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Content Trajectories, Instructional Materials, and Curriculum Decisions

Content Trajectories, Instructional Materials, and Curriculum Decisions. PROM/SE Ohio Mathematics Associates Institute Spring 2005. Agenda for 6-8. Identifying “Big Ideas” Trajectories for Measurement: Area, Perimeter and Area Instructional Materials and Content Trajectories

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Content Trajectories, Instructional Materials, and Curriculum Decisions

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  1. Content Trajectories, Instructional Materials, and Curriculum Decisions PROM/SE Ohio Mathematics Associates Institute Spring 2005

  2. Agenda for 6-8 • Identifying “Big Ideas” Trajectories for Measurement: • Area, Perimeter and Area • Instructional Materials and Content Trajectories • Lunch--12:00 p.m. • Mapping Benchmarks & Indicators to Instructional Materials • Reflections & Next Steps PROM/SE Ohio 2005 Spring Mathematics Associates Institute

  3. Characteristics of a Coherent Mathematical Trajectory • Every component has a mathematical reason for being included • Designed with awareness of students’ understandings and misunderstandings • Sequence developed with clear sense of developmental levels • Ideas build on each other • Mathematical sequence and connections are defensible • Ideas become increasingly more sophisticated Handout #1 PROM/SE Ohio 2005 Spring Mathematics Associates Institute

  4. Brainstorming the “Big Ideas” Trajectory • Measurement: Area, Perimeter and Volume • What are the “big ideas” in measurement for • area? • Perimeter? • Volume? • How would you organize these ideas to form a trajectory of mathematical content? PROM/SE Ohio 2005 Spring Mathematics Associates Institute

  5. Trajectory Posters • Replace with Measurement bullets Worksheet #1 PROM/SE Ohio 2005 Spring Mathematics Associates Institute

  6. Low Cognitive Demand • Tasks rely heavily on memorization or following a routine procedure • Require little thinking or reasoning • Focused on correct answers • Explanations focus solely on how a procedure was used and lack a connection to concepts or meaning Handout #2 PROM/SE Ohio 2005 Spring Mathematics Associates Institute

  7. Middle Grades Task Set • Sort the middle grades tasks for grade 6-8 by levels of cognitive demand • Record the task number and indicate the level (low, moderate, or high) on Worksheet 2A • Share your classifications with your team members • Discuss any differences and why they may have occurred • Try to resolve any disagreements about levels PROM/SE Ohio 2005 Spring Mathematics Associates Institute

  8. Moderate Cognitive Demand • Tasks require several different processes and relate two or more mathematical concepts (e.g., multi-step problems) • Procedures are connected to underlying concepts and meanings and cannot just be followed mindlessly • Students are asked to make connections among representations and may be asked to give some explanations. PROM/SE Ohio 2005 Spring Mathematics Associates Institute

  9. High Cognitive Demand • Tasks require significant analysis and reasoning • Students have to put ideas together in ways they have not seen before in a lesson or in ways that make connections to other previously learned mathematical concepts • There is no predictable rehearsed approach suggested by the task or example Handout #2 PROM/SE Ohio 2005 Spring Mathematics Associates Institute

  10. Instructional Materials & Content Trajectories Individually or in Pairs • Identify and record the core mathematical knowledge by lesson on Worksheet 2c • Indicate the developmental level (I, D, S, A) • Indicate the cognitive demand for each lesson (low, moderate, high) Worksheet 2B PROM/SE Ohio 2005 Spring Mathematics Associates Institute

  11. Instructional Materials Summary Table Worksheet 2C PROM/SE Ohio 2005 Spring Mathematics Associates Institute

  12. Summary of Instructional Materials Review As a team • What are some areas your materials handled well? • Describe any gaps that you identified. • Identify overlaps and decide upon the importance. • What mathematical content seems to be irrelevant and doesn’t appear to fit? • What issues did you find with developmental levels? • What issues emerged regarding the cognitive demands of tasks? PROM/SE Ohio 2005 Spring Mathematics Associates Institute

  13. Mapping to Benchmarks & Indicators • Identify the appropriate Benchmark or Indicator for each idea you listed on Worksheet 2C • Code indicators • Black - at expected grade level • Red - expected at higher grade • Blue - expected at lower grade • Yellow - not addressed at all in instructional materials • Which indicators occur in multiple grade levels? Why? • Where do gaps exist and how might you address them? Worksheet 3a PROM/SE Ohio 2005 Spring Mathematics Associates Institute

  14. Building New Tasks from Old • Select 2-3 tasks/problems from your instructional materials that you classified as low cognitive demand tasks. • Identify the mathematics in the task/problem and describe how it relates to the mathematical goals of the lesson. • Modify the problem so that is has a moderate or high cognitive demand • Record problem on chart paper to post • Describe how the revised task pushes students thinking. PROM/SE Ohio 2005 Spring Mathematics Associates Institute

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