Making numbers using different representations

A further response to the Early learning Goals: published in the TES, 2nd September 2020

Mathematics in the EYFS:  One step forwards, two steps back

In his recent article for TES, Julian Grenier points out that we need to interrogate the criticisms of the changes to the Early Years Foundation Stage (EYFS). He cites our TES article, ‘a mathematical dog’s dinner’ as an example of recent criticism. As an expert special interest group in mathematics for this age group, we in the Early Childhood Mathematics Group (ECMG) provide expert opinion based upon research evidence and our criticisms are not merely due to ‘change fatigue’. In our article, we identified some significant issues with the mathematics in the revised EYFS. In the spirit of interrogation, in this article we focus specifically on the new Early Learning Goals (ELGs) for mathematics and clarify which aspects are supported by research evidence.

The EYFS matters

A recent report by the children’s commissioner for England, Anne Longfield, reminds us of the importance of getting it right in early years.  The EYFS framework is crucial for ensuring children get the best educational beginnings with the ELGs setting the standard by which we determine whether children are achieving well, providing early opportunities to identify and support learning in order to pre-empt future potential difficulties. 

Mathematics in EYFS was in need of revision

The ELGs for mathematics have remained the same since 2012 and contain significant issues.  Most notably, counting on/back and doubling/ halving are not supported by research for 4 and 5 year olds (Gifford 2014).  There are also some aspects which are not priorities for this age range (such as ordering numbers to 20) or are unclear (for example including distance instead of length in measures).  Clearly, the goals for mathematics were in need of revision.

Only partially research informed: one step forwards, one step back

As the governments’ EYFS consultation response explains, the early learning goals need to reflect the ‘latest evidence’ and ‘the strongest predictors of future attainment’ in order to support young children to have secure understanding in early years and beyond.  It is also essential that children form positive attitudes towards mathematics and sustainable mathematical well-being so the way that they learn is as important as what they learn.      

The revised early learning goals for mathematics include statements which are worrying on both counts:

Number ELG

Children at the expected level of development will:

  • Have a deep understanding of number to 10, including the composition of each number;
  • Subitise (recognise quantities without counting) up to 5;
  • 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.

Numerical Patterns ELG

Children at the expected level of development will:

  • Verbally count beyond 20, recognising the pattern of the counting system;
  • Compare quantities up to 10 in different contexts, recognising when one quantity is greater than, less than or the same as the other quantity;
  • Explore and represent patterns within numbers up to 10, including evens and odds, double facts and how quantities can be distributed equally.

We have interrogated the new ELGs and identified which are supported by research evidence for this age group (details are available in our response document, ECMG 2020).  Whilst some aspects are supported by research evidence for this age group, others are not (identified in bold). These are a real concern and a retrograde step. 

Missing important predictors of future learning: one step forwards, two steps back

The most controversial change is the removal of shape, space and measures from the ELGs.  This directly contradicts research evidence that early spatial skills are predictive of later mathematical achievement (Hawes & Ansari 2020) and that teaching these improves mathematics in general, including number understanding (Cheng & Mix 2014; Hawes et al. 2017). Spatial mathematics education also has potential for improving attitudes to mathematics and school readiness (Verdine et al. 2017) as well as being a route to improving mathematics achievement (2017:102) and PISA test scores (Sorby & Panther 2020).  Also omitted from the ELGs is the key assessment for understanding counting, counting out a number of objects from a larger group (Johnson et al. 2019). We continue to question why these important aspects for future development are not included in the ELGs.

A better alternative

As a group, ECMG proposed alternative goals in our response to the consultation on the EYFS reforms.  These age-appropriate descriptors contain the learning which research has shown to be the key predictors of future attainment.    

Number ELG

Children:

  • with numbers to 12:
  • count out a number of objects from a larger group
  • match numerals to amounts,
  • compare and estimate numbers,
  • predict adding or taking one.
  • subitise up to 5 and recognise how numbers are made up of other numbers
  • solve practical problems including adding, subtracting and sharing

Shape, Space and Measures ELG

Children:

  • make comparisons of length, weight and capacity
  • begin to identify the rule in a pattern
  • select and combine shapes for a purpose and talk about their properties
  • follow directions and describe positions and routes

Unfortunately, the concerns of practitioners, parents and researchers from the EYFS consultation response went unheeded and the goals were rolled out with only minor changes to the wording.  This was a missed opportunity to address the issues and to improve the goals for both children and practitioners.

Criticisms of the EYFS reforms are valid and must be listened to

As a Group, we welcome the new focus on understanding numbers to 10 and on subitising and view these as a positive development. However, it is clear that the new ELGs ignore the DfE’s own commissioned pilot research (EEF 2019). This reported unfortunate drill-type approaches due to the requirement to ‘automatically recall’ abstract number facts as well as the side-lining of shape, space and measures due to being removed from the ELGs. Neither of these are desirable for four and five year olds and neither are supported by research.  These indicate that our concerns are justified.   

Clearly, criticisms of the EYFS are not opposition for opposition’s sake.  They are not causing ‘needless anxiety’ for practitioners but are raising genuine concerns when faced with the prospect of a curriculum which is not entirely age-appropriate or evidence-based. Mathematics in the EYFS was in need of change but not all change is good.  Unfortunately, the curriculum changes for mathematics represent one step forwards and two steps back.  

References

Cheng, Y.  & Mix, K.S. (2014). Spatial training improves children’s mathematics ability. Journal of Cognition and Development, 15(1) 2-11. https://doi.org/10.1080/15248372.2012.725186

Early Childhood Mathematics Group (2020). Response to the EYFSP consultation. https://earlymaths.org/response-to-eyfsp-consultation/

Education Endowment Foundation (2019) Early years foundation stage reforms: pilot report https://educationendowmentfoundation.org.uk/public/files/Projects/Evaluation_Reports/Early_Years_Foundation_Stage_Profile_(EYFSP)_Reforms.pdf

Hawes, Z. & Ansari. D. (2020). What explains the relationship between spatial and mathematical skills? A review of evidence from brain and behavior. Psychonomic Bulletin and Review, 27, 465-482.

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. http://dx.doi.org/10.1080/14794802.2014.895677

Hawes, Z., Moss, J., Caswell, B., Naqvi, S. & MacKinnon,S. (2017). Enhancing children’s spatial and numerical skills through a dynamic spatial approach to early geometry instruction: effects of a 32 week intervention. Cognition and Instruction, 35(3), 236-264. https://doi.org/10.1080/07370008.2017.1323902

Johnson, N.C., Turrou, A.C., McMillan, B.G., Raygoza, M.C. & Franke, M.L (2019) “Can you help me count these pennies?” Surfacing preschoolers’ understandings of counting, Mathematical Thinking and Learning, 21:4, 237-264. https://doi.org/10.1080/10986065.2019.1588206

Sorby, S.A. & Panther, G.C. (2020). Is the key to better PISA math scores improving spatial skills? Mathematics Education Research Journal 32, 213–233. https://doi.org/10.1007/s13394-020-00328-9

Verdine, B.N., Golinkoff, R. M., Hirsh-Pasek, K. & Newcombe, N. S. (2017) Links between Spatial and Mathematical Skills across the Preschool Years. Monographs of the Society for Research in Child Development, 82, no. 1 (March): 1–150. https://doi.org/10.1111/mono.12285