Exploring
Cognitive Demands of
Mathematical Tasks
Milwaukee Public School
Bernard Rahming
Mathematics Teaching Specialist
[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
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.
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Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation
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
High Level Cognitive
Demands
 Memorization Tasks
 Procedures With
Connections to
understanding, meaning
or concepts/Tasks
 Procedures Without
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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Cognitive Demands and Features
Sample Tasks
Task
A
Level of
Cognitive Demand
Doing Mathematics
Explanation of
Categorization
Features
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
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)
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Factors associated with the decline of HighLevel 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 highlevel performance
• Task build on students’ prior knowledge
• Sufficient time to explore
(Adapted from Stein, Smith, Henningsen, & Silver, (2009))
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www.mmp.uwm.edu
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