Encouraging Productive Struggle in Math: Building Number Sense and Independent Thinkers

By Brittany Goerig

Basic math fact recall remains important, but instruction should go further. Teachers must help students understand the relationships between numbers so they can develop flexible strategies and solve problems independently. When students learn that productive struggle is a normal—and valuable—part of learning mathematics, they become stronger critical thinkers and better prepared for future academic work and careers.

Preparing students to navigate an uncertain job market requires teaching them to think for themselves. Encouraging productive struggle, fostering a collaborative community of learners, and integrating regular math talks cultivate the number sense and reasoning skills students need. These classroom practices create confident, independent problem solvers who can choose efficient strategies and justify their thinking.

Struggling Is Productive

Modern math classrooms increasingly embrace productive struggle by allowing students time to reason through problems rather than rushing to the correct answer. Instead of teachers prescribing procedures, they present tasks that invite students to explore and notice numerical patterns. Over time, students internalize strategies naturally after working with a series of related problems, often called number strings, which highlight relationships within and between numbers.

When students are given space to wrestle with ideas, the strategies they develop arise from meaning and sense-making, not rote memorization. This process builds deeper understanding and transferable skills: students learn why a method works and when it is useful, which prepares them for more advanced concepts such as proportional and functional reasoning.

Creating a Community of Learners

Math is not simply black-and-white. Some approaches are more efficient or elegant than others, but all strategies can be useful stepping stones. Teachers can build a community of learners by valuing every student’s voice and ability, encouraging explanation and justification, and treating mistakes as learning opportunities. A classroom culture that accepts varied answers and invites students to discuss their thinking creates safety for risk-taking and growth.

Research highlighted by Pamela Weber Harris shows that students typically progress from counting strategies to additive thinking, then to multiplicative and proportional thinking. For example, a student thinking additively about 8 + 7 might see 8 + 2 = 10 and then add the remaining 5 to get 15. As students advance, they begin to think multiplicatively—seeing groups of numbers—so a problem like 6 × 7 might be reasoned as 6 × 6 = 36 plus one more group of 6 equals 42.

When students remain stuck in counting-by-ones, they face difficulties later when instruction moves toward proportional and functional reasoning. Creating routines and tasks that promote efficient strategies helps students make the transition from counting to chunking and grouping numbers. This shift supports long-term mathematical growth and prepares learners for complex problem solving in middle school and beyond.

In my teaching experience, I accepted all answers when students posted or shared them. When students explained an incorrect answer, they frequently recognized the error in the act of explaining and corrected their reasoning for the class. Rather than penalizing wrong answers, I treated them as opportunities to try alternate approaches and to model how mathematicians refine thinking. The goal is to build a safe environment where learners can take intellectual risks and develop a deeper comprehension of concepts.

Incorporating Math Talks

Math talks are a practical, classroom-based strategy for making students’ thinking visible. The aim is for students to look at a problem and determine which strategy best fits the numbers involved. Because much of strategy selection occurs mentally and may not appear on paper, guided conversations allow classmates to hear and see multiple approaches. Teachers gain insight into students’ thought processes, and students learn from peers’ strategies.

For example, if a student explains 7 + 8 by saying “8 + 2 = 10, plus 5 equals 15,” the teacher sees an additive chunking strategy. If another student counts up from 8—“9, 10, 11, 12, 13, 14, 15”—the teacher recognizes an opportunity to introduce a more efficient approach. Presenting a targeted number string that models chunking can help the second student adopt a faster method. Math talks focus on reasoning rather than speed: they are brainstorming sessions about the most efficient and flexible paths to a solution.

Regularly scheduled math talks followed by targeted practice help students notice patterns, compare strategies, and refine their approaches. Over time, learners gain an internal toolkit of methods they can choose from depending on the problem, enhancing both accuracy and fluency.

Practical Steps for Teachers

– Present number strings that build on one another so students can detect patterns.
– Encourage multiple solution paths and invite students to explain their reasoning aloud.
– Normalize productive struggle and frame mistakes as diagnostic moments for instruction.
– Use math talks to surface strategies and decide which concepts need further modeling.
– Create routines that move students from counting to additive thinking, then to multiplicative and proportional reasoning.

By emphasizing productive struggle, fostering a respectful classroom community, and using math talks to make thinking explicit, educators can develop students’ number sense and mathematical reasoning. These practices produce learners who can select efficient strategies, justify their choices, and adapt their thinking as problems become more complex.

About the Author

Brittany Goerig is a product manager at hand2mind and lead author and co-creator of Daily Math Fluency. Before that, she served as a K–5 mathematics consultant and was an elementary and middle school teacher for 17 years.

This article was originally published by The Learning Counsel, a research institute and news media hub focused on the shift in education to digital curriculum.