Cognitively Demanding Tasks

Overview

Providing math tasks with high cognitive demand conveys high expectations for all students by challenging them to engage in higher-order thinking. When students work with these complex or ill-structured problems, they explore and make conceptual connections and can practice Algebraic Thinking, Geometric Reasoning, and Statistical Reasoning.

Use It in the Classroom

Watch how this sixth grade teacher introduces an open-ended task. By allowing for multiple representations, students at different levels of prior understanding are able to successfully approach the same task in multiple ways.

Teachers should focus on helping each student achieve productive struggle as they work on these tasks. Differentiating support (e.g., providing background knowledge and/or targeted modeling) while still maintaining the rigor of the problem has been shown to be important in ensuring that all students engage in high-level thinking. Teachers can also assign these tasks individually to provide extra challenge or in a small group or whole class to provide supports. Whatever the structure, it is critical for teachers to ask probing questions and provide feedback during the process, and having discussions after these tasks builds Mathematical Flexibility and provides opportunities to address misconceptions.

Design It into Your Product

Videos are chosen as examples of strategies in action. These choices are not endorsements of the products or evidence of use of research to develop the feature.

Learn how ST Math requires students to problem solve through exploration. As students solve these challenging, cognitively demanding puzzles, they develop their conceptual understanding in topics like Algebraic Thinking and Proportional Reasoning.

Products can also use cognitively demanding tasks to focus students' Attention on the underlying concepts behind math procedures like Operations. To build conceptual knowledge, one of the primary goals of these tasks, products must provide what research describes as "sufficient (not too little, not too much)" time for students to use cognitive effort and solve these problems. Designing ways to monitor if students are still working through the task or have become disengaged can help find the right time for each student.

View References

Resources

Below are additional examples, research, and professional development. These resources are possible representations of this strategy, not endorsements.

Examples

Creating a Math Task Culture

Video of several classroom examples of using cognitively demanding tasks

Examples

Problems of the Month

CCSS-aligned math tasks targeting math thinking and reasoning

Professional Development

Productive Struggle

Free CE-credit webinar where teachers discuss how to build deep conceptual understanding in mathematics

Professional Development

Tasks, Questions, and Practices

NCTM blog connecting math tasks to Standards for Mathematical Practice