Professional Organization of Educators
President, Colorado Council of Teachers of Mathematics
President’s Message in the Spring 2016 issue of the Colorado Mathematics Teacher (CMT), the CCTM professional journal.
A coworker of mine creates puzzles and posts them for us to solve. Here’s a recent one:
ipip ipip ipip
ipip ipip ipip
ipip ipip ipip
ipip ipip ipip
Invariably, someone in the office gets an answer really quickly, and you’ll hear a chorus of “Wait! Don’t tell me!”
This phrase is one of my favorites as a math teacher – when my students would say, “Wait! Don’t tell
me,” I knew they were hooked. They wanted to figure things out for themselves, and it was exciting to struggle the right amount. They preferred a bit of struggle over just being told how to solve a problem or find an answer. In Principles to Actions, NCTM names “supporting productive struggle in learning mathematics” as one of the Mathematics Teaching Practices.
As teachers, there is a temptation to keep our students from struggling. The word itself brings a
negative connotation, and many of us became teachers because we want to help,not because we want students to struggle! Many of us have seen students struggle to the point of frustration,
causing them to give up, shut down, or become disruptive to the learning of others.
However, productive struggle doesn’t create those negative feelings or behaviors.
The good kind of struggle feels more like wanting to solve that puzzle myself, without someone just telling me the answer. Accomplishing something that is difficult is far more rewarding than accomplishing something that was made easy.
So how do we keep struggle from becoming unproductive? In this article, “Support Struggling Students with Academic Rigor,” published by ASCD (formerly doing business as the Association for Supervision and Curriculum Development), Robyn Jackson contrasts productive struggle with destructive struggle. She suggests that learning happens when students struggle
in ways that lead to understanding, that make their effort feel worthwhile, and that leave them feeling
empowered and efficacious. Alternately, learning is blocked when students’ struggle leaves them feeling frustrated, abandoned, and inadequate. Teachers can plan for productive struggle by providing rich tasks and problems for students to engage with, anticipating student difficulties, and planning questions and supports that don’t remove all opportunity to struggle.
For instance, when fifth grade students begin adding and subtracting fractions with unlike denominators (CCSSM 5.NF.A.1), a problem such as 2/3 + 5/4 might be a struggle. If directed to reason about the relative size of each fraction in order to estimate the value of their sum, students can move past an initial block and begin to consider their previous work with fractions as inroads to understanding the problem. They might consider using fraction manipulatives, a number line model, or their own sketch to conclude that the sum is close to two. A teacher might suggest a strip diagram to help students consider the different size parts of each fraction, and a well-formulated question can activate students’ background knowledge about equivalent fractions, allowing them to reason their way to the sum of 23/12 without being told a specific algorithm or approach for calculating this answer. Teachers planning together in a PLC or grade-level team can support one another in designing the right questions, suggestions, and tools that keep students in the sweet spot of struggle that is productive.
As you grapple with creating productive struggle for your own students, you might consider Carol
Dweck’s book Mindset, or Jo Boaler’s article “Unlocking Students’ Math Potential” (found here), or Triumph Learning’s research summary white paper “Productive Struggle for Deeper Learning”
(found here), all of which enhance the ideas in Principles to Actions. I’d love to hear
what other resources you’ve found helpful, or what you’ve learned about how to foster productive
struggle in your classroom. Write me and tell me about it (email@example.com)!
When I first began my teaching career, I thought my measure of success would be my students telling me that math was easy. Now, however, I would prefer my students say that math is sometimes hard, that it is worth working at, and that math always makes sense. Still wondering about the ipip puzzle? Here’s a hint: it’s a great riddle for a third grade math student!