Exploring Cognitive Demands Part 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

2 We Are Learning To Further our understanding of the cognitive demands of mathematical tasks. 2. Explore the factors associated with the decline or maintenance of cognitive demands.

3 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.

4 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)

5 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)

6 Math Task Discussion Individually work on the problem Share your problem solutions at your table

7 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.

8 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

9 Reading: “Using Cognitively Complex Tasks in the Classroom” Individually read pages Reading Lens: In what ways do teacher actions during the setup and implementation phases impact the cognitive demands of mathematical tasks?

10 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)

11 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.

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

13 Cognitive Demands and Features TaskLevel 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

14 Group Reading Activity Table Group Readings 1~ “Maintenance of high-level cognitive demands” 2~ “Decline into procedures” 3~ “Decline into unsystematic exploration” 4~ “Decline into nonmathematical activity”

15 Group Poster Activity 1~Maintenance 2~Procedures 3~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)

16 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

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

18 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.

19 “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)

20 Building Academic Vocabulary Cognitive Demand Step 5: Think – Pair - Share

21 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.

22 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”?