Step 1: Brain-based explanation

So we know that we need to activate and connect with our students’ prior knowledge so that new learning is truly understood and remembered. But why is this the case?

Let’s start by talking about memories. Memories aren’t stored like they are on a computer. If you took 100 pictures all with blue in them and stored the images on your computer, the blue would be contained in every single picture. However, we’ve got a part of our brain which detects different colours: blue, green, red. Every blue object in your memory will be connected to the blue area. The computer is much less efficient than the brain (but much more accurate!).

A diagram showing how basic objects are remembered

This diagram shows the memory of a child who has a yellow cup after a few repetitions. Here is how the process works:

  • The small group of cells, represented by the yellow spot, is connected to the shapes that make up a cup, and to the colour of that cup. The memory is simply a spot with connections, and so it takes a very small amount of space. In a photograph you’d have all the information about the shape of that cup, but, in a memory, you just have the links to the information.
  • Let’s say this child learnt the yellow cup, and later on they learn that the thing mummy drinks from is similar. Because it has some things in common, it’s connected. All the cups are joined together.
  • Eventually the child has one general thing called a cup, which has no colour and no particular shape. It’s a thing for holding liquid, so someone can say “cup your hands” and that makes sense to the child, because that’s the cup shape that they have in their brain.
  • All other cups are connected to this cup memory. Other cups are variations but fit this general pattern, so when the child see a brand new cup, they recognise it as a cup.

There isn’t one place in the brain for memories – memories are simply links.

For example, the memory for actions is in the same place as the action, while the names of things tends to be in the lower, left back part of the brain. However, you have no sense yourself that this is the case!

Memory as a hierarchy

In our brains we’ve got cells which detect edges, with dark on one side and light on the other, at all sorts of different angles, and other cells which are detecting colour. You could say we have very basic shapes at the lowest level, and more complex objects are remembered just as the links to these basic shapes. Clever eh?!

A diagram showing memory as a hierarchy

The spots in the basic objects level in the diagram may represent your memories of table and chair, for example, and the spot in complex objects could be your memory of kitchen furniture. So everything is linked together in some sort of a hierarchy.

The knowledge in a student’s head (and in yours) is also hierarchical. Sometimes, the reason why you get students who still can’t do maths is because the links are missing.

The evidence suggests that linking new learning to prior knowledge is absolutely vital. There is actually no way the brain can understand something unless it’s linked to prior knowledge. The exception is learning by rote, but this type of learning can be easily lost because the connections aren’t there.


Many students who seem to be “no good at maths” have been significantly helped by a tutor who takes them back and back until they find what the student can do. “Can you count to three?” “Yes I can count to three.” “Can you add two and three?” “Yes, I can add two and three, but it’s fractions – I can’t do fractions.” You build people back up again. They can make several years progress in a few months if they go back to the prior knowledge.

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