Developing a Learning Progression for Curriculum, Instruction, and Student Learning: An Example from Mathematics Education

Date

2018-01-01

Author

Fonger, Nicole L.
Stephens, Ana
Blanton, Maria
İşler Baykal, Işıl
Knuth, Eric
Gardiner, Angela Murphy

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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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.

Subject Keywords

Equivalence, Algebra and algebraic thinking, Mathematics, Learning, Instruction, Curriculum, learning progressions

URI

https://hdl.handle.net/11511/42127

Journal

COGNITION AND INSTRUCTION

DOI

https://doi.org/10.1080/07370008.2017.1392965

Collections

Department of Mathematics and Science Education, Article

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Citation Formats

N. L. Fonger, A. Stephens, M. Blanton, I. İşler Baykal, E. Knuth, and A. M. Gardiner, “Developing a Learning Progression for Curriculum, Instruction, and Student Learning: An Example from Mathematics Education,” COGNITION AND INSTRUCTION, pp. 30–55, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/42127.