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

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

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

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?

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

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

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

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.

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

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

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

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?

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

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.