Mistakes as Windows, What Students’ Errors Reveal About Their Mathematical Thinking
Across classrooms, especially in foundational years, many children struggle with mathematics, not because they are unable to learn or build basic foundational skills, but because their mistakes are often treated as dead ends rather than serving as starting points to mastery.
The Daara Innovation Fund Project, executed by four country organizations: TEP Centre in Nigeria, Zizi Afrique Foundation in Kenya, Funda Wande in South Africa, and eBASE in Cameroon, focused on strengthening foundational numeracy by identifying and treating errors commonly made by learners.
TEP Centre started this project with the objective of understanding how teachers use learner errors to support their pedagogy and to provide both beneficiaries with alternative pathways to solving these errors in numeracy. Along the way , the programme revealed that mistakes in mathematics can be viewed as a lens showing how learners think, what they misunderstand when attempting to reach the correct answer to a question, and where teachers could intercept, not with judgment but with guidance.
The Daara Innovation Fund set out to do something simple but powerful: to look closely at learners’ mistakes in mathematical operations and listen to what they were trying to say.
What we noticed
Before solving a problem, it is important to find the cause and to know what areas the struggles are located. To do this, we began with an assessment of content knowledge. Using simple digit operations, learners were encouraged not just to give answers but to show their calculations.
That is where things got interesting!
There seemed to be a pattern with the way learners performed simple operations. Lining the path were errors that were conceptual, procedural (not understanding the difference in smaller and larger digits), and factual (basically mixing up the sums/signs).
Once we saw the types of mistakes, we stopped asking. What is the right answer? And started asking, What is this child thinking?
What we did
We supported teachers to view mistakes not as failures, but as opportunities to better understand how their students think. Therefore, rather than simply marking answers as wrong, teachers were coached on how to start engaging in meaningful conversations with learners to uncover the reasons behind their errors. With this shift in mindset, classroom teaching and learning became more responsive. Teachers could quickly adapt their lessons, building on learners’ needs in real time and create environments where learning felt more supportive and inclusive.
One teacher said, “I used to mark errors and move on. Now I pause; I ask why the child made that error. That conversation changes everything.”
Through this work, we have seen a direct impartation on learners, with each learner’s journey reflecting a conscious shift from rote practice to reflective learning.
What it changed
Classrooms began to feel different for both learners and teachers.
- Teachers felt more confident in diagnosing misconceptions.
- Students became more willing to try, knowing mistakes were a welcome avenue to learn.
- Learning was not about getting it right on the first try but about understanding the concepts that are being taught and applying these techniques.
Why this matters
In the words of James Joyce, “Mistakes are the portals of discovery”.
Every child makes mistakes, but when we treat those mistakes as mere noise, we miss the signals they send.
With error analysis, teachers can now decode that signal and guide learners from confusion to clarity.
At TEP Centre, we have seen that excellent teaching isn’t just about delivering content. It is about noticing the small things, especially when they go wrong, because most times, a mistake isn’t the end of learning. It is the very beginning of greater learning.
As we continue this journey, we invite other educators to pause when errors appear, don’t be in a hurry to just grade, take a moment to ask: Why did this child choose this method? What does their approach tell me about their understanding? How can I support them to move from confusion to clarity?
These simple questions can turn mistakes into stepping stones for deeper learning.
If you have read to this point and you are curious about how to begin using error analysis in your classroom, start with a simple prompt: What is this child trying to say with this answer? You just might uncover a powerful insight hidden beneath the mistake.
Together we can make our classrooms places where mistakes are not feared but welcomed as invitations to think differently and see things from other perspectives.