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Maria Blanton - UMass Dartmouth Eric Knuth - UW Madison Project Associates Angela Gardiner

algebra.wceruw.org. kaputcenter.umassd.edu/projects/ea/alg_ready. Analyzing an Early Algebra Learning Progression (EALP) for Grades 3–8 NSF PI Meeting December 1-3, 2010. Maria Blanton - UMass Dartmouth Eric Knuth - UW Madison Project Associates Angela Gardiner Isil Isler Tim Marum

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Maria Blanton - UMass Dartmouth Eric Knuth - UW Madison Project Associates Angela Gardiner

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  1. algebra.wceruw.org kaputcenter.umassd.edu/projects/ea/alg_ready Analyzing an Early Algebra Learning Progression (EALP) for Grades 3–8 NSF PI Meeting December 1-3, 2010 Maria Blanton - UMass DartmouthEric Knuth - UW Madison Project Associates Angela Gardiner Isil Isler Tim Marum Ana Stephens

  2. algebra.wceruw.org kaputcenter.umassd.edu/projects/ea/alg_ready (part of) Analyzing an Early Algebra Learning Progression (EALP) for Grades 3–8 NSF PI Meeting December 1-3, 2010 Maria Blanton - UMass DartmouthEric Knuth - UW Madison Project Associates Angela Gardiner Isil Isler Tim Marum Ana Stephens

  3. Project Overview From 35,000 ft: • Long term goal of looking at impact of early algebra: How does a sustained early algebra education develop ‘algebra-ready’ students for middle grades (and beyond)? From 10,000 ft: • Preliminary work to above goals: • Develop the EALP • Develop EALP-based assessments for grades 3-8, empirically test the EALP and refine assessments and potential intervention On the ground (focus for today): • Analyzing an EALP for algebra in grades 3-8

  4. Prior Steps - Year 1 • understand meanings for LP

  5. Learning Progression (LP) A learning progression is meant to provide an ordering of concepts/understandings/skills that build toward a more sophisticated understanding of an important idea or topic (NRC, 2007).

  6. Learning ProgressionKey Characteristics  based on the logic of the discipline, current learning research, and curricular frameworks and standards • specifies lower and upper anchor points • specifies grade level competencies and connections between them  informs the design of appropriate instructional strategies and learning tasks, and grade-level assessments • identifies key transition points

  7. Learning ProgressionProcess & components(based on Shin et al, 2009) • Identify the Big Ideas • Identify associated Constructs • ….necessary to understand big ideas. • Create Claims/understandings • …that specify nature of knowledge/skills/understanding expected of students regarding a construct. • Specify Evidence • …from student work that indicates student has acquired knowledge/skills/understandings identified in claim • Identify Difficulties and Misconceptions • …that students have with a construct • Identify Research Base • …that supports the claims about the knowledge/skills/understandings expected of students

  8. Prior Steps - Year 1 • Understand meanings for LP • gather information on • research • curricula • frameworks/standards • mathematics regarding important algebra ideas in elementary grades through Algebra 1. • synthesize ideas to draft an EALP for grades 3-8

  9. EALP Five content domains (Big Ideas): • Generalized Arithmetic (GA) • Equality, Expressions, Equations, and Inequality (EEEI) • Functional Thinking (FT) • Variable (VAR) • Proportional Reasoning (PR)

  10. EALP Each content domain (Big Idea) is organized around the following 4 strands (based on Kaput (2008): • generalizing relationships (relationships) • expressing relationships (representations) • justifying generalized relationships (justifying) • reasoning with relationships (reasoning)

  11. EALP Each content domain (Big Idea) consists of • tables that identify the constructs, claims/understandings, evidence, difficulties/misconceptions and research base within each strand for the Big Idea. • a grade-by-grade progression (grades 3-8) that details how Big Ideas develop (or can be developed) across the grades, what content would be developed at a particular grade, and what skills/understandings are expected for that content.

  12. algebra FT EEEI GA VAR PR Focus: • FT and EEEI • Strands 1 and 2 (relationships and representations) • constructs and claims STRAND 1 STRAND 2 ETC GRADE-BY-GRADE PROGRESSION OF IDEAS

  13. Small-Group Focus Questions Review portion of LP in your group (~10 minutes) • Do the Constructs identified for each strand seem appropriate (complete, cohesive, aligned) for that strand? Are there any additional constructs we should consider? • Do the Claims/Understandings seem appropriate (complete, cohesive, aligned) for the given construct? Are there any additional claims we should consider? • Do the grade summaries seem reasonable and appropriate?

  14. Questions for further discussion • What are key transition points between elementary and middle grades for FT or EEEI? • How should solving equations be addressed in elementary grades so that it leads to more formal algebraic procedures for solving equations in later grades? • What algebraic aspects of proportional reasoning can be included in the elementary grades as a way to strengthen important algebra ideas in middle grades (e.g., slope)? • Are there other mathematical domains (BIG IDEAS) that should be considered in the elementary grades as a route into algebra?

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