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

This article was originally published on the Royal Society's Advisory Committee on Mathematics Education (ACME) blog.

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 for Mathematics and Numeracy.

What predicts success in mathematics?

We actually know a lot from research about building mathematical success in the early years, and we could do this more effectively than at present. 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 were encouraged to 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, eg 'the fiveness' of 5. Other early predictors of success are:
  • recognising numbers as dice and dominoes patterns
  • comparing numbers like 5 and 7, saying which is more
  • predicting the result of adding or taking away one.

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

While the specialists on the APPG panel agreed that understanding the meaning of numbers is a priority for early years mathematics, this key idea is not apparent in the Numbers Goal for five year olds (DfE, 2013). Instead it focuses on the skill of 'counting reliably' and adding by counting on, which research shows is expected of most children when 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 (Nunes et al, 2009). We therefore need to consolidate children's understanding in the early years, rather than try to accelerate untypical performance.

How to produce children with mathematics difficulties

Research has also shown us how to create young children with negative attitudes to mathematics and we seem to be going the right way about it:

• creating mathematics anxiety blocks working memory space and prevents learning (Maloney et al, 2013). If children have not developed secure number concepts they 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 they can learn through effort (Dweck, 2006). However, by grouping children in reception classes, we effectively tell some they are of 'low ability' for mathematics (Boaler, 2013).

It is interesting that high performing jurisdictions avoid both of these, by having a later school starting age, giving children more time to consolidate basic number understandings, and by not 'ability grouping' children (OECD, 2012).

• accelerating expectations is unlikely to meet the needs of disadvantaged children. We know it takes a long time for children to synthesise all the knowledge, skills and understandings involved in developing number sense (Munn, 1996). However, the EYFS (DfE, 2012) identifies mathematics as a focus or 'Prime' area only for the over threes, but with unrealistic expectations for most reception children.
• mathematics anxiety is also created by anxious teachers and parents (Maloney et al, 2013) and inappropriate expectations seem likely to foster their anxiety. The APPG identified practitioner knowledge and confidence as an area for development, alongside support for parents. The current proposals for post-16 core mathematics could help develop confidence and interest for prospective early years practitioners - and parents. However we need more education and training for early years educators to increase understanding about early mathematics. Clearer guidance is also needed about children's likely learning trajectories so that practitioners can assess and plan and parents know what to expect.

Effective and appropriate early years mathematics pedagogy

The good news is that we know a lot about this: it involves approaches which are common in early years settings (Gifford, 2005):

• playing and playfulness eg blockplay, number rhymes
• games and activities indoors and out, eg cooking, goal scoring
• routines eg snacktime, tidying up.

Two important aspects for practitioners to develop are:

• subitising, or recognising number patterns as on a dice: this develops familiarity with number combinations, eg seeing six as double three
• problem solving and 'sustained shared thinking' (Siraj Blatchford et al, 2002).

The characteristics of effective learning from the EYFS (DfE, 2012) could provide a useful basis for exemplification:

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

What is needed is a clear progression of 'big ideas' to develop number sense - giving guidance on what to look for and how to provide for it. Like such curricula in other countries, such as New Zealand (NZ Ministry of Education, 2010) it needs to be based on research, with detailed exemplars matching the key ideas (unlike the present and previous versions (STA, 2012; EE, 2012). Big ideas would include number values to 10 and 20, comparing numbers and numbers within numbers: contexts would include outdoor and indoor activities and games, like scoring goals or cooking, routines like snack time and rhymes and stories, including opportunities for discussing puzzles and problems (see NRICH's EYFS activities).

References:

Ashcraft, M.H. & E.P. Kirk. (1998) 'On the cognitive consequences of mathematics anxiety' in The development of mathematical skills, ed. C. Donlan, 175-96. Hove: Psychology Press Ltd.

Beilock, S. (2006) Choke: What the Secrets of the Brain Reveal about Getting It Right When You Have to New York: Free Press

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

Boaler, J.(2013) Ability and Mathematics: The mindset revolution that is reshaping education. ForumӬ 55 (1).

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

Department for Education (2012) Statutory Framework for the Early Years Foundation Stage.  Retrieved from http://media.education.gov.uk/assets/files/pdf/e/eyfs%20statutory%20framework%20march%202012.pdf

Department for Education (2013) Early Years outcomes: A non-statutory guide for practitioners and inspectors to help inform understanding of child development through the early years. Retrieved from https://www.gov.uk/government/publications/early-years-outcomes

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

Early Education (2012) Development matters in the Early Years Foundation Stage. Retrieved from http://www.foundationyears.org.uk/wp-content/uploads/2012/03/Development-Matters-FINAL-PRINT-AMENDED.pdf

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

Gifford, S. & F. Rockliffe (2012) 'Mathematics difficulties: does one approach fit all?' Research in Mathematics Education 14 (1) 1-15

Gifford, S. & J. Davenall (2012) 'Developing counting through play' Primary Mathematics 16 (2) 11-13

Maloney, E.A., Schaeffer, M.W. & S. L. Beilock (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

New Zealand Ministry of Education (2010) Number: early learning progression 

http://nzmaths.co.nz/number-early-learning-progression

Nunes, T., Bryant, P. , Sylva, K. & Barros, R. (2009) Development of Maths Capabilities and Confidence in Primary School DCSF-RR118 http://dera.ioe.ac.uk/11154/1/DCSF-RR118.pdf

OECD PISA 2012 results

http://www.oecd.org/pisa/keyfindings/pisa-2012-results-volume-v.htm

Sammons, P., Sylva, K., Melhuish, E., Siraj-Blatchford, I., Taggart, B. and Elliot, K. (2002) Technical Paper 8a: Measuring the Impact of Pre-school on Children's Cognitive Progress over the Pre-school Period. London: Institute of Education, University of London.

Siraj-Blatchford, I., Sylva, K., Muttock, S., Gilden, R. and Bell, D. (2002) Researching Effective Pedagogy in the Early Years, (REPEY) Research Report 356. London: Department of Education and Skills.

Standards & Testing Agency (2012) EYFS Profile exemplification for the level of learning and development expected”¨at the end of the EYFS: Mathematics ELG11 - Numbers London: STA.  Retrieved from  http://www.education.gov.uk/search/results?q=EYFS

Standards & Testing Agency (2013) 2014 Early Years Foundation Stage Profile Handbook.  Retrieved from https://www.gov.uk/government/publications/early-years-foundation-stage-profile-handbook-2014

Trundley, R. (2008) The value of two Mathematics Teaching, 211, 17-21

Williams, P (2008) Independent review of mathematics teaching in early years settings and primary schools London: DCSF