The Tension Between Theories of Learning and Instruction in Mathematics Education
Abstract
This article addresses the contradiction between the assumption that the goal of mathematics instruction is to transmit knowledge to students and the view that students construct mathematical knowledge by reorganizing their cognitive structures. Transmission and constructivist analyses of communication are contrasted. It is concluded that the task of accounting for successful instruction is not one of explaining how students take in and process information transmitted by the teacher. Instead, it is to explain how students actively construct knowledge in ways that satisfy constraints inherent in instruction. A brief case study is presented to support this contention, and general implications that take account of both cognitive and noncognitive instructional goals are discussed.
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Practically every theory of learning requires a form of instructor feedback so that students are aware of their own level of understanding.
“Regarding feedback, practically every theory of learning requires a form of instructor feedback so that students are aware of their own level of understanding (Cobb, 1988;Cooper et al., 2006;Davis et al., 1990;Steffe, 1996;Zemke & Zemke, 1995).”
From The Effects of Online Homework on Achievement and Self-efficacy of College Algebra Students (2009) · cites this paper as Cobb, 1988
Cited by
Sorted by citations
Strategy Instruction in Mathematics
Goldman, S. R. (1989) · Learning Disability Quarterly · doi:10.2307/1510251 · Cited by 92 · see citing works
The Effects of Online Homework on Achievement and Self-efficacy of College Algebra Students
Brewer, D. S. (2009) · Utah State University · doi:10.26076/e6cf-1985 · Cited by 25 · see citing works
- Authors
- Cobb, P.
- Corresponding author
- Cobb, Paul
- ORCID
- Cobb, Paul
- Venue
- Educational Psychologist
- Publisher
- Informa UK Limited
- Published
- 1988-03-01
- Volume
- 23
- Issue
- 2
- Pages
- 87-103
- ISSN
- 0046-1520 (ISSN-L)
- 1532-6985
- OpenAlex
- W1964259363
- Cited by
- 264
- References
- 0
- Citations by year
- 2026: 2 · 2025: 2 · 2024: 3 · 2023: 4 · 2022: 12 · 2021: 10 · 2020: 8 · 2019: 5 · 2018: 9 · 2017: 8 · 2016: 8 · 2015: 14 · 2014: 7 · 2013: 7 · 2012: 5
- FWCI
- 71.60
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Educational Psychologist (publishedVersion)
- Funders
- National Science Foundation
- Spencer Foundation
- Topics
- Social Sciences › Education › Mathematics Education and Teaching Techniques
- Physical Sciences › Mathematics › Applied Mathematics › Mathematics Education and Pedagogy
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Visual and Cognitive Learning Processes
- Keywords
- mathematics education, constructivism, knowledge transmission, cognitive structure, student knowledge construction, learning objectives
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