## Maths Memos

## Early years mathematics: how to create a nation of mathematics lovers?

If we want to create more positive attitudes and higher achievement in mathematics, what better place to start than in the early years?

This was the thinking of the new All Party Parliamentary Group (APPG) for Maths and Numeracy, which has recently produced their recommendations for the early years.

**What predicts success in
mathematics?**

We actually know a lot from research about building mathematical
success in the early years. A large scale study of pre-school
experiences (Sammons
*et al*. 2002, Siraj-Blatchford
*et al*. 2002) found two key factors which predict
progress:

**parents providing a home learning environment**, where, for instance, children paint, draw and play with letters and numbers;**pre-school settings providing adult-led mathematics focused activities**, such as number rhymes and games, alongside independent play.

We also know from research that a key focus for early
mathematics is developing **number sense**, especially
understanding number symbols, e.g. 'the fiveness' of 5'. Other
early predictors of success are:

- recognising numbers as dice and dominoes patterns
- comparing numbers like 5 and 7
- predicting the result of adding or taking away 1.

After this, children need to develop understanding of numbers as
made up of other numbers, including number combinations (Geary
2011, Gifford 2014)**.**

The specialists on the
APPG for Maths and Numeracy panel agreed that number sense
should be the priority for early years mathematics. However, this
is not the message of the current
'Numbers Goal' for 5 year olds (which includes a mixture of
items, focusing on skills such as 'counting reliably', and adding
by counting on, which research shows is not expected of most
children before they are 6 years old (Cross *et al*. 2009).
Research
has shown that focusing on reasoning and understanding rather than
knowledge is more likely to increase achievement in primary school
It therefore makes sense to consolidate children's basic number
understanding in the early years, rather than try to accelerate
untypical performance, and to work with parents and practitioners
in fostering number sense.

**How to produce children with mathematics
difficulties**

We also know a lot from research about creating children who lack confidence in mathematics:

**Creating mathematics anxiety****blocks working memory space**and prevents learning (Maloney*et al*. 2013). Children who cannot make sense of numbers are likely to be anxious about arithmetic.**Children with 'fixed mindsets',**who believe they are naturally no good at mathematics, are less successful than those who have a 'growth mindset' and believe everyone can learn through effort (Dweck, 2006). Putting children in a 'low ability' group for mathematics in reception classes effectively communicates low expectations to the children and their teachers, and they are likely to stay in the 'bottom group' in later years.

It is interesting that high-performing jurisdictions tend to have a later school starting age and do not group children by 'mathematics ability': perhaps they give children more time to develop basic number sense, with the expectation that all can learn.

**We know it takes time for children to develop number
sense:** they need to gradually synthesise all the
knowledge, skills and understandings involved (Munn 1996). However,
the
Early Years Foundation Stage (EYFS) identifies mathematics as a
'prime' area only for the children over the age of three, but with
unrealistically high expectations for reception children.
Accelerated expectations are unlikely to foster understanding,
especially for disadvantaged children.

**Mathematics anxiety is also created by anxious teachers
and parents** (Maloney *et al.* 2013) inappropriate
expectations seem likely to foster their anxiety. The
APPG for Maths and Numeracy identified practitioner confidence
and knowledge of early mathematics as an area for development,
alongside support for parents. Current and recent guidance (
STA 2014,
Early Education 2012) has a jumble of items, with no clear
progression of big ideas or linked examples, which is unlikely to
build educators' confidence in assessment and planning. It
seems that currently we are going the right way to create
mathematics anxiety instead of fostering confidence for all.

**Effective and appropriate early years mathematics
pedagogy**

The good news is that we actually know a lot about effective approaches, building on current early years practice (Gifford 2005). These include:

**playing and playfulness**e.g. blockplay, number rhymes**games and activities indoors and out**, e.g. cooking, goal scoring**routines**e.g. snack time, tidying up.

Two important aspects for practitioners to develop are:

**subitising,**or recognising number patterns: this develops familiarity with number combinations, e.g. seeing 6 on a dice as double 3**problem solving and 'sustained shared thinking'**(Siraj Blatchford*et al*. 2002), which involve discussions about mathematics.

The characteristics of effective learning from the Early Years Foundation Stage could therefore provide a useful basis for exemplification:

- playing and exploring
- active learning
- creating and thinking critically.

Clear guidance is needed, identifying 'big ideas' to look for. It should be based on research, with engaging exemplars (e.g. Clements and Sarama, 2009; New Zealand Ministry of Education 2010; Nrich, 2014). This might take us some way in helping teachers and parents create a generation of children who achieve an early years 'Numbers Goal' of confident number sense and love maths!

**Dr Sue Gifford is an ACME member
and Principal Lecturer in mathematics education in
mathematics education at Roehampton
University.**

**References:**

Boaler, J. (2009) The Elephant in the Classroom: helping children learn and love maths. London: Souvenir Press.

Clements, D. H. and Sarama, J. (2009) Learning and teaching math: the learning trajectories approach. London: Routledge.

Cross, C.T., Woods , T. A. & Schweingruber, H. (2009) Mathematics learning in early childhood: paths towards excellence and equity. Washington DC: National Academies Press.

Dweck, C.S. (2006) Mindset: the new psychology of success. New York: Ballantine Books.

Geary, D.C. (2011) Cognitive predictors of achievement growth in mathematics: a five year longitudinal study. Developmental Psychology, 47(6), 1539-1552.

Gifford, S. (2005) Teaching mathematics to 3 - 5s: developing learning in the Foundation Stage Maidenhead: Open University Press.

Gifford, S. (2014) 'A good foundation for number learning for five year olds?' An evaluation of the English Early Learning 'Numbers' Goal in the light of research' Research in Mathematics Education 16 (3) 219-233

Maloney, E.A., Schaeffer, M.W. & Beilock, S. L. (2013): Mathematics anxiety and stereotype threat: shared mechanisms, negative consequences and promising interventions, Research in Mathematics Education, 15:2, 115-128.

Munn, P. (1996) 'Teaching and learning in the pre-school period' in M.Hughes (ed) Teaching and learning in changing times Oxford:Blackwell.

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