Response to EYFSP consultation 2019/20

Including our proposed Early Learning Goals, July 2020

The government’s proposed changes to the Early Years Foundation Stage Profile, Early Learning Goals for mathematics, are intended to ensure that all children have a good grasp of [numeracy]; they are based on the latest evidence in child development and they reflect the strongest predictors of future attainment (DfE 2019:10). A major change is the replacement of the Shape, Space and Measures Goal with a Numerical Pattern Goal, so there are now two Goals focused on number. Both the pilot proposal (DfE, 2018), and its revised version (DfE, 2019) are an improvement on existing ELGs for five year olds in many aspects, reflecting current research on predictors (Early Intervention Foundation, 2018). However some changes seem negative (including the notable omission of problem solving), some are aspirational and not supported by research, and some will have unintended consequences according to the evaluation of the pilot (Education Endowment Foundation, 2019). The newest version ignores issues raised by the evaluation, while adding in new aspects without explanatory justification. As evidence is not acknowledged for any Goals, the issue is therefore whether the current proposals provide a sound mathematical foundation for five year olds, based on available evidence.

With regard to Number, the proposed ELG is broadly in line with current research, according to the Early Intervention Foundation, (2018). It emphasises understanding numbers to 10 instead of 20 as currently. It includes the important skill of subitising, ie recognising small numbers of things without counting. Regarding arithmetic, it emphasises understanding number composition, or the way numbers are made up of other numbers, and no longer includes counting on and back to add and subtract. The Numerical Pattern Goal implicitly recognizes that patterning is an important predictor. However, other aspects are problematic.

The 2019 revision has removed the previous explanation of ‘understanding of number to 10’, which listed linking names of numbers, numerals, their value, and their position in the counting order, all of which are key predictors of mathematics attainment (EIF, 2018). Also strangely omitted is the key assessment for understanding counting, counting out a number of objects from a larger group (Johnson et al, 2019). The Numerical Pattern ELG adds count confidently beyond 20, recognising the pattern of the counting system, which has confused those who thought the new focus was on numbers to 10. This acknowledges that children’s verbal counting develops separately from their object counting and is helped by pattern recognition, although children have to count to 40 or 50 before the repeated sequence in ‘twenty one, twenty two…’ is evident. Only counting verbally up to 20 is typically expected of five year olds, who commonly omit 13 or 15 (Johnson et al, 2019): therefore counting verbally beyond 20 seems a more suitable recommendation for the curriculum rather than an achievable Goal. (NB In the final 2020 version confidently was changed to verbally.) The new phrase, ‘deep understanding of number to 10’ is now explained as ‘including the composition of each number’, emphasising the importance of part-whole understanding, which links addition and subtraction (Resnick, 1983). This is expanded in the Numerical Pattern Goals as explore and represent patterns within numbers up to 10, including evens and odds, double facts and how quantities can be distributed equally: this impliesappropriately (if rather verbosely) that children make number patterns with objects and images. However, no research seems to support five year olds understanding the composition of each number to 10. Another problematic aspect, identified by the EEF evaluation (2019), is the expectation to automatically recall number bonds. This seems to promote rapid testing of abstract facts:

They’re actually having to just know. It takes the love of it out. They’re having quizzes at lunchtime and snacktime, going, ‘What’s double one? Double two? Double three?’ They’re not able just to play with number at the moment. We’ve lost that.’ (EEF, 2019:23).

‘Quick-fire quizzes’ seem inappropriate for four and five year olds and likely to create anxiety which prevents learning (Deans, 2019). Teachers in the pilot also wondered whether children ought to have an understanding of the information as well as being able to recall it (EEF, 2019:22). This is in line with research which suggests that children gradually learn number bonds through visual images and problem solving, using their conceptual understanding of numbers and operations to check results (Deans, 2019; Siegler and Braithwaite, 2017). The national curriculum for year 1 echoes this by specifying represent and use number bonds (DfE, 2013:103). The focus on ‘automatic recall’ seems more likely to produce superficial learning and stressful pedagogy with younger children.  However, the latest version retains ‘recall’, adding without reference to rhymes, counting or other aides, presumablyin order to clarify ‘automaticity’. It might have been more helpful to suggest age-appropriate ways for children to learn number bonds, for instance by partitioning groups of objects, or subitising (eg seeing two threes within six dots) and to retain problem solving, so children might apply number facts with understanding. However, despite recent research suggesting that mathematical problem solving supports both the development of executive functions and mathematics (Clements and Sarama, 2016), this has strangely been omitted from the current proposals.

The Numerical Pattern ELG may be based on research about patterning as predictive of later achievement (Rittle-Johnson, 2016; EIF, 2018). However, with this age group, it is linear repeating patterns with objects, and not numerical patterns, which are significant, with key aspects including recognizing the repeating core unit and regular arrangements (such as the dice 5 image). Instead, the proposed Goal includes a mixture of counting, number patterns and comparison, with Compare sets of objects up to 10 in different contexts, considering size and difference. The latter seems obscurely related to pattern and teachers were unsure whether it referred to different sizes of sets or objects (EEF, 2019). (In the final 2020 version the last phrase was changed to recognising when one quantity is greater than,  less than or the same as the other quantity). The ECMG suggests that key pattern aspects could be included within current goals, by emphasising subitising and visual composition within Number, and spatial patterning within Shape, Space and Measures.

The proposed EYFSP would omit shape, space and measures from the Goals, adding it to the curriculum as indicated by the Mathematics Educational Programme:

Developing a strong grounding in number is essential for providing children with the platform to excel mathematically. Children should be able to count confidently, develop a deep conceptual understanding of the numbers to 10, the relationships between them and the patterns therein. By providing frequent and varied opportunities to build and apply this understanding –such as using manipulatives- children will develop a secure base of knowledge from which mathematical mastery is built. In addition, children’s curiosity about number, shape, space and measure should be encouraged and furthered through opportunities to apply their growing understanding of the mathematical world to the world around them. (DfE, 2019:15)

It seems obviously desirable that young children develop early familiarity with the properties of shape and measures and the language to describe and compare these, in order to progress in learning about geometry and measures in Key Stages1 and 2. There is increasing evidence that early spatial skills are predictive of later mathematical achievement (Young et al, 2018) and that teaching these improves mathematics, including number understanding (Cheng & Mix, 2014; Hawes et al, 2017). Research points to a focus on spatial reasoning, which includes visualizing spatial relations, which is underpinned by a range of spatial experiences, including construction and puzzle activities. Spatial mathematics education also has potential for improving attitudes to mathematics for underachieving groups and individuals: according to Verdine et al (2017) improving spatial experiences prior to school entry is likely to increase children’s readiness for school. (2017: 93) and optimizing spatial performance may be an underutilized route to improving mathematics achievement. (2017:102).Research therefore points to the need to foster early spatial thinking: including this in a Goal is likely to encourage teaching and investment in this area, including professional development and resources. If spatial reasoning is not included in a Goal it will become sidelined, as reported by teachers in the pilot (EEF, 2019, p22), and senior managers are unlikely to prioritise it as a focus for teaching and funding (eg for quality construction materials) thereby further disadvantaging some children.

The ECMG therefore proposes the following Goals and an educational programme which foregrounds positive attitudes and mentions enjoyment, as for other areas, while specifying the focus for shape, space and measures, as for number.

Children’s enjoyment and curiosity about number, shape, space and measures should be fostered through their interactions with people and the world around them. Developing a strong grounding in number and spatial reasoning is essential for all children to develop life-long confidence and competence in mathematics. Children should be able to count confidently, developing deep understanding of numbers to 10, the relationships between them and the patterns therein, through the use of a range of manipulatives. Children should begin to make comparisons about size, length, weight, capacity and time. They should engage in construction and pattern-making activities and learn about position and direction. Mathematical development, like all effective learning, depends upon playing and exploring, active learning, and creating and thinking critically.

Number Goal 2019 * (final 2020 version)	ECMG proposed Number Goal	Rationale
Children at the expected level of development will:	With numbers to 12, children:	Numbers to 12 indicate that counting can continue past the boundary and offer more interesting composition facts.
have a deep understanding of number to 10, including the composition of each number	count out a number of objects from a larger group, match numerals to amounts,compare and estimate numbers, predict adding or taking one.	Each of these aspects has been found by research to indicate deep understanding of numbers and counting and is predictive of later achievement.
subitise (recognise quantities without counting) up to 5	Children subitise (recognize a number of items without counting) up to 5	Subitising is generally considered to contribute to early number understanding.
automatically recall (without reference to rhymes, counting or other aides) number bonds up to 5 (including subtraction facts) and some number bonds to10, including double facts.	and recognise how numbers are made up of other numbers. They solve practical problems including adding, subtracting and sharing.	This emphasises understanding part-whole relations connecting addition with subtraction. This can include conceptual subitising and exploring patterns of visual arrangements of numbers. No level is specified, as research is lacking for this age group: younger children may just recognize that 3 includes 2 and 1. Problem solving is included to require application of addition and subtraction strategies.
Numerical Pattern Goal 2019
count confidently beyond 20*, recognising the pattern of the counting system  *(verbally count beyond 20)		included in the educational programme
compare sets of objects up to 10 in different contexts,* considering size and difference; *(recognising when one quantity is greater than,  less than or the same as the other quantity)	See above: practical problems including ..sharing.	Sharing problems provide important experience of comparing numbers practically. The meanings of ‘size and difference’ are ambiguous in the pilot goal.
explore and represent patterns within numbers up to 10, including evens and odds, double facts and how quantities can be distributed equally.		This is covered above by recognise how numbers are made up of other numbers, and sharing problems. There is no research evidence to show that concepts of evens and odds are understood at this age, so these are better left to KS1.
	Children communicate their mathematical thinking in a range of ways.	This is to ensure that understanding is assessed through a range of modes and that children connect different representations of number relations and concepts.

Shape, space and measures
Current Goal	ECMG Proposal	Rationale
Children use everyday language to talk about size, weight, capacity, position, distance, time and money to compare quantities and objects and to solve problems.	Children: make comparisons of length, weight and capacity	This reduces the number of aspects teachers must assess. ‘Comparisons’ includes language and practical problem solving. ‘Length’ replaces ‘size’ (which is non-specific) and ‘distance’ (an aspect of length). Research does not indicate ‘time’ and ‘money’ conceptual understanding for this age group, so these are omitted.             ‘Position’ is included in the sentence about ‘space’ below.
They recognise, create and describe patterns.	begin to identify the rule in a pattern	The predictive early patterning skill is identifying the core unit of repeat.  ‘Rule’ is suggested to include a greater range of patterns.
They explore characteristics of everyday objects and shapes and use mathematical language to describe them.	select and combine shapes for a purpose and talk about their properties	This encourages a focus on properties of shapes and the way they fit together, with decision making and verbal explanation to show reasoning about these. Contexts would include construction and puzzles.
	follow directions and describe positions and routes	This involves key aspects of spatial reasoning ie bodily movement and orienting, understanding positional and directional language and identifying locations and spatial relations between objects. Contexts might include obstacle courses and treasure hunts.

References

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

Clements, D.H., Sarama, J. & Germeroth, C. (2016) Learning executive function and early mathematics: directions of causal relations Early Childhood Research Quarterly, 36 79-90. doi:10.1016/j.ecresq.2015.12.009

Deans for impact (2019) The science of early learning. Austin, TX: Deans for Impact https://deansforimpact.org/resources/the-science-of-early-learning/

Department for Education (2013) The national curriculum in England: Key stages 1 & 2 framework document

https://www.gov.uk/government/publications/national-curriculum-in-england-primary-curriculum

Department for Education (2018) Statutory framework for the early years foundation stage (pilot version)

Department for Education (2019) Early years foundation stage reforms: Government consultation

https://consult.education.gov.uk/early-years-quality-outcomes/early-years-foundation-stage-reforms/

Early Intervention Foundation (2018). Key competencies in early cognitive development: things, people, numbers and words. https://www.eif.org.uk/report/key-competencies-in-early-cognitive-development-things-people-numbers-and-words

Education Endowment Foundation (2019) Early years foundation stage reforms: pilot report https://educationendowmentfoundation.org.uk/projects-and-evaluation/projects/early-years-foundation-stage-profile-pilot

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. doi: 10.1080/10986065.2019.1588206

Resnick, L. B. (1983). A developmental theory of number understanding. In H. Ginsburg (Ed.),The development of mathematical thinking (pp. 109–151). New York: Academic Press.

Rittle-Johnson,B., Fyfe,E.R., Hofer, K.G., Farran, D.C. (2016). Early math trajectories: low income children’s trajectory mathematics knowledge from ages 4 to 11, Child Development doi: 10.1111/cdev.12662

Siegler, R. S. & Braithwaite, D. W. (2017). Numerical develop­ment. Annual Review of Psychology, 68, 187-213. http://doi.org/10.1146/annurev-psych-010416-044101

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. doi: 10.1111/mono.12285

Young, C.J., Levine, S.C. & Mix, K.S. (2018). The Connection Between Spatial and Mathematical Ability Across Development. Frontiers in Psychology, 04 June.  https://doi.org/10.3389/fpsyg.2018.00755

Sue Gifford, December 2019