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

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PROM/SE Ohio 2005 Spring Mathematics Associates Institute 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

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PROM/SE Ohio 2005 Spring Mathematics Associates Institute 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

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PROM/SE Ohio 2005 Spring Mathematics Associates Institute 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?

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

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PROM/SE Ohio 2005 Spring Mathematics Associates Institute 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

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PROM/SE Ohio 2005 Spring Mathematics Associates Institute 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

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PROM/SE Ohio 2005 Spring Mathematics Associates Institute 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.

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PROM/SE Ohio 2005 Spring Mathematics Associates Institute 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

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PROM/SE Ohio 2005 Spring Mathematics Associates Institute 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

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PROM/SE Ohio 2005 Spring Mathematics Associates Institute Instructional Materials Summary Table Section/ Investigation Core MathematicsDevelop. Level Cognitive Demand Lesson Worksheet 2C

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PROM/SE Ohio 2005 Spring Mathematics Associates Institute 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?

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PROM/SE Ohio 2005 Spring Mathematics Associates Institute 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

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PROM/SE Ohio 2005 Spring Mathematics Associates Institute 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.

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