Exploring Cognitive DemandsPart 2

Rosann Hollinger Lee Ann Pruske

Sharonda M. Harris Bernard Rahming

January 20, 28, 2010

Math Teacher Leader Meeting

Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation

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We Are Learning To . . .

1. Further our understanding of the cognitive demands of mathematical tasks.

2. Explore the factors associated with the decline or maintenance of cognitive demands.

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Success Criteria

You will be successful if at the end of the session you can– identify the cognitive demand levels of

mathematical tasks– describe the factors that lead to the maintenance or

decline of high-level cognitive demands during setup and implementation of mathematical tasks.

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Cognitive Demands…

“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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The Fencing Task Ms. Brown’s class will raise rabbits for their spring science fair.

They have 24 feet of fencing with which to build a rectangular rabbit pen to keep the rabbits.

a) If Ms. Brown’s students want their rabbits to have as much room as

possible, how long would each of the slides of the pen be?

b) How long would each of the sides of the pen be if had only 16 feet of fencing?

c) How would you go about determining the pen with the most room for any amount of fencing? Organize your work so that someone else who reads it will understand it.

Source: Stein, Smith, Henningsen, & Silver, (2000)

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Math Task Discussion

Individually work on the problem

Share your problem solutions at your table

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Math Task

Cognitive Demand Level

Individually work on the problem

Share your problem solutions at your table

Using the handouts from December, determine the cognitive demand level of the math task.

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Four Levels of Cognitive Demands 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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Reading: “Using Cognitively Complex Tasks in the Classroom”

Individually read pages 24-26.

Reading Lens: In what ways do teacher actions during the setup and implementation phases impact the cognitive demands of mathematical tasks?

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Mathematical Tasks Definition

“…not only the problems written in the textbook or a teacher’s lesson plan, but also the classroom activity that surrounds the way in which those problems are set up and actually carried out by teachers and students.”

Stein, Smith, Henningsen, & Silver, (2000)

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Tasks in the Classroom

Setup Phase: Teacher communicates to students expectations- what to do, how to do it, and with which resources.

Implementation Phase: From the time students begin to work until the next task begins.

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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 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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Cognitive Demands and Features

Task Level of Cognitive Demand

Explanation of Categorization

Features

Fencing Problem

Doing Mathematics There is no pathway suggested by the task. The focus is on looking for the underlying mathematical structure.

•Requires an explanation•Involves multiple steps•Uses a diagram

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Group Reading Activity

Table Group Readings1~ “Maintenance of high-level cognitive demands”

2~ “Decline into procedures”

3~ “Decline into unsystematic exploration”

4~ “Decline into nonmathematical activity”

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Group Poster Activity

1~Maintenance 2~Procedures3~Unsystematic 4~ Nonmathematical

Individually read your section

As a group discuss the highlights of the section

Create one poster per section capturing the important points (What Teachers do/Students do)

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Poster Presentations

In your notebook create a graphic organizer for note taking

Maintenance of high-level cognitive demands

Decline into procedures

Decline into unsystematic exploration

Decline into nonmathematical activity

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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 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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December Homework

Mathematical Tasks Discussion

Each person presents one of their tasks.

Justify why it is Doing Mathematics or Procedures with Connections

As a table group, discuss the possible factors involved in maintaining or declining the level of cognitive demands in the set up or implementation phases of the math task in the classroom.

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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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Building Academic Vocabulary

Cognitive Demand

Step 5: Think – Pair - Share

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Success Criteria

You will be successful if at the end of the session you can– identify the cognitive demand levels of

mathematical tasks– describe the factors that lead to the maintenance

or decline of high-level cognitive demands during setup and implementation of mathematical tasks.

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Feedback Form Question

In what ways have you used your knowledge and understanding of cognitive demands in your roles of “leader of self” and “leader of others”?