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

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 curr...

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Bibliographic Details
Published in:Cognition and instruction 2018-01, Vol.36 (1), p.30-55
Main Authors: Fonger, Nicole L., Stephens, Ana, Blanton, Maria, Isler, Isil, Knuth, Eric, Gardiner, Angela Murphy
Format: Article
Language:English
Subjects:
Academic Achievement
Algebra
algebra and algebraic thinking
Case Studies
Curricula
curriculum
Curriculum Design
Curriculum Development
Curriculum Implementation
Curriculum Research
Elementary School Mathematics
Elementary School Students
equivalence
Grade 3
Grade 4
Grade 5
instruction
Instructional Design
Learning
Learning Processes
learning progressions
Longitudinal Studies
Mathematical Concepts
Mathematical Logic
mathematics
Mathematics Education
Mathematics Instruction
Pilot Projects
Research and Development
Science Education
Science Instruction
Teaching Methods
Thinking Skills
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Summary: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.
ISSN:0737-0008
1532-690X
DOI:10.1080/07370008.2017.1392965