Memory in Maths: accounts of how we improved our Mathematics curriculum (part 4)

Hana Aslam

AHT Maths, Forest Gate Community School

Memory in Maths

OLD NOTEBOOK FROM MATHS CLASS?

I HAVE NO MEMORY OF THIS PLACE

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So where were we? Ah yes, a throwback to 2002 at a cashpoint in Asda with my dad. Not to my surprise, he had recently got a brand new debit card and he’s got no clue of his pin number to his card. Routinely he punched in his previous card’s PIN number exactly three times before it got blocked and the worst part is, his phone battery died and could not remember the house phone number to call up for his pin number! What an inconvenience that was! Memory in maths is that exact frustration. As a pupil, you’re sitting an assessment and you forget a skill you routinely know but somehow forget because the question has gone from ‘what is the probability of tossing a fair coin and getting tails?’ to the notoriously known question ‘Hannah has n sweets… and show that n^2 - n - 90 = 0.’

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Memory skills in maths is completely different to numeracy. Numeracy is knowing what to do in a problem with the fundamental numerical skills and KOs required. Memory skills are maintaining those key ideas over and over again until you wake up reciting the quadratic formula from a slumber some dream! We have Memory KOs from year 7 to year 11 with some increasing challenge across the pathways. Ms Noor has made the initial KOs with my help and Mr Mirza has now adapted the memory KOs to fit our long term plan. For example in year 7 pathway D, a KO can be ‘I can memorise the times table up to 15’. This KO is also found in pathways C, B and even A. We have embedded a ‘Memory Skills’ question in our starter. Along with four other questions ‘Last lesson’, ‘Last week’, ‘This year’ and ‘Last year’. This allows constant revisit of the main KOs every lesson throughout the year.

Template for Maths lesson starter at FGCS

These are not skills that require prior knowledge but it is important to recall to be used in numeracy and many other aspects of Maths, Statistics, Science, Geography, Computer Science and many other subjects. This particular KO will then be developed into recalling square, cube and prime numbers in Year 8 and even exact trigonometric values.

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With all these numbers and facts to remember, what is the best way to memorise? There are well-known techniques such as Memory Palace, Spaced repetition, use of Mnemonics and so on. These all work for different skills. In Maths it is often easier to understand the proof of a theorem rather than reciting it over and over. For instance, there are 7 main circle theorems and all of them are examined along with its proof. When I was a pupil myself, I could not memorise these theorems without understanding how they were created in the first place. In 2004, OCR and the other exam boards did not have circle theorem-proof as part of their specification, not even at A level. With a dial-up internet connection and numerous hours at the library, I managed to understand one proof of circle theorem. Why just the one? One was enough to make a connection to the other proofs of circle theorems. It was all about making links and how these links create these circle theorems.

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Working memory is a system for temporarily storing and managing the information required to carry out complex cognitive tasks such as learning, reasoning, and comprehension. Working memory is involved in the selection, initiation, and termination of information-processing functions such as encoding, storing, and retrieving data.

One test of working memory is memory span, the number of items, usually words or numbers, that a person can hold onto and recall. In a typical test of memory span, an examiner reads a list of random numbers aloud at about the rate of one number per second. At the end of a sequence, the person being tested is asked to recall the items in order (we have been tested on our school vision like this in twilights and LG meetings). The average memory span for normal adults is 7 items.

Before I end, let’s have a look at the importance of memory used in Maths and beyond. In an article by Cambridge Mathematics states;

• Students who struggle with mathematics may have difficulties with working memory; this explains around 25% of differences in mathematical outcomes

• Classroom strategies such as using manipulatives, repetition, and breaking down tasks into smaller steps may help to reduce working memory load

• Working memory training alone does not lead to better outcomes in mathematics attainment

Source: https://www.cambridgemaths.org/espresso/view/working-memory-for-mathematics-learning/

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Don’t scroll up! What are the first ten digits of pi (ℼ)?

Why did I mention this irrational number over and over again in this blog?

Just like with any important facts, types of number, formulae and theorems (with their proofs!) we need to see and recall them again and again...and again!

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