Exploring Cognitive Demands of Mathematical Tasks

Milwaukee Public School

Bernard Rahming

Mathematics Teaching Specialistrahminbv@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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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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