Exploring%20Cognitive%20Demands%20of%20Mathematical%20Tasks

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Exploring Cognitive Demands of Mathematical Tasks

• Milwaukee Public School
• Bernard Rahming
• Mathematics Teaching Specialist
• rahminbv_at_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

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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

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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

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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 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
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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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(No Transcript)
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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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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

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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

A representation of how mathematical tasks unfold
during classroom instruction. (Stein Smith,
1998, Mathematics Teaching in the Middle School)
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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)
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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

(Adapted from Stein, Smith, Henningsen, Silver,
(2009))
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Thank you
www.mmp.uwm.edu