Cognitive Demands of Mathematical Tasks Scaling Up STEM

Cognitive Demands of Mathematical Tasks Scaling Up STEM Learning with the VCL Summer Institute 2011

What is Cognitive Demand? Discuss what you think Cognitive Demand of a Mathematics Task is. What picture comes to mind when you think of Cognitive Demand? 2

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) 3

Four Levels of Cognitive Demand in Mathematical Tasks Low Level Cognitive Demands v v Memorization Tasks Procedures Without Connections to understanding, meaning or concepts Tasks High Level Cognitive Demands v v Procedures With Connections to understanding, meaning or concepts/Tasks Doing Mathematics Tasks Stein, Smith, Henningsen, & Silver, (2009) 4

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Table Group Sort Activity Deal out the 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. 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 6

Discussion of Sorting Activity 7

Reflection v Which of the four levels of cognitive demand are you most comfortable with -why? v Which one do you understand the least -why? v Something I want to know more about is…? 8

Mathematical Tasks Framework 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) 9

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 (Adapted from Stein & Smith, 199 Stein, Smith, Henningsen, & Silver, (2009) 10

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 highlevel performance • Task build on students’ prior knowledge • Sufficient time to explore • (Adapted from Stein, Smith, Henningsen, & Silver, (2009)) 11

Questions? 12