Are All Math Tasks Created Equally? Lee Ann Pruske Dana Thome Pruskelx @Milwaukee.k12.wi.us Thomedk@Milwaukee.k12.wi.us National Conference of Teachers of Mathematics Indianapolis, IN April 2011 Add mps logo

We Are Learning To . . . Understand and identify the cognitive demand levels of mathematical tasks.

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.

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

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

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.

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

Pink handout

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.

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

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

“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)

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.

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…?

Thank you for coming! www.mmp.uwm.edu Resources can be found at Pruskelx @Milwaukee.k12.WI.US Thomedk@Milwaukee.k12.WI.US Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation

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)