Are All Math Tasks Created
Equally?
Lee Ann Pruske
Dana Thome
Pruskelx @Milwaukee.k12.wi.us
[email protected]
National Conference of Teachers of Mathematics
Indianapolis, IN
April 2011
We Are Learning To . . .
Understand and identify the
cognitive demand levels of
mathematical tasks.
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Success Criteria
We will be successful if at the end of the
session, we can understand and identify
the features of the four levels of
cognitive demand of mathematical
tasks, and begin to understand where
the tasks are located in your textbook
materials.
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Building Academic Vocabulary
Discuss with your shoulder partner what
you think Cognitive Demand is.
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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, (2000)
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Reading: “Analyzing Mathematics
Instructional Tasks”
Individually read the article.
Each person share one idea from the
article at your table.
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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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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.
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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
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Materials Discussion
Where do you find high level cognitive
demand questions in your curricular
materials?
Turn and talk to a neighbor.
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“When teachers take the
opportunity to analyze the tasks,
they become more alert to the
potential for slippage between
intentions and actions in their
teaching.
Stein, Smith, Henningsen, & Silver, (2000)
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Success Criteria
We will be successful if at the end of the
session, we can understand and identify
the features of the four levels of
cognitive demand of mathematical
tasks, and begin to understand where
the tasks are located in your textbook
materials.
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Take Aways…
As you walk away, think about these three
questions:
Which of the four levels of cognitive demand
are you most comfortable with?
Which one do you understand the least?
Something I want to know more about is…?
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Thank you for coming!
Resources can be found at
www.mmp.uwm.edu
Pruskelx @Milwaukee.k12.WI.US
[email protected]
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation
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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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