The Struggle is Real: Tasks, Academic Status and Productive Problem-Solving

By Geoff Krall
October 26, 2016

As we wonder why students fail to persevere in problem solving, it behooves us to consider the accumulating layers of math experiences and messages students have received and how that is manifesting itself in our classrooms. Instead of asking, “why won’t my students work harder?” it might be worth considering what they think of themselves as young mathematicians (or even if they think of themselves as young mathematicians). 

Students do not experience math in isolation. As they engage in a task they bring to the table years of accumulated experience and varying levels of self worth in mathematics. Recent research on mindsets and mathematics is both highly informative and a bit daunting. It’s terrifying and potentially paralyzing to consider that the real issue a student is having may not be that they fail to understand the Pythagorean Theorem, but rather that they view themselves as bad at math (and that they fail to understand the Pythagorean Theorem). The former is much easier to rectify. It’s relatively easy to design a lesson on, say, periodic functions. It is incredibly challenging to design a lesson on periodic functions that explicitly and universally sends the message that each student is a smart and capable mathematician. And then to reinforce that message throughout the course of a school year. 

And yet, a great teacher does just that. She employs high quality tasks and works to rebuild student mindsets about themselves as mathematicians, or their “status.” And the two interact with one another bidirectionally: tasks and status, status and tasks. There is an inextricable link between the tasks that teachers are employing and academic status of a student. A student that finds meaning in a task and thinks of themselves as mathematical is more likely to persist in productive struggle. 

Students experience years of mathematics before they enter your classroom. They may enter with a negative view of the discipline and a negative view of themselves in the discipline. It takes sustained effort and doggedness to chip away at those layers of sediment that have built up over time. But it is possible. New research and strategies are providing pathways forward that ensure that students can rebuild their own self-worth in math. Of course, it does take consistent vigilance, time, and effort. So one might say to a teacher: this is our problem through which we must productively struggle.

Be sure not to miss Geoff's session at the 2017 NCTM Annual Meeting in San Antonio:

The Struggle is Real: Tasks, Academic Status and Productive Problem-Solving
Developing a culture of productive struggle in classrooms requires holistic vigilance. We often treat such problems in isolation: if only I had the right tasks, if only students demonstrated enough grit, if only... We'll examine the relationship between quality tasks and student mindsets which together promote an environment of productive struggle.