1 / 16

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

drew
Download Presentation

Content Trajectories, Instructional Materials, and Curriculum Decisions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related