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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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| Published in: | Cognition and instruction 2018-01, Vol.36 (1), p.30-55 |
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| Main Authors: | , , , , , |
| Format: | Article |
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| cites | cdi_FETCH-LOGICAL-c382t-33921daba57e952a3ea6a58f377f2faa4d8d207d07d32f4dca921c9cd890bdc23 |
| container_end_page | 55 |
| container_issue | 1 |
| container_start_page | 30 |
| container_title | Cognition and instruction |
| container_volume | 36 |
| creator | Fonger, Nicole L. Stephens, Ana Blanton, Maria Isler, Isil Knuth, Eric Gardiner, Angela Murphy |
| description | 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. |
| doi_str_mv | 10.1080/07370008.2017.1392965 |
| format | article |
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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. 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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.</description><subject>Academic Achievement</subject><subject>Algebra</subject><subject>algebra and algebraic thinking</subject><subject>Case Studies</subject><subject>Curricula</subject><subject>curriculum</subject><subject>Curriculum Design</subject><subject>Curriculum Development</subject><subject>Curriculum Implementation</subject><subject>Curriculum Research</subject><subject>Elementary School Mathematics</subject><subject>Elementary School Students</subject><subject>equivalence</subject><subject>Grade 3</subject><subject>Grade 4</subject><subject>Grade 5</subject><subject>instruction</subject><subject>Instructional Design</subject><subject>Learning</subject><subject>Learning Processes</subject><subject>learning progressions</subject><subject>Longitudinal Studies</subject><subject>Mathematical Concepts</subject><subject>Mathematical Logic</subject><subject>mathematics</subject><subject>Mathematics Education</subject><subject>Mathematics Instruction</subject><subject>Pilot Projects</subject><subject>Research and Development</subject><subject>Science Education</subject><subject>Science Instruction</subject><subject>Teaching Methods</subject><subject>Thinking Skills</subject><issn>0737-0008</issn><issn>1532-690X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>7SW</sourceid><recordid>eNp9kF1rFDEUhgdRcK3-hELA286aj8lmxivLdtXKFgVb8C6c5qPOMpOsJxm1_fVm2LreCYEceN8nH09VnTK6ZLSlb6gSilLaLjllaslEx7uVfFItmBS8XnX029NqMXfqufS8epHSrkxcMrWoHi7cTzfEfR_uCJCtAwzz-AXjHbqU-hiIj0jWE2JvpmEaz8hlSBknk0t2RiBY8jVP1oV8pN-S80A2v2HcD454jCO5gvzdjZB7k8jGTgZm-GX1zMOQ3KvH_aS6eb-5Xn-st58_XK7Pt7URLc-1KP9hFm5BKtdJDsLBCmTrhVKee4DGtpZTZcsS3DfWQOmbzti2o7fWcHFSvT6cu8f4Y3Ip612cMJQrdRHWUdl0XJWWPLQMxpTQeb3HfgS814zqWbP-q3mmlH7UXLjTA-eKoCOz-cSYauiq_ZfvUo54LDStbFijmpK_O-R9KKJH-BVxsDrD_RDRIwTTJy3-_4Q_hp-Yxg</recordid><startdate>20180102</startdate><enddate>20180102</enddate><creator>Fonger, Nicole L.</creator><creator>Stephens, Ana</creator><creator>Blanton, Maria</creator><creator>Isler, Isil</creator><creator>Knuth, Eric</creator><creator>Gardiner, Angela Murphy</creator><general>Routledge</general><general>Taylor & Francis, Ltd</general><general>Taylor & Francis Ltd</general><scope>7SW</scope><scope>BJH</scope><scope>BNH</scope><scope>BNI</scope><scope>BNJ</scope><scope>BNO</scope><scope>ERI</scope><scope>PET</scope><scope>REK</scope><scope>WWN</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-6245-4062</orcidid></search><sort><creationdate>20180102</creationdate><title>Developing a Learning Progression for Curriculum, Instruction, and Student Learning: An Example from Mathematics Education</title><author>Fonger, Nicole L. ; 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| ispartof | Cognition and instruction, 2018-01, Vol.36 (1), p.30-55 |
| issn | 0737-0008 1532-690X |
| language | eng |
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| source | JSTOR Archival Journals and Primary Sources Collection; ERIC; Taylor and Francis Social Sciences and Humanities Collection |
| 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 |
| title | Developing a Learning Progression for Curriculum, Instruction, and Student Learning: An Example from Mathematics Education |
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