When many students (and sometimes parents) encounter difficulty in maths, they see it as a red flag — a sign they’re “not good at maths.” But research shows the opposite: grappling with challenges is not only normal, it’s necessary for developing mathematical understanding. This process is often called productive struggle — the idea that wrestling with ideas, making mistakes, and persisting through challenges are critical for deep learning.
What is Productive Struggle?
Productive struggle is the deliberate opportunity for students to engage with challenging mathematical tasks, rather than being given immediate answers or overly simplified steps. Hiebert and Grouws (2007) describe it as students “expending effort to make sense of mathematics, to figure something out that is not immediately apparent.” It’s not about frustration for its own sake, but about experiencing the right level of challenge.
As Peter Sullivan (2011) puts it:
“Students learn mathematics most effectively when they work on problems they do not yet know how to solve.”
This powerful idea captures why we should resist the temptation to rush in with answers.
Why is Struggle Important?
- Deeper Conceptual Understanding
When students are guided through struggle instead of being rescued, they’re more likely to connect ideas and build lasting understanding (Hiebert & Grouws, 2007).
- Growth Mindset and Resilience
Jo Boaler (2016) highlights that mistakes actually grow new synapses in the brain. Struggle shifts the narrative from “I can’t do this” to “I haven’t figured it out yet.”
- Confidence and Independence
Students who learn to persist through challenge develop mathematical confidence. They become more willing to attempt unfamiliar problems and less reliant on step-by-step instructions.
I remember when I was beginning to learn about teaching maths, I thought that being able to take every idea and break it down into incremental, bite-sized chunks was the most valuable skill for a teacher. There are times when this can be valuable for some students, but it is certainly not always the most effective approach. When every step is handed to them, learners may focus on memorising procedures rather than understanding underlying concepts or developing problem-solving skills. Just like a good teacher should be skilled at explicit instruction, as well as skilled at creating opportunities for student-led learning, and recognise the need for balancing these.
How Can Teachers and Tutors Foster Productive Struggle?
- Choose Rich Tasks
Use open-ended problems where there may be multiple solution strategies, such as investigations from NRICH or tasks that require reasoning beyond rote procedures. (There are links to wonderful sources of rich tasks included on my Resources page https://mathsthatclicks.net/resources )
- Ask Guiding Questions
Instead of telling students the next step, ask: “What do you notice?”, “Can you try a simpler case?”, or “What patterns are emerging?”
- Normalise Mistakes
Frame errors as evidence of thinking, not failure. Share your own “productive mistakes” when modelling solutions.
- Provide Strategic Scaffolds
Offer hints or structures that support thinking without removing the challenge. For example, break down a large problem into parts, or provide a visual representation.
- Use Enabling and Extension Prompts
An important skill for keeping students productively struggling is the creation of enabling and extension prompts — carefully designed questions or hints that guide thinking without giving away the answer. Sullivan, Mousley and Zevenbergen (2006 a,b) highlight how well-crafted prompts can scaffold learning, extend reasoning, and maintain engagement in challenging mathematical tasks. I’ll write about this topic in more detail in a future post, including practical examples of prompts that encourage persistence and deeper thinking.
Ultimately, learning to lean into struggle in maths mirrors life itself; real growth happens when we wrestle with challenges, not when the path is smooth. Helping students see this makes the classroom a place where they don’t just learn maths, but also resilience for the real world.
References
- Boaler, J. (2016). Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching. Jossey-Bass.
- Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 371–404). Charlotte, NC: Information Age.
- National Council of Teachers of Mathematics (NCTM). (2014). Principles to Actions: Ensuring Mathematical Success for All. NCTM.
- Sullivan, P. (2011). Teaching Mathematics: Using Research-Informed Strategies. Australian Council for Educational Research.
- Sullivan, P., Mousley, J., & Zevenbergen, R. L. (2006). Teacher actions to maximize mathematics learning opportunities in heterogeneous classrooms. International Journal of Science and Mathematics Education, 4(1), 117–143. https://doi.org/10.1007/s10763-005-9002-y
- Sullivan, P., Mousley, J., & Zevenbergen, R. L. (2006). Developing guidelines for teachers helping students experiencing difficulty in learning mathematics. In P. Grootenboer, R. Zevenbergen, & M. Chinnappan (Eds.), Identities, Cultures and Learning Spaces Volume 2: Proceedings of the 29th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 496–503). Mathematics Education Research Group of Australasia (MERGA). https://merga.net.au/Public/Publications/Annual_Conference_Proceedings/2006_MERGA_CP.aspx