Productive Struggle & Math Rigor

Importance of Productive Struggle in Math

The process of productive struggle has encouraging applications to math education in particular. Only 33% of US eighth-graders scored “proficient” or “advanced” in math on the National Assessment of Educational Progress in 2015, leading many students to feel like they are not a “math person”, even though research shows everyone is capable of mathematical thinking.

It’s often the quick calculators and good memorizers who are praised the most in math class. However, Stanford professor Jo Boaler warns that instruction based solely on memorization and arithmetic can lead students to misunderstand and dislike math. Test results show that the highest achievers are those who can see the bigger picture and make connections between different mathematical concepts. There’s a growing body of research that shows that getting students to the point of productive struggle is one of the keys to achieving deeper learning and creative problem solving.

“We don’t need students to calculate quickly in math. We need students who can ask good questions, map out pathways, reason about complex solutions, set up models and communicate in different forms.”

How productive struggle can help prepare students for new assessment problems

No longer do assessment questions merely ask students to apply the procedure to the problem. Instead, students are asked to come up with the procedure on their own.

Old Sample Test Question:

Source: Grade 5 from the
California Standards Test (California Dept. of Ed)

New Sample Test Question:

Source: Sample grade 5 math problem from
Smarter Balanced Assessment Consortium

Consider how this 5th grade sample high-stakes test question could be solved in multiple different ways.

To solve the problem, students must have a conceptual understanding of the question and then employ their own creative solution. The graphic above shows three ways to visualize the solution to the problem, and three methods to arrive at a solution.

It is important that we teach students early on that they are free to apply their own unique thought process when faced with new problems.

By providing opportunities for students to share their reasoning and celebrating their different ways of thinking, teachers will encourage the process of productive struggle. Students engaged in this process build the creativity and confidence that allows them to attempt new challenges and problems they have never seen before.

How Can Productive Struggle Help Build Mathematical Rigor?

The goal of rigorous math instruction is to guide students toward becoming highly capable creative problem solvers in non-routine situations. Productive struggle is a state of effortful learning that helps students builds these skills.

When creative thinking and non-routine application of concepts is high and remains high, students are experiencing the kind of rigorous problem solving that encourages deeper learning. Productive struggle is like a muscle, the more students experience it, the longer they can persist and engage in this high level of thinking.