Productive Struggle in the Mathematics Classroom

Contributed by Sheila Aherin

“Many findings suggest that some form of struggle is a key ingredient in students’ conceptual learning.”   (Hiebert and Grouws 2007, 388).

The idea of allowing my students to “struggle” was counterintuitive to me as a teacher. It seemed much more efficient to walk students through one or more examples, and then students practiced what I showed them. I used manipulatives as a regular part of my instruction, and I modeled math concepts to help students understand. Students participated in hands-on activities similar to what I had modeled for them. This “I do/you do” structure was something that felt right to me in order for my students to develop conceptual understanding.

However, I began to learn more about the importance of productive struggle in developing conceptual understanding. I offered more challenging problems for students to tackle without my direct instruction. Students could try out and compare different strategies. Their understanding of mathematical concepts deepened. The power of productive struggle in developing deep conceptual understanding became clearer to me. I guess you could say that I experienced my own productive struggle in the process!

So my next challenge was to find additional, worthwhile tasks that my students would find interesting and that would also stretch their thinking. Supporting students as they work through these tasks can be tricky. I had to ask myself the following questions:

  • What strategies should I use to best support students’ work?
  • How do I encourage students to think about different ways to solve a problem?
  • How do I identify the difference between productive struggle and just struggling in general?
  • What questions do I ask to foster classroom conversation?

enVisionmath2.0 provides a Solve & Share task at the beginning of each lesson. This problem-based experience encourages students to try multiple strategies as they work to connect prior learning to the lesson. The Solve & Share encourages students to persevere in the development of deep mathematical understanding. They engage in productive struggle. Teacher’s Edition lesson notes include strategic questions to ask before, during, and after the task to facilitate students’ learning.

The print and online Teacher’s Edition provides sample student work so that students can critique strategies without feeling pressure to share their own work until they are ready.  Teachers collect students’ work; they can upload it right into the course to easily share in the future!

How do you support students as they work on the Solve & Share tasks? How do students share their work? What are some classroom management tips that you use to successfully manage these tasks?

To learn more about problem-based learning with your students, check out the My Pearson Training enVisionmath2.0 Problem Based Learning tutorial.

Hiebert, James S., and Douglas A. Grouws. 2007. “The Effects of Classroom Mathematics Teaching on Students’ Learning.” In F. K. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning, 371–404).Charlotte, NC: Information Age Publishing.

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