TY - JOUR
T1 - Developing a Learning Progression for Curriculum, Instruction, and Student Learning
T2 - An Example from Mathematics Education
AU - Fonger, Nicole L.
AU - Stephens, Ana
AU - Blanton, Maria
AU - Isler, Isil
AU - Knuth, Eric
AU - Gardiner, Angela Murphy
N1 - Publisher Copyright:
© 2018 Taylor & Francis Group, LLC.
PY - 2018/1/2
Y1 - 2018/1/2
N2 - 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.
AB - 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.
KW - algebra and algebraic thinking
KW - curriculum
KW - equivalence
KW - instruction
KW - learning
KW - learning progressions
KW - mathematics
UR - http://www.scopus.com/inward/record.url?scp=85038373795&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85038373795&partnerID=8YFLogxK
U2 - 10.1080/07370008.2017.1392965
DO - 10.1080/07370008.2017.1392965
M3 - Article
AN - SCOPUS:85038373795
SN - 0737-0008
VL - 36
SP - 30
EP - 55
JO - Cognition and Instruction
JF - Cognition and Instruction
IS - 1
ER -