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Are you interested in the education of very young children? Certainly, if you are an early years or primary teacher or researcher, or have small people of your own, you will be. If you teach or are involved with the education of older learners, you may perhaps think this is tangential.
The problem is that young children’s experiences colour the rest of their lives. We know from longitudinal studies that early emotional experiences, attachments (or the lack of them), nutrition and exercise all have long term effects. These seem so fundamental that perhaps considering early mathematical experiences in the same context seems relatively unimportant. But there is a reason why we should all be concerned about what, and how, mathematics is taught to early learners.
Whilst the learning of maths doesn’t follow a clear hierarchical structure, nevertheless there is a fundamental knowledge and skill which needs to be in place in order to progress. The firmer the foundation, the higher the mathematical edifice can be built. Conversely, the less firm the foundation, the lower the edifice; and the less the mathematical knowledge and skill, the less confident or competent the learner is likely to be, to the extreme extent of being unable to function in society. And, to continue the story, this not only has implications for the happiness and well-being of individuals: recent calculations indicated that innumeracy also ‘poses …. a cost to the UK economy, estimated to be £20 billion a year’1.
This is pretty serious. What do we know about how and what young children should experience in their early education in order to be successful mathematically? What does research say about the way small children learn best, and what knowledge and skills they should be expected to acquire, in order to have the best chance of being mathematically confident and capable, thereby contributing positively to the nation’s well-being?
The Framework we are designing here at Cambridge Maths is predicated on research and evidence. We know, for example, that for children to develop a flexible understanding of number, they need, amongst other things, to link the names of the numbers to the numerals, their value, and their position in the counting order. These are key predictors of mathematics attainment2. We know that playing with number and solving simple problems involving addition, subtraction and sharing support both mathematical understanding and the development of executive functions3. So it is worrying that these essential building blocks of early mathematics have been removed from the latest version of the English Early Learning Goals (ELGs)4, and replaced with ‘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’.
Number is of course not the only constituent of mathematics. There is extensive research suggesting a strong correlation between spatial skills and success in many strands of mathematics; some obvious such as geometry, but also others including mental arithmetic, calculus and algebra5. Children who have good spatial skills are more likely to succeed in STEM subjects6, so promoting spatial skills in the early years may have the potential for creating long-term positive effects on mathematical performance.
This evidence of course applies to all children. The research on sex differences is mixed, but there is some evidence that the connection between mathematical achievement and spatial skills may be stronger for girls than boys7, even though traditionally girls are not provided with as much very early spatial experience (e.g. puzzle play, playing with blocks) as boys8. Neglecting spatial skills development in girls (and other underrepresented groups) is a hindrance to their progress in maths. Access to high quality spatial experiences is an equal opportunity issue.
For all these reasons it is disappointing that whilst shape, space and measure are included in the curriculum description, there is no mention of them at all in the revised ELGs. The message to heavily pressed teachers is that spatial stuff is less important. This was evidenced in the findings of the independent pilot of the ELGs, evaluated by the Education Endowment Foundation9 last year.
Nick Gibb, Minister for Schools Standards, said the consultation would “help to make sure the early years foundation stage framework will make a difference to a child’s education as they move through the early years to more formal schooling”.
I think it will only make a positive difference if those who are serious about using robust research evidence to drive policy challenge these notable omissions in their responses to the consultation. You can view it here.
1National Numeracy (2019) Numerate nation? What the UK thinks about numbers.
2Early Intervention Foundation 2018 Key competencies in early cognitive development, things, people, numbers and words.
3Clements, D. H., Sarama, J. & Germeroth, C. (2016). Learning executive function and early mathematics: Directions of causal relations. Early Childhood Research Quarterly 36 79–90.
5,6Hawes, Z., Moss, J., Caswell, B., et al. (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 35 236–264.
7Levine, S. C., et al. (2012). Early puzzle play: A predictor of preschoolers’ spatial transformation skill. Developmental Psychology 48(2) 530–542.
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