Productive Struggle in Math

When differentiation is part of classroom instruction it is helpful to create a learning environment that has clear expectations.

Productive struggle in math is one expectation that should be required of ALL students. The type of scaffolding provided can be differentiated based on student readiness levels, yet it is important not to lose the integrity of the math problem/task. Productive struggle is one of the eight lesson components outlined by the Principles to Actions (NCTM 2014). It encourages students to become mathematical thinkers. When encouraging productive struggle, it is important to focus on the strategies students use and the footprints of thinking they show when trying to solve a problem. Students need to accept that the process of grappling with a problem is just as important as the answer.

What might this look like in the classroom? What are some examples of productive struggle math problems? One lens to look at is opening up problems. In other words, offer problems that have multiple entry points for students of different readiness levels and that have more than one solution.

Here's the Answer...What's the Question is a strategy that allows students to generate many varied responses to one answer. Displaying student responses can help broaden students' understanding and allow students to see the different lenses that can be used to "see" mathematics. Click on the image below to grab a copy of these cards and see an example of possible responses.

Here is another idea. Pose a problem with various details. Notice there is no question. Click on the image below to grab a copy.
There are two options for how to proceed with this type of problem. Have students create a question based on the information provided. Students will have to be selective in what information they want to use when creating their problems. Depending on readiness levels, criteria can be given to provide more structure in determining the type of problem students need to generate. Students then should solve their problems to ensure that the problem they created is doable. Students then can exchange problems with each other.

A different twist on this activity would be to create questions and have groups of students sift through the information presented to find the information necessary to solve their particular problem. Students can list the necessary information and then solve showing their footprints of thinking on chart paper or by using an online whiteboard or screencasting tool. Students can share out and notice the similarities and differences between the data needed to solve each problem. The discussion can lead to how determining what is important is based on the purpose of a given task. Click on the image below to grab a copy.
Here are some posters to inspire productive struggle. You can click on the image below to grab a copy.

How do you create experiences of productive struggle for students in your classroom?
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