Working memory, fluency and practice - the science of learning mathematics

Experts in cognitive psychology have shaped our understanding of how children learn mathematics. What their work tells us is fascinating - and it makes perfect sense to parents and teachers. 

This animation and blog article explore the cognitive science of learning mathematics - explaining how different types of memory are involved, why speed is important and how practice is key to developing maths fluency.

I'd like to credit Dr. Helen Abdazi from the University of Texas for her work on this: click here to view her video lecture.

The Working Memory Bottleneck

Dr Abadzi, a cognitive scientist at University of Texas, argues that people are “basically prisoners to their working memory”, which contains everything in their minds at any given moment. 

Working memory can only hold a small amount of information and it lasts only a few seconds, so the information must pass through it rapidly or it gets lost. Working memory can become a bottleneck in our brain function - making even simple thought processes feel complex as we go forwards and backwards get to the answer.

Instant Recall is Critical

But there is a way round the working memory bottleneck. Dr Adbrizi explains that when children practise tasks like mental arithmetic, it becomes automatic and unconscious, freeing up space in the working memory for more complex calculations. 

This means it's not enough simply to be able to work out a calculation - what matters is getting it right, instantly and effortlessly.

Working memory is also limited in capacity - studies show on average we can only hold 7 items in memory for 12 seconds. 

Put simply - as soon as item no 8 pops into the working memory another item falls out to make way. However, rapid recall of maths facts allows learners to jump the queue - avoiding the working memory bottleneck

It's also clear that focus and concentration go hand-in-hand with developing working memory. If a learner is distracted while doing a maths calculation, it easily overloads their working memory and disrupts their thinking.

Explicit and Implicit Memory

We have two types of long-term memory - psychologists call these explicit and implicit. 

The explicit memory is the bit we're aware of - such as being able to recall a fact such as the name of a capital city. Explicit memory gets all our attention and yet its potential is dwarfed by its big sister, the implicit memory - the iceberg under the water

Implicit memory is the unconscious memory of skills and how to do things, such as playing guitar or riding a bike. These memories are typically acquired through repetition and practice, and are composed of automatic skills so deeply embedded that we're no longer aware of them. 

By helping children truly master the essential foundation skills in maths we shift the load from their conscious explicit memory to their unconscious implicit memory. With this comes a level of maths fluency needed to excel in higher order maths skills - such as analytic thinking and complex problem solving.

Teachers are in the construction business. Memory networks are like bricks and mortar. If you want the second floor - it had better start after your put the first one in
Dr. Abdazi

The Importance of Practice

It's interesting that after acquiring fluent skills we tend to forget the effort and practice that developed them - but this makes perfect sense because we've made them unconscious

The danger is we also lose respect for the amount of effort and practice it takes for our children to acquire the same skills. Dr. Abdazi explains the science behind acquiring fluent skills in maths:

  • Memories are stored in neural connections;
  • Few neural connections are created at a time - because it involves building proteins which takes time;
  • We remember best the information we saw most recently and most often;
  • Practice and repetition over time works.


The cognitive science of learning mathematics, however compelling, isn't the same as real evidence. Fortunately, academic research into learning mathematics has tracked many learners over their entire school life looking for vital statistical connections between early learning and later success.

The conclusions are pretty clear - and they support the cognitive science:

The Institute of Education, London:  "The development and importance of proficiency in basic calculation" ( July 2013 ) 

Key Findings:

Basic calculation fluency (accurate and rapid solution of single digit addition problems and complementary subtractions) is the strongest correlate of success in mathematics in primary school and the most frequent symptom of difficulties in mathematics.

Full Paper (PDF)

I hope you have found this look at memory and how it relates to how children learn maths interesting and useful. I'd recommend taking a look at Dr. Adbazi's video lecture and if you have any feedback, please get in touch.

I'm Ged McBreen ex-maths teacher, parent and co-founder of Komodo.

About KomodoKomodo is a fun and effective way to boost primary maths skills. Designed for 5 to 11-year-olds to use in the home, Komodo uses a little and often approach to learning maths (15 minutes, 3 to 5 times per week) that fits into the busy routine. Komodo users develop fluency and confidence in maths - without keeping them at the screen for long.

Find out more about Komodo and how it helps thousands of children each year do better at maths - you can even try Komodo for free.

And now we've got Komodo English too - check it out here.

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