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.

1 comment for “Early years mathematics: how to create a nation of mathematics lovers?”

  1. Gravatar of Donna-Lynn ShepherdDonna-Lynn Shepherd
    Posted Tuesday, January 6, 2015 at 11:24 AM

    I agree wholeheartedly! This is very well-explained and highlights the relevant evidence from research - a sensible answer to a very important question.

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