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Beyond the Answer: Developing Reasoning and Problem Solving in Maths
Developing mathematically fluent problem solvers through culture, metacognition and varied problem-solving experiences.
Claire Williams
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Reteaching that works: why repeating explanations fails and how to adapt teaching to secure understanding
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by Alexandra Park Research School
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Jennifer is Assistant Director of Alexandra Park Research School and Trust Lead for Early Career Teacher Development at The Greater Manchester Education Trust.
“Insanity is doing the same thing over and over again and expecting different results.”
Whether or not Einstein actually said it, the quote captures a familiar feature of classroom practice: when pupils do not understand, we often quickly repeat the same explanation and hope they get it the second time.
The increased focus on adaptive teaching within the profession has been an important step in developing more responsive and inclusive classrooms. Effective formative assessment is central to this, allowing teachers to elicit evidence of pupil understanding and adapt teaching in response.
When misconceptions arise or understanding has not yet been secured, teachers can respond in the moment by re-teaching. But often, this re-teaching closely resembles the original explanation, meaning that if the initial explanation did not secure understanding, simply repeating it is unlikely to change the outcome.
"If pupils do not understand an idea, they do not need to hear the same explanation again; they need to encounter it differently."
As Wiliam (2011) argues, the value of formative assessment lies not simply in checking for understanding, but in how teachers respond to the evidence it provides.
From a cognitive perspective, Willingham (2009) highlights that learning depends on how new information connects to prior knowledge. If an explanation hasn’t connected the first time, repeating it is unlikely to build that connection.
Instead of repeating the same explanation, effective re-teaching involves changing the approach. The Education Endowment Foundation’s Check, Adapt resource captures this idea clearly: when pupils misunderstand, teachers are encouraged to explain differently, use new examples or analogies, and model the task step by step.
1. Change the representation
Re-teaching is most effective when we change the conditions of the explanation. If the original explanation relied on a PowerPoint slide, the re-teach might involve modelling the idea live on the whiteboard, breaking it down into small steps while narrating the thought process.
2. Change the analogy
Use a different analogy to highlight the underlying structure of the concept which pupils have misunderstood.
3. Change the concrete example
Select a new concrete example or non-example that makes the underlying structure of a concept more explicit.
4. Plan for more than one explanation
Before the lesson, consider alternative ways to explain key ideas. What diagram, analogy or model could be used if the first one doesn’t land?
5. Check the re-teach
Re-check understanding after re-teaching to ensure misconceptions have been addressed and the re-teach has secured understanding before moving on.
Alongside this, our Clip from the Classroom example below shows how diagnostic questions can be used to identify misconceptions in real time and guide the teacher’s next steps:
👉 Watch: Using diagnostic questions to identify and address misconceptions
In the clip, I use carefully designed questions to surface what pupils are actually thinking, rather than relying on volunteers or assumptions. This provides clear evidence of understanding across the class, allowing me to respond deliberately – whether that means pausing to re-teach, adapting the explanation, or building on secure understanding.
Before any effective re-teaching can take place, teachers need to rigorously check whole-class understanding. This will provide the evidence needed to identify misconceptions and make informed decisions about whether to move on, provide additional support, or re-teach content differently.
A science teacher introduces electrical currents using the familiar water pipe analogy: electricity flows through wires like water through pipes, with the battery acting as a pump.
A diagnostic question reveals a misconception: some pupils believe current is “used up” by the bulb, much like water being lost from a leaking pipe.
Rather than repeating the same explanation, the teacher re-teaches using a rope loop model. Pupils see that the rope moves continuously around the loop and is not “used up”.
When pupils do not understand, what do you change about the explanation so that they encounter the idea in a different way?
Wiliam, D. (2011). Embedded Formative Assessment, Chapter 2
Willingham, D. (2009). Why Don’t Students Like School? Chapter 2
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