1. Are All Math Tasks Created Equally?
Lee Ann Pruske Dana Thome
National Conference of Teachers of Mathematics
Indianapolis, IN
April 2011
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2. We Are Learning To . . .
Understand and identify the cognitive demand levels of mathematical tasks.

3. 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.

4. Building Academic Vocabulary
Discuss with your shoulder partner what you think Cognitive Demand is.

5. 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)
At about 5 min now

6. Reading: “Analyzing Mathematics Instructional Tasks”
Individually read the article.
Each person share one idea from the article at your table.
10-15 min with debrief Decide what the debrief is and which big ideas should be surfaced.

7. 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

8. Pink handout

9. 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.
10 min to sort 15 min to debrief.

10. Explanation of Categorization
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
Handout key to groups

11. Materials Discussion
Where do you find high level cognitive demand questions in your curricular materials?
Turn and talk to a neighbor.
5 min discussion

12. “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)

13. 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.

14. 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…?

15. Thank you for coming! www.mmp.uwm.edu Resources can be found at
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation

16. Mathematical Tasks Framework
Figure 1.3
TASKS
As they appear in curricular/ instructional materials
As set up by teachers
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)