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?

Math Framework for Differentiation

Differentiation in the math classroom requires some intentional planning to address the various readiness levels of students in the classroom. Here is a template to help create a canvas for differentiation for an upcoming unit or topic. By creating a framework, it allows students to enter learning at their level while ultimately having the goal to move students to a higher level of challenge. Click on the image below to download a copy.

Here is an example of a completed math framework. This example has many varied activities to address the different readiness levels of students. The goal is to pick and choose resources and ideas that keep the level of challenge appropriate. Recycling these skills throughout the school year by revisiting the framework can benefit students. After a unit, it is important to go back and reflect on what worked and what did not work. With each school year, the framework may need to be tweaked based on the readiness levels of students. Click on the image to grab a copy.

To begin, start with the standards. It is important to integrate content standards and Standards for Mathematical Practice. By flipping the standards to "I Can..." statements, it makes them more accessible to students.

Keeping a pulse on student readiness helps drive differentiation throughout a unit or topic. It is important to identify that zone of proximal development for students where there is the right amount of challenge where learning takes place ~ not too easy, not too hard. To address student readiness levels consider varying the challenge for students and having students choose the "right fit" when completing problems.

Varying the challenge for students can be accomplished through "What's Your Path?" This structure is designed prior to a unit of instruction. To design a "What's Your Path?" for a unit consider your curricular resources and other supplemental materials that will provide the right amount of challenge for students. It is helpful to use preassessment data when crafting the paths. Based on student readiness, students can enter either Path A or Path B. Path A being the on level skill/standard; Path B allowing for the extension of a particular skill. The goal to keep in mind is that entering the paths is fluid for students based on readiness at any given time during a unit. Click on the image below to grab a copy.

Choosing the Right Fit is another way to address the various readiness levels of students in the classroom. When students are asked to problem solve simply remove the numbers and wa-la, you have created a differentiated task. The integrity of the math problem does not change. Only the numbers do. Differentiated sets of numbers can be added for students to then "choose the right fit." In this way, students have some control over the level of difficulty. Or, all numbers can be removed.  Students drive for understanding by choosing "right fit" numbers that they feel are an appropriate challenge for them. Sometimes when students select their own numbers, they may find that their chosen numbers will not necessarily work with the problem. What a great learning experience for them to discover!

Locating resources to address the readiness levels of students can be challenging at times. Here is a list of some sites that might be helpful in planning differentiated learning opportunities for students.

Get to Know Your Students as Mathematicians

Getting to know your students as mathematicians can help with differentiation in the math class. As teachers, we gather data about our students through observations, class performance, and assessments. We also can learn about students by asking them to reflect upon themselves as mathematicians.

Below you can find three surveys students can fill out to reflect who they are as learners. Students simply shade in the heights of the bars in terms of how much each column relates to them. Add the element of color and display to spotlight learners as mathematicians. This metacognitive reflection on behalf of students can go a long way. When completing these surveys, students are creating a voice and leaving an imprint for themselves as learners. Use these charts in planning different learning opportunities for your students. Have your students tap into areas of strength and venture into areas that may not always be in their comfort zone.

These surveys can be shared with parents as well to help them see their child's perception of himself/herself as a learner.

Having students fill these surveys out at the beginning of the year, middle of the year, and end of the year can help students reflect on changes they may have seen occur throughout the year. Students can be challenged to create goals to become more comfortable in areas that may not be their strengths.

My Math-o-Meter can be used by students to rank their comfort level with each of the concepts.

The Math Survey can be used to tap into your aspiring mathematicians' learning styles.

The To Show What I Know... survey can be used for students to view themselves through a different lens and not just as mathematicians.

What are some ways you get to know your students as mathematicians?