The Cognitive Demand of Tasks

How does the selection of high level tasks prepare our students to meet the demands of the Common Core Learning Standards?

CFN 609 Principals’ Conference February 7, 2013

As we move into the second decade of the 21st century, one thing is clear:

Our country needs highly trained workers who can wrestle with complex problems. Especially needed are individuals who can think, reason and engage effectively in quantitative problem solving. Research shows the instructional practices used in many of our nation’s classrooms will not prepare students

for these new demands.

National studies have shown that American students are not routinely asked to engage in conceptual thinking or complex problem solving.

If we want students to develop the capacity to think, reason, and problem solve then we need to start with high-level, cognitively complex tasks.

Tasks are central to students’ learning, shaping not only their opportunity to learn but also their view of the subject matter. We learn through a process of

knowledge construction that requires us to actively manipulate and refine information and then integrate it with our prior understandings.

Quote 1 : 5 Practices for orchestrating Productive Mathematics Discussions, Smith and Stein, Quote 3: Educational Research and Evaluation, 2(4) Stein, M.K, 1996, Quote 2: Stigler and Hiebert 1999, Quote 4: Adding it up, NRC 2001

Quality Review Rubric: 1.1Designing engaging, rigorous and coherent curricula….

Well Developed:B) Rigorous habits and Higher- order skills are emphasized in

curricula and academic tasks and are embedded in a coherent way across grades and subjects so that all learners, including

ELLs and SWDs, must demonstrate their thinking.C) Curricula and academic tasks are planned and refined using

student work and data so that individual and groups of students, including the lowest and highest achieving students, ELLs and

SWDs, are cognitively engaged.

Danielson’s Framework for Teaching: 1e

Highly EffectivePlans represent the coordination of in-depth content

knowledge, understanding of different students’ needs and available resources (including technology), resulting in a series of

learning activities designed to engage students in high-level cognitive activity. These are differentiated, as appropriate, for

individual learners. Instructional groups are varied as appropriate, with some opportunity for student choice. The lesson’s or unit’s structure is clear and allows for different

pathways according to diverse student needs.

How can we make sure we are providing our students with opportunities to engage with

high level tasks?

The Task Analysis Guide ( Smith and Stein 1998)

The Task Analysis Guide provides a general list of characteristics of low-level and high level

mathematical tasks and thus can be used to analyze the potential of tasks to support students’ thinking

and reasoning. The guide is intended to help teachers match tasks with their goals for student

learning.

5 Practices for Orchestrating Productive Mathematics Discussions, Smith and Stein 2011

Mathematics Task Analysis Guide

At your tables:

• Take a moment to review the Task Analysis Guide (TAG).

• Work through the four tasks independently (or with a partner). Use the TAG to determine the cognitive demand of each of the tasks.

• Share your categorization in pairs then as a table. Be prepared to justify your conclusions using the TAG. Come to consensus at the table.

Proportional Relationships

Use the TAG to determine the cognitive demand of each of the tasks. Share your categorization in pairs then as a table. Be prepared to justify your conclusions using

the tag.Identify the CCSS for Mathematical Content and Practices used.

Subtraction Tasks

Use the TAG to determine the cognitive demand of each of the tasks. Share your categorization in pairs then as a table.. Be prepared to justify your conclusions using

the tag.Identify the CCSS for Mathematical Content and Practices used.

Math Task Analysis Guide Reflections

What are your thoughts on the process of identifying the characteristics that best

describe the cognitive demand of each task?

How might teams of teachers integrate this tool and what are the implications?

At your tables:

Identify the CCLS for Mathematical Content and which Math Practices students will have the

opportunity to use. Which standard/s are best addressed by these

tasks?

Relating the cognitive demand of tasks to the Mathematical Practices…

What relationships do you notice between the cognitive demand of the written tasks and the

CCSS for mathematical Practices listed?

Characteristics of Tasks that align with CCLS standards for Mathematical Practice

• High Cognitive Demand (Stein et. al., 1996; Boaler & Staples, 2008

• Significant Content, meaning they have the potential to leave behind important residue (Hiebert et.al, 19970

• Require justification or explanation (Boaler and Staple, 2008)• Make connections between two or more representations

(Lesh, Post& Behr, 1987)• Open Ended (Lotan, 2003; Borasi & Fonzi, 2002)• Multiple ways to enter the task and show competence

(Lotan, 2003)

Increasing the Cognitive Demand of TasksStrategies for Modifying Textbook Tasks

Sources for Developing Rich tasks

• Exemplars• Modifying existing Textbook/Program tasks• DOE Instructional Bundles• www.Parrconline.org• www.georgiastandards.org• www.schools.utah.gov• www.EngageNY.org• www.illustrativemathematics.org• www.map.mathshell.org• www.insidemathematics.org

Tasks“There is no decision that teachers make that has a greater

impact on students’ opportunities to learn, and on their perceptions about what mathematics is, than the selection or creation of the tasks with which the teacher engages students in studying mathematics.”

Lappan and Briars, 1995

“Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking.”

Stein, Smith, Henningsen, & Silver, 200

“Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking.”

Stein, Smith, Henningsen, & Silver, 2000

Thank you for your attention.