7 maths mastery strategies to help learners retain knowledge

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Forgetting is a natural part of learning, but there are a few simple things you can do to slow the process. Here are seven handy tips to help learners retain knowledge.

Every teacher is all too familiar with the scenario where pupils have apparently forgotten everything they’ve previously learned on a subject. This can be explained by the forgetting curve, which describes a decrease in the brain’s ability to retain knowledge.

So, what can you do to help learners remember? Here’s my list of top tips to help learners retain knowledge.

1. Teach it properly to start with!

Anyone who has been teaching for more than a few years will be familiar with the old-style spiral curriculum, where the topic changes each week (and sometimes within a week). The theory behind this is sound — keep revisiting topics so that learners don’t have time to forget. Sadly, in practice, there’s never enough time to embed learning. When you move on to the next topic, learners tend to forget everything.

A spiral approach to learning is fundamental to the maths mastery approach, with one key difference. The first time you teach a topic, you do slow and spend a lot of time exploring all aspects of a concept. Learning is reinforced by using it to reason and problem solve. If a child masters a topic first time around, they have a stronger foundation to work when they revisit they learning in the future.

2. Build up step by step

Children get lost in their learning when they’re asked to make a sudden jump in understanding. Breaking down a mathematical concept into smaller steps is an easy way to make sure learners don’t get confused.

Sounds straightforward. However, as adults, we all suffer from what can be described as ‘the curse of the expert’. We’re all experts in the maths we’re teaching our learners and can’t imagine what it’s like to not know it. This makes it incredibly difficult to break the learning down into sufficiently small steps.

Fortunately, a maths mastery approach like Maths — No Problem! provides those small steps for us. When the small steps in a lesson or lesson sequence have been constructed for learners based on research and in-class refinement, the process of learning becomes significantly easier.

3. Create strong mental images

Children can find it hard to learn facts by rote, especially when they can’t picture what the facts actually mean. The Concrete, Pictorial, Abstract approach is designed to help learners build strong mental images of the maths they are learning. Instead of being disembodied facts, children learn to visualise the meaning of the fact.

Can they ‘see’ the array that goes with 8 × 8, for example? If so, they will also know that it’s a square number without having to learn this as a separate fact. Building strong mental images reduces the amount of learning required.

4. Find patterns and connections

Maths is made up of patterns. Even though the connection between ½, 0.5 and 50% may be obvious to us, learners won’t always see the connection unless they’ve been taught to look for it.

My class calls this lazy maths — using something you already know to work out something new. They take great delight in this, letting us all know when they spot a way of using lazy maths! Not only does this reduce the amount of maths they need to learn, but it also deepens the connections between their new and existing knowledge.

All new learning needs to be connected to things already known, and the greater the number of connections formed, the more securely new knowledge is embedded.

5. Variation is key

How often do we show learners one way of carrying out a procedure, or one representation of a concept? If we want them to have a secure, deeply embedded understanding then we need to make sure they’re exposed to the complete picture.

We don’t only show learners a range of representations of what something is, we also need to show them what it is not, so they can test out their developing understanding.

Teach them to recognise what’s the same and what’s different about two representations. Value different ways of solving an equation, so that learners can spot the connections between the different methods (further embedding their learning).

This is what makes the phrase “three ways is a clever day” so powerful in the classroom. Think carefully about the variation you use in your initial teaching and make sure you also use it when reviewing or revisiting a concept.

6. Revisit, revisit, revisit

As learners are taught new topics, their memory of previous learning can get a little hazy. Cognitive neuroscience reinforces the importance of regularly reviewing previous learning. Practice makes permanent. When we revisit something we’ve already covered, it helps our learners to retrieve the knowledge stored in their memories.

Homework provides a great opportunity to ask pupils to return to a previous topic. Not only does revisiting topics help to keep learners on their toes, but seeing topics alongside new learning helps children make connections between different areas of maths. The more connections learners create, the more secure their learning will be.

Each time a learner is asked to revisit a topic, they strengthen their memory. And over time, the gap between each time a topic is revisited becomes longer as their memories become stronger.

Make sure your learners know why they are revisiting prior learning — do they understand what’s happening in their brain when they are learning? Or when they are asked to recall previous knowledge?

7. Accept that learning takes time

Learning is usually defined as a permanent change in long term memory. So don’t be misled into confusing performance: the ability to carry out a procedure taught in today’s lesson, with learning: the ability to use that knowledge weeks or months after it was taught.

To securely embed learning, we need to accept that it will take time. At first, memories are closely linked to the time or place in which the content has been taught. This is known as episodic memory. If the context changes, learning is apparently lost — this explains why your new class have apparently forgotten content you thought they knew. A change of teacher or classroom is enough to disrupt their memory.

The good news is, as topics are revisited over time and their learning becomes more secure, it detaches from the original learning context and forms semantic memory, which is long-lasting. Semantic memories are not easily formed. Our learners need to know that it takes hard work.

Retaining knowledge relies on one important thing: building learners’ confidence. Children who know they have a range of strategies to draw on are resilient learners. Moving their understanding away from maths being black and white, or right and wrong, gives your learners the confidence to get stuck in and give things a try. And what more could we ask?

was one of the first Teaching for Mastery specialists trained by NCETM. She works as a maths consultant with schools new to the mastery approach, and is a contributor to the Blog.
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