Monday / September 16

# Planning for a Lesson with Productive Struggle

The importance of struggle comes into play when someone is learning to tie their shoes, drive a car, or perfect a jump shot. Working through the struggle allows the learner to be successful. A question to reflect upon: Do you value this same struggle for your students while learning mathematics?

If you answered yes, give yourself a pat on the back. Valuing struggle is an important step in utilizing productive struggle as it plays a crucial role in learning mathematics. However, simply proclaiming that struggle is important is not enough. You must make sure your actions in the classroom support what you value about struggle so learning is advanced. In Productive Math Struggle:  A 6-Point Action Plan for Fostering Perseverance, we explore six specific actions you can implement in your own context to ensure that your students are experiencing and learning from productive struggle during your mathematics lessons. Here, we share some instructional moves you can incorporate into your practice immediately that promote struggle.

### Planning for a Lesson with Productive Struggle

A good task is a necessary ingredient for allowing productive struggle to thrive because it asks students to think rather than repeat a procedure that has been taught. So in planning for a math lesson, it is vital to select a rich task for the students to investigate. Some curricular resources offer such a task. However, often there are instances when you might need to take an existing task and modify it. A strategy, such as Agree or Disagree, can be utilized to help you enrich a task. With this approach, you share a fictitious student’s reasoning (or strategy) and ask your students to determine whether they agree or disagree with the thinking. Here is an example:

 Original Task Modified Task With “Agree or Disagree” Strategy Find the sums.   3/4 + 7/4 = ______   2/3 + 2/3 = ______   1/5 + 2/5 = ______ Jason found the sum of 3/4 + 4/4 to be 7/8. Do you agree with Jason? Use pictures and numbers to show your thinking.

The original task requires students to add fractions with like denominators. Problems such as this invite the use of procedures and do not necessarily promote understanding. Due to the nature of the task, often more problems are given to students to fill instructional time. In contrast, the modified task draws students into thinking about Jason’s reasoning. This second task, which is more robust, allows students to grapple with a context and engage in sense making. In essence, it replaces quantity with quality.

Once a task is selected or modified, it is important to do the task and anticipate how students will attempt to solve it, both correctly and incorrectly. Working with colleagues is beneficial during this process as others often think of different strategies than you might on your own. As you engage in this anticipating step, also think about what you might do to support your students as they dive into the task. By having a better sense of the strategies your students might use, the places where they might experience struggle, and how you might respond in the moment, you can be more prepared to provide the appropriate support for students.

### Supporting the Productive Struggle During the Lesson

As a lesson unfolds, you make decisions on how to navigate student struggle. While there isn’t one tried and true method to use to do this, there are ‘struggle moves’ that you can consider to support students as they work through struggle. A ‘struggle move’ is an In-the-moment instructional decision intended to keep students on a trajectory towards the stated learning goal without removing the opportunity to engage in mathematical thinking.

One struggle move you can utilize when a student might be experiencing an impasse is to ask questions that prompt metacognitive thinking. This is simply asking students the questions you would ask yourself when you’re stuck. Such questions might include:

• What is something you know about the problem?
• Does this remind you of another problem?

While these questions may seem obvious, students may not initially come up with them on their own. Giving students something to ponder might be just what a student needs to jumpstart their thinking and continue working on the task.

To be best prepared to ask one of these metacognitive questions, it is important to take a moment during planning to think through what you might ask, when you might ask it, and how the question might be received. Is the question specific to the problem or generalizable to other problems? Is it a question that can be answered? Having a few questions in mind prior to the lesson decreases the likelihood you ask a question that adds to a student’s struggle during the lesson. Rather, you are ready to prompt a student to think about what they could do to work through it.

A second struggle move you can utilize while students are working on a task is to examine the numbers being used. Sometimes the struggle rests in performing calculations rather than in determining what calculations are needed to arrive at a solution. For example, if a task involves finding the volume with fractions, it is quite possible a student’s struggle is with performing operations with fractions rather than finding the volume. Suggesting a student initially try removing the numbers to think about what needs to be done may help them get started. Then, you may encourage the student to replace the fractions with whole numbers, which will allow them to focus on developing a strategy for finding volume. Once the solution path is determined, they can return to the original numbers to arrive at their answer.

While we have shared just a few instructional moves to capitalize on struggle, we hope you consider using one or more of these strategies in your mathematics classroom. It is important to note that there isn’t one right way to support students as they experience struggle during a math lesson. What works to support one student is often different than what is needed to support another student. However, by having a number of instructional strategies to draw upon, you can better assist all students as they engage in productive struggle to learn mathematics.

#### Tags

Susie Katt is the K-2 Mathematics Coordinator in Lincoln, Nebraska. In this role, she coordinates professional development, assessment, and curriculum development. Susie is an author for a national mathematics curriculum. She frequently speaks at state, regional, and national conferences. Susie is a special appointment lecturer for the University of Nebraska-Lincoln, a Robert Noyce Master Teaching Fellow, and a member of various state committees. She serves NCTM in a variety of ways which include chair of the Editorial Panel for the Teaching Children Mathematics journal, member of program committees for annual meetings and regional conferences, and speaker at NCTM institutes. Kevin J. Dykema is an 8th grade math teacher in Mattawan, Michigan and serves on several building and district committees. He is a professional learning consultant and is a frequent speaker at national, regional, and local conferences. Kevin is active in state and national professional organizations recently serving on the Board of Directors for the National Council of Teachers of Mathematics and as a board member and annual conference chair for the Michigan Council of Teachers of Mathematics.