Math: The Pros & Cons of Productive Struggle

In a recent post, I wrote about card sorts as a tool to promote mathematical conversations and mentioned the value of “productive struggle” in the math classroom.

This phrase has recently appeared on the growing list of educational buzzwords that are part of our professional lives these days.

Although I am personally convinced that productive struggle is a necessary component for student growth, I am less sure of how to successfully implement it my own classroom.

So the thought of how to help my students engage in productive struggle has been on my mind all summer. I started by researching the origins of the phrase, which can be defined as “students expend(ing) effort to make sense of mathematics, to figure something out that is not immediately apparent” (Hiebert and Grouws, 2007).

That didn’t sound so intimidating. Teachers certainly want students to put forth effort to find out things that aren’t instantly apparent. I went on to read many interesting articles and studies regarding productive struggle. I’ve learned a lot, although I am by no means an expert. I’d definitely consider myself a novice in this area.

When it comes to productive struggle, there are so many questions to address. A few that come to mind are:

• How much guidance should the teacher provide?
• What “hints” if any should be given to students?
• What type of work motivates students to engage in productive struggle?
• How do you insure that the struggle is productive and not merely frustrating?

These are questions I will continue to work on as the new school year unfolds. In the meantime, I’d like to invite you to engage in some discussion here. Let me start by sharing a recent personal experience I had as a student engaged in productive struggle.

Struggle, from the student point of view

When I attended several math workshops this summer, basically as a “student,” the idea of productive struggle was very much on my mind. In one workshop, we essentially worked various math problems with a partner, without direct instruction from our teacher.

This chance to put on the hat of a student learner is one of the best things that’s happened to me as an educator. The opportunity to struggle as I tried to figure things out provided some needed perspective on both the value of productive struggle and the potential pitfalls.

First, the positives

I learned so much more by puzzling out different problems for myself (and with a partner) than I would have if someone had just worked through the problem with me. For example, there was a certain problem that I could not get to make sense. It wasn’t really that hard; I just couldn’t make it “click.” I went home and let it percolate, and then I sat down to work on it some more, and it came to me. A formula suddenly made sense to me in a different way, and I did it for myself! I felt a tremendous amount of personal satisfaction.

As the workshops progressed, I enjoyed the challenge of solving problems that I didn’t know the answer to ahead of time (the situation our students are usually in). It was fun!

I know it’s unrealistic to think that students will always enjoy the activities we plan for them, but I do think that allowing students to engage in more frequent productive struggle can result in satisfaction, and even fun for some students, if properly scaffolded (which is another conversation).

I remember so much from the activities I worked on, especially the ones that were difficult for me. As a teacher, the “sticky learning” that resulted from working hard to find a solution made a big impression on me. Sometimes I get discouraged when students struggle, but I need to rethink that. So long as we’re supported and find our way through the challenge, struggle has some real benefits.

But there are potential pitfalls

I enjoyed my time as a student and the opportunity to engage in productive struggle. However, I can also attest to the frustration, irritation, and even embarrassment that was sometimes a by-product.

There were times when I did not feel like I had an entry point to begin working on a problem, and I couldn’t even think how to ask a good question. (Working with a partner helped – sometimes just a peek at their work was all I needed.)

Other times, I would be asked a question and find it difficult to put the answer into words. Sometimes it took me longer than one class to grasp a certain concept, and it might even be the next day before I fully understood it.

On several occasions I would work a problem differently than others in the group and would be embarrassed to share what I did, afraid that I had done it the “wrong way.” And there were times I wasn’t sure about my work and I didn’t want my instructor looking at my paper.

Haven’t we all had this same experience with our students? Until this summer, I don’t think I fully understood how vulnerable you feel when someone looks at your paper and can see any and all of your shortcomings and mistakes.

I do realize that a trusting classroom culture is a big part of making students feel comfortable, but that only goes so far. My teachers this summer were truly nice people and did a great job of creating very positive classroom cultures, yet I still struggled with feelings of inadequacy at times.

My summer take-aways

This is what I learned from my experience as a student:

• Students can experience significant personal satisfaction from productive struggle. (I did!) That brand of satisfaction cannot be purchased in any other way.
• Learning with a partner can take some of the frustration out of problem-solving while keeping the challenge (and the fun).
• Classroom culture is essential! I think empathy and respect help students work productively. It is vital to be respectful and sensitive to students’ feelings. I realized that I need to get to know my students even better, and I need to be aware that students have different comfort levels. (Note to self: spend more time at the beginning of the year getting acquainted).
• It’s okay if students make mistakes. Let them know that repeatedly. Making mistakes is simply part of the learning process. I made plenty this summer, and I learned more than I ever have.
• An activity is not automatically a failure if a student doesn’t finish in the time I have allotted. Time spent figuring things out is productive time.
  
• For productive struggle to be successful, students need to be given assignments that they are willing to “expend effort” on, as well as assignments that challenge them and stretch their thinking skills. At the same time, the assignment shouldn’t be so difficult that students become discouraged. Easy, right?

What have you noticed about “productive struggle” in your own classroom or professional learning experiences?

RESOURCES

► Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371–404).

► Harnessing the Power of the Productive Struggle (Ellie Cowen, Edutopia)

► Let Your Students Fail (Derek Pipkorn, Mathematics Teaching in the Middle School blog, National Council of Teachers of Mathematics)

► Productive Struggle – Part 2 (Andrew Stadel’s blog)

► Productive Struggle in Mathematics (Interactive STEM Research Brief, Education Development Center)

► The Role of Productive Struggle in Teaching and Learning Middle School Mathematics (Hiroko K. Warshauer)