The latest iteration of the EYFS Framework (DfE 2020) has included some contentious changes. For mathematics these are the removal of shape, space and measures as statutorily assessed and the inclusion of “automatic recall” as an early learning goal (ELG):
“Automatically recall (without reference to rhymes, counting or other aids) number bonds up to 5 (including subtraction facts) and some number bonds to 10, including double facts.” (DfE 2020)
In this blog I focus on the term ‘automatic recall’ and look at how, since we are stuck with it, we might work ethically and responsibly alongside it. Elsewhere I have discussed the changes to the EYFS and the primary mathematics curriculum more generally: https://info125328.wixsite.com/website/post/why-are-we-so-worried
and the importance of shape, space and measures and why it should be included as an ELG here: https://famly.co/blog/the-child/helen-williams-spatial-reasoning/
The Early Childhood Mathematics Group (@EChildhoodMaths) of which I am a member, lays out its reasons for, and the research behind, objections to some of the changes to the ELGs here: https://earlymaths.org/a-mathematical-dogs-dinner-2/
Those of us objecting to the term “automatic recall” have been painted as being ‘against’ working towards fluency. This is fallacious. Fluency is rightly one of the three aims of the mathematics National Curriculum, along with reasoning and problem solving. For some reason, it is fluency that has been the national focus since 2014, despite research pointing to reasoning as being the greatest predictor of later achievement (Nunes et al 2009). Why this is, is probably the subject of a another blog.
I don’t think it is correct to use the terms ‘fluency’ and ‘automatic recall’ interchangeably. This definition of fluency comes from 2104, when the National Curriculum introduced it as an aim:
“To be mathematically fluent one must have a mix of conceptual understanding, procedural fluency and knowledge of facts to enable you to tackle problems appropriate to your stage of development confidently, accurately and efficiently.” (NCETM 2014)
‘Automatic recall’ as a term seems to have been slipped in fairly recently, since the introduction of the 2014 National Curriculum, and it is difficult to find a definition for this. A dictionary definition defines ‘automatic’ as: “done or occurring spontaneously, without conscious thought or attention”. Conceptual understanding is seen as being at the root of fluency; for automatic recall this does not appear to be the case. This, to me, is critical. To imply that a four- or five-year-old should have recourse to abstract number facts “without thought or attention” is dangerous. This term implies a drilling of abstract number facts, particularly with the inclusion of the words: “without reference to rhymes, counting or other aids”. For four- and five-year-olds this is not appropriate. Time for principled non-compliance 1 (House 2014).
Before moving on to exploring some games that I have found effective – and fun – to play with four- and five-year-olds working fluently with small numbers, it is worth pointing out that what follows is not about getting children to achieve this Goal. It is about what we do instead as part of young children’s entitlement to high quality early mathematics. What follows is based firmly in building children’s confidence, their competence and their enjoyment; as well as working on developing children’s executive functioning.
Executive functioning (EF) is defined as children’s ability to supervise, or regulate, their own thinking and behaviour. These skills are critical for young children’s learning and are predictive of later mathematics achievement, as well as wider school success. I came across an authoritative article last year which examined how small changes to a simple game aimed at developing numerical competencies can also work on developing important higher-order executive function skills (Joswick et al 2019). I realised that a game that I had been working on and with for years fitted this narrative, where there would be an additional emphasis on children’s executive functioning. Here it is.
I have to thank and credit the sadly missed BEAM (Be a Mathematician) team and in particular the ILEA pack “Count Me In” (no publication date!) for this idea.
Boss Person and X-ray eyes
You need: a shallow box or tray, 10 buttons or similar, 6 cards numbered 0,1,2,3,4,5, (the children can make these) and a partner.
To play: Decide who starts as the Boss. The other person (the one with X-ray eyes) goes away until they are called back. The Boss chooses two cards, places them in the box and counts the correct amount of buttons into the tray for each card. Now check how many buttons there are altogether and push the buttons into one pile. Hide one of the cards.
Call back your partner. Tell them with their X-ray eyes, by looking in the box, they have to work out which number is written on the hidden card.
Swap roles and play again choosing two different cards each time.
Let’s examine what is involved in this game as it stands here. The Boss is being asked to combine two small quantities and their partner is reversing this process; so, in effect they are modelling the relationship between addition and subtraction. 3 + 5 = 8 : 8 – 3 = 5
They are linking the numerals to the amounts and using the total amount to find the missing number. It is a wonderful revelation when the person with the X-ray eyes can ‘see’ the hidden number (yes, they are allowed to touch the buttons). The adult can, after they are successful, ask these questions: “How do you know there is a 3 on the hidden card?” and “How else do you know there is a 3 on the hidden card?”
To deepen and strengthen the mathematics, we can make several alterations to this game over time, varying the mathematical demand:
· Instead of pushing the buttons together, the Boss removes one card but keeps the two amounts separate and arranges each quantity so we can easily see at a glance how many there are. This shifts from using counting to subitising in exploring the composition of numbers.
· We play with two sets of 0-5 cards (allowing double facts); and eventually, with 0-10 cards (to extend bond practice to 20).
· We choose three cards and remove one, looking at how a total is composed of three small quantities.
· We spend time playing with one total, say 6, and hide the buttons instead of the number-card.
By keeping the total constant, we reinforce the bonds within that one total and work towards fluency – a recall of these number facts based on conceptual understanding. Over time, we work on each total in turn.
· We extend the mathematical ideas into different problem-solving contexts. A story context is very powerful. See Oxford Owl’s wonderful animations of five animals, based on the must-have book ‘Making Numbers’ (Back, Griffiths and Gifford 2016) for a great way to introduce this: https://www.oxfordowl.co.uk/welcome-back/for-school-back/default/series-landing-pages/pd-books/making-numbers
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Executive Functioning
What has executive functioning got to do with all this? EF includes three categories:
(1) inhibitory control,
(2) working memory, and,
(3) attention shifting and cognitive flexibility.
In relation to the original Boss Person game:
Inhibitory control stops the child from making a wild guess, just grabbing and looking at the hidden card, or watching what the Boss does;
Working memory is exercised as the child remembers how the game works and that the number of buttons will match the total of the two chosen cards; and,
in relation to attention shifting and cognitive flexibility, the child has to move between the whole quantity and the two part-quantities, as well as shift between being the Boss and the person with X-ray eyes.
To reduce the load on a child' executive functioning, play with an adult where the adult isvthe person with the X-ray eyes.
So, it is important, for their executive functioning development, that the children exercise control when playing these games. Simply following adult instructions and answering the adult’s question “So, what number is on my hidden card?” won’t cut the mustard.
“Switching the focus from child thinking to adult teaching is particularly unfortunate for mathematics, as building positive learning dispositions is essential in order to prevent maths anxiety, as well as to develop children who are confident mathematical thinkers and problem solvers.”
(ECMG 2020)
Finally
I have found repetition of a simple game, which is enjoyed by my children and can be played independently, and that we can vary over time, to be a powerful way of fostering fluency with Reception age (as well as younger and older) children. I am clear why and when I make the alterations and that these changes are based on my observations of the children when they play independently.
Such games should not be used a stepping-stone to tick off, or to spend an undue amount of time on, this goal:
“Automatically recall (without reference to rhymes, counting or other aids) number bonds up to 5 (including subtraction facts) and some number bonds to 10, including double facts.” (DfE 2020)
But rather, as rich and meaningful mathematical experiences in their own right. I will remain vehemently opposed to ‘automatic recall’ as a useful measure of achievement for all four- and five-year-olds. I believe there are three questions to ask with reference to any assessment Goal:
· What is its purpose?
· Is it based on evidence?
· Does it describe typical achievement?
If assessment is to be trusted, it needs to be reliable and based on what we know from research as indicative of later achievement. Goals need to describe what is typical development, describing what almost all children are likely to achieve at the end of their Reception year. This Goal does not fit these criteria. Inappropriate and over-ambitious targets are likely to discourage teaching for depth and understanding. So, let’s enjoy the games, deepen the learning and forget the ‘automatic recall’ Goal. Creative non-compliance.
Over 30 years ago, Martin Hughes undertook some seminal research into young children’s ability to do arithmetic (Hughes 1986). As part of this research he played a game of hiding blocks in and out of a box, finding that children between the ages of three and five were perfectly able to solve small number addition and subtraction problems in this context, but when this was followed by an abstract question such as: “What is three and one more?” the same children were unable to answer:
"Ram: Three and what? One what? Letter? I mean number?
MH: How many is three and one more?
Ram: One more what?
MH: Just one more, you know?
Ram: (disgruntled) I DON’T know.
(Hughes 1986:45)
Helen J Williams, October 2020
Footnote
1
Principled non-compliance is a notion developed by Dr Richard House. It refers to professionals invoking the age-old Hippocratic Oath of ‘Do No Harm…’ to support their refusal to comply with Government impositions which professionals know will harm their clientele – in this case, the young children they work with.
References
Back, J., Griffiths, R. and Gifford, S. (2016). Making Numbers: Using manipulatives to teach arithmetic. Oxford: OUP
Department for Education (2020). Statutory Framework for the Early Years Foundation Stage: Setting the standards for learning, development and care for children from birth to five. EYFS Reforms Early Adopter Version. London: HMSO https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/896810/EYFS_Early_Adopter_Framework.pdf
ECMG (2020). Response to the DfE publication ‘Non-statutory Guidance for the EYFS: Development Matters’. https://earlymaths.org/response-to-development-matters-september-2020/
House, R. (2014). “ 'Principled Non-compliance’: an idea whose time has come?” Nursery World. https://www.nurseryworld.co.uk/opinion/article/principled-non-compliance-an-idea-whose-time-has-come
Hughes, M. (1986). Children and Number: Difficulties in Learning Mathematics. Oxford: Basil Blackwell
ILEA (year unknown). Count Me In: 23 number games using a pack of 0-100 cards. London: ILEA
Joswick, C., Clements, D.H, Sarama, J., Banse, H.W. and Day-Hess, C.A. (2019). Double Impact: Mathematics and Executive Function. Teaching Children Mathematics 25:7. NCTM.
NCETM (2014). Mathematics Glossary for Teachers in Key Stages 1 to 3. London: DfE
Nunes, T., Bryant. P., Sylva, K. and Barros, R. (2009). Development of Maths Capabilities and Confidence in Primary School. London: DCSF. Research Report DCSF RR118