Developing a learning progression for curriculum, instruction, and student learning: An example from mathematics education
Open accessAbstract
Learning progressions have been demarcated by some for science education, or only concerned with levels of sophistication in student thinking as determined by logical analyses of the discipline. We take the stance that learning progressions can be leveraged in mathematics education as a form of curriculum research that advances a linked understanding of students learning over time through careful articulation of a curricular framework and progression, instructional sequence, assessments, and levels of sophistication in student learning. Under this broadened conceptualization, we advance a methodology for developing and validating learning progressions, and advance several design considerations that can guide research concerned with engendering forms of mathematics learning, and curricular and instructional support for that learning. We advance a two-phase methodology of (a) research and development, and (b) testing and revision. Each phase involves iterative cycles of design and experimentation with the aim of developing a validated learning progression. In particular, we gathered empirical data to revise our hypothesized curricular framework and progression and to measure change in students. thinking over time as a means to validate both the effectiveness of our instructional sequence and of the assessments designed to capture learning. We use the context of early algebra to exemplify our approach to learning progressions in mathematics education with a focus on the concept of mathematical equivalence across Grades 3-5. The domain of work on research on learning over time is evolving; our work contributes a broadened role for learning progressions work in mathematics education research and practice.
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The context of numerical equalities based on arithmetic properties has been highlighted for its potential to promote relational thinking.
“The context of numerical equalities based on arithmetic properties has been highlighted for its potential to promote this type of thinking [7,15,19].”
From Third Grade Students’ Use of Relational Thinking (2021) · cites this paper as [7]
Teaching has a positive effect on relational thinking when it is linked to promoting the understanding of the equal sign as a representation of equivalence.
“Teaching has a positive effect on relational thinking when it is linked to promoting the understanding of the equal sign as a representation of equivalence [7,23].”
From Third Grade Students’ Use of Relational Thinking (2021) · cites this paper as [7]
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- Authors
- Fonger, N. L., Stephens, A., Blanton, M., Isler, I., Knuth, E., & Gardiner, A. M.
- Affiliations
- Syracuse University (US)
- University of Wisconsin–Madison (US)
- Tahoe Environmental Research Center (US)
- Middle East Technical University
- The University of Texas at Austin (US)
- Corresponding author
- Fonger, Nicole L.
- Venue
- Cognition and Instruction
- Publisher
- Informa UK Limited
- Published
- 2017-12-18
- Volume
- 36
- Issue
- 1
- Pages
- 30-55
- ISSN
- 0737-0008 (ISSN-L)
- 1532-690X
- OpenAlex
- W2779085024
- Cited by
- 46
- References
- 47
- Citations by year
- 2026: 2 · 2025: 6 · 2024: 5 · 2023: 3 · 2022: 9 · 2021: 10 · 2020: 5 · 2019: 3 · 2017: 3
- FWCI
- 10.73
- Type
- journal article
- Language
- en
- Open access
- green
- hdl.handle.net
- Licence
- cc-by-nc-nd
- Locations
- Cognition and Instruction (publishedVersion)
- OpenMETU (Middle East Technical University) (submittedVersion, cc-by-nc-nd)
- Funders
- Directorate for Education and Human Resources (DRL-1207945, DRL-1219605/1219606)
- Institute of Education Sciences (R305B130007)
- Topics
- Social Sciences › Education › Mathematics Education and Teaching Techniques
- Social Sciences › Education › Science Education and Pedagogy
- Physical Sciences › Mathematics › Applied Mathematics › Mathematics Education and Pedagogy
- Keywords
- learning progression, mathematics education, early algebra, mathematical equivalence, curriculum framework, instructional sequence, assessment design, curriculum development
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