
Pages: 26
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-1098-6065
EISSN: N/A
A Framework for Characterizing Students' Cognitive Processes Related to Informal Best Fit Lines
Groth, Randall E.; Jones, Matthew; Knaub, Mary
Mathematical Thinking and Learning: An International Journal, v20 n4 p251-276 2018
Informal best fit lines frequently appear in school curricula. Previous research collectively illustrates that the adjective informal does not translate to cognitive simplicity. Using existing literature, we create a hypothetical framework of cognitive processes associated with studying informal best fit lines. We refine the framework using data from a cycle of design-based research about building students' understanding of covariation. The refined framework includes student thinking processes for signifying observations as data, signifying data with scatterplots, perceiving aggregates in scatterplots, perceiving trends in aggregates, signifying trends with straight lines, and using straight lines as estimation tools. We explain how students' perceptions of aggregates can proceed from the inside-out as well as from the outside-in. We also demonstrate how the amounts of variation encountered at different points in time and the extent to which students perceive straight lines to be abbreviations of linear covariation are important considerations for teaching and research.
Descriptors: Models, Cognitive Processes, Student Attitudes, Graphs, Mathematics Instruction, Thinking Skills, Grade 8, Correlation, Mathematical Concepts, Computation
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 - Descriptive
Education Level: Grade 8
Audience: N/A
Language: English
Sponsor: National Science Foundation (NSF)
Authoring Institution: N/A
Grant or Contract Numbers: DRL1356001