How we learn Maths




Learning is not the same as memorising facts. We learn by understanding concepts deeply!

REMEMBER: Learning only happens when you build your own unique understanding of a concept based on your past experiences and your existing knowledge.

In the early stages of learning a concept, it can take up a lot of space in our brain as we try to make sense of it. As we progress, we add new ideas to our existing ideas within these concepts.

When that new knowledge can be securely connected to our existing knowledge and integrated within our existing knowledge to form a deeper, coherent understanding, then knowledge compression takes place. This means that even though we have more knowledge in our brain, it takes up less space!


This means that even though we have more knowledge in our brain, it takes up less space! If we are unable to build on our existing knowledge by connecting new knowledge to what we already know and understand, we can land up with large chunks of disconnected knowledge stored in our brain.


When new knowledge cannot be connected, we have to use rote learning (memorising ‘off by heart’ without understanding) to remember everything. But knowledge compression cannot happen with disconnected, rote-learned information.

This results in our brain becoming so full that we cannot remember or use the information! This then stops you from learning more advanced concepts.

Understanding concepts in maths requires perseverance but once knowledge compression takes place, these mastered concepts are able to be used with little effort to solve maths problems involving more complex concepts.

To make us more efficient at solving maths problems, we can practise using concepts that are already mastered BUT only once we fully understand them and have compressed them with related concepts to form our knowledge.

Practising with a concept develops fluency – this means we can retrieve information about a concept quickly and easily in order to use that information.

Fluency results in automaticity. Automaticity is when we can use a concept almost without thinking about it anymore because we fully understand it and we can apply it in different situations.

It’s a bit like learning to drive a car. In the beginning, we struggle to learn how to change gears, we concentrate on what each foot does on each pedal but once we have mastered it, we start to perform it better and better as we become more fluent. Then we develop automaticity and we don’t even think about our feet and the pedals when we are driving the car.



  1. 3 Ways to Boost Students’ Conceptual Thinking – by Carla Marschall
  2. Fluency without Fear – by Jo Boaler