exploring cognitive demands of mathematical tasks milwaukee public school bernard rahming...
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Exploring Cognitive Demands of Mathematical Tasks
Milwaukee Public School
Bernard Rahming
Mathematics Teaching [email protected]
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
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AgendaParticipants will :Develop their understanding of cognitive demand
levels of mathematical taskEngage 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
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Success CriteriaWe 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
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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
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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
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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
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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)
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Table Group Sort ActivityLay 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
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”. 2nd Edition, pg. 9, Fig. 1.3
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Cognitive Demands and Features Sample Tasks
Task Level of
Cognitive Demand
Explanation of Categorization
Features
A Doing Mathematics There 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
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ReflectionRespond 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
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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
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Mathematical Tasks Framework
Figure 1.3
TASKSAs they appear in curricular/ instructional materials
TASKSAs set up by teachers
TASKSAs implemented by students
StudentLearning
A representation of how mathematical tasks unfold during classroom instruction. (Stein & Smith, 1998, Mathematics Teaching in the Middle School)
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
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(Adapted from Stein & Smith, 199 Stein, Smith, Henningsen, & Silver, (2009)
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
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(Adapted from Stein, Smith, Henningsen, & Silver, (2009))
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www.mmp.uwm.edu