1. Exploring Cognitive Demands of Mathematical Tasks Milwaukee Public School Bernard Rahming Mathematics Teaching Specialist rahminbv@milwaukee.k12.wi.us April 16, 2011 National Council of Teachers of Mathematics Indianapolis, IN Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation

2. 2 Agenda Participants will :  Develop their understanding of cognitive demand levels of mathematical task  Engage in activities of identifying cognitive demand levels of mathematical tasks  Discuss factors of maintenance and decline of mathematical tasks during setup and implementation. Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation

3. 3 Success Criteria We will be successful if at the end of the session..  We understand and can identify the features of the levels of cognitive demand of mathematical tasks.  We can articulate the factors of maintenance and decline of cognitive demand levels during setup and implementation. Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation

4. 4 Building Academic Vocabulary Discuss with your shoulder partner what you think Cognitive Demand is. What picture comes to mind when you think of Cognitive Demand? Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation

5. 5 Cognitive Demand… “The kind and level of thinking required of students in order to successfully engage with and solve the task.” Stein, Smith, Henningsen, & Silver, (2009) Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation

6. 6 Reading: “Analyzing Mathematics Instructional Tasks” Individually read the entire article. Each person share one idea from the article at your table. Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation

7. 7 Four Levels of Cognitive Demand in Mathematical Tasks Low Level Cognitive Demands  Memorization Tasks  Procedures Without Connections to understanding, meaning or concepts Tasks High Level Cognitive Demands  Procedures With Connections to understanding, meaning or concepts/Tasks  Doing Mathematics Tasks Stein, Smith, Henningsen, & Silver, (2009)

8. 8 Table Group Sort Activity Lay out the 4 green category cards Deal out the 8 blue Mathematical Task Cards to everyone in the group. Refer to the “Task Analysis Guide” for criteria. As you place your Mathematical Task cards into a category, explain your reasoning. Help each other justify the placements. Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation

9. Table Group Sort Activity Sample activity cards were adapted from Stein, Smith, Henningsen, & Silver, (2009). “Implementing standards-based mathematics instruction: A casebook for professional development”. 2 nd Edition, pg. 9, Fig. 1.3 9

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11. 11 Cognitive Demands and Features Sample Tasks TaskLevel of Cognitive Demand Explanation of Categorization Features ADoing MathematicsThere is no pathway suggested by the task. The focus is on looking for the underlying mathematical structure. Requires an explanation Uses manipulatives Involves multiple steps Uses a diagram Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation

12. 12 Reflection Respond to the following:  Which of the four levels of cognitive demand are you most comfortable with -why?  Which one do you understand the least -why?  Something I want to know more about is…? Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation

13. 13 Four Levels of Cognitive Demand in Mathematical Tasks Low Level Cognitive Demands Memorization Tasks Procedures Without Connections to understanding, meaning or concepts Tasks High Level Cognitive Demands Procedures With Connections to understanding, meaning or concepts Tasks Doing Mathematics Tasks

14. 14 Mathematical Tasks Framework Figure 1.3 TASKS As they appear in curricular/ instructional materials TASKS As set up by teachers TASKS As implemented by students Student Learning A representation of how mathematical tasks unfold during classroom instruction. (Stein & Smith, 1998, Mathematics Teaching in the Middle School)

15. Factors associated with the decline of High- Level cognitive Demand Students press teacher to reduce complexity of the task, explicit steps Teacher rescue students from struggle Teacher shifts emphasis from meaning, concepts, or understanding to correctness or completeness of answer Not enough time or too much time Classroom management 15 (Adapted from Stein & Smith, 199 Stein, Smith, Henningsen, & Silver, (2009)

16. Factors associated with the maintenance of High-Level Cognitive Demand Scaffolding of student thinking and reasoning Students provided with means of monitoring their own progress Teachers of capable students model high- level performance Task build on students’ prior knowledge Sufficient time to explore 16 (Adapted from Stein, Smith, Henningsen, & Silver, (2009))

17. 17 www.mmp.uwm.edu