By Derek Pipkorn, posted August 3, 2015 –

In my first post, I emphasized the importance of finding the greatest area of need in a mathematics classroom. After discovering that fostering productive struggle would become the focus at my school, I set out to create opportunities for my students to struggle and fail collectively. My goal for this post is to share an example of how I fostered productive struggle, as well as show the feedback I received from my students during this transformative year of struggle.

This year, I taught eighth-grade Honors Geometry. My group of students had high expectations for themselves, as they’ve always easily found success in mathematics. I shared early on that it was my intent to push them toward failure because this would build them up for success. Believe me when I say that their jaws dropped to the floor. They’ve never had a teacher tell them that there is an expectation of failure. My analogy of a trainer working with a professional athlete helped them better understand my intentions.

Option A vs. Option B

I’ve shared two options of how to go about teaching tangent and secant segments. In years past, I would have used Option A because I needed to keep up with pacing and knew that I would find immediate success. Students would be asked to replicate this example over and over with several combinations of numbers and variables.

 Option A:

With Option B, I simply share the theorem and let my students go. The only direction I gave them was that they must create a sketch and show a proof of the theorem. After each student individually made an attempt, the noise level in the room slowly built until everyone was justifying their thinking and critiquing the reasoning of others. Does this sound familiar? (M.P.3) The beauty of Option B is that most students were asking questions of their peers to better understand the mathematics. I was there to facilitate, but I rarely needed to step in during their moments of struggle.        

Option B:

If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.

After teaching both Option A and Option B, the level of understanding that my students gained after completing this exercise was apparent. The energy exhibited in the classroom from students persevering through their struggles was exhilarating.

This is an example of the type of feedback I’ve received from my students all year. Fostering productive struggle in a mathematics classroom builds a stronger classroom community and helps achieve a growth mindset in all of our students. As Principles to Actions: Ensuring Mathematical Success for All reminds us, “Teaching that embraces and uses productive struggle leads to long-term benefits, with students more able to apply their learning to new problem situations” (NCTM 2014, p. 48).

In my next post, I will share what it takes to help create a classroom of mathematically proficient students. 

Derek Pipkorn, dpipkorn@mtsd.k12.wi.us, is the middle school math specialist for the Mequon-Thiensville School District in Mequon, Wisconsin. He is an Editorial Panel member for NCTM’s Classroom Resources Committee and a Board Member on the Wisconsin Math Council. Pipkorn can be found tweeting at @mrpipkorn.