“Recently sat through a meeting talking about children all moving towards achieving ELGs and moving through the same learning at the same time. Just gotta say - for anyone who understands young children and their development - this is nonsense. That’s all.”
This tweet from Elaine Bennett @KeepEYsUnique, an experienced reception teacher and fellow member of the Early Childhood Mathematics Group https://earlymaths.org , has brought into focus for me the ongoing debate about progression documents and learning trajectories. In this blog I would like to spell out what I see as the very real difference between the two in relation to learning and teaching mathematics. In the process I discuss so-called ‘small steps’ of learning, teaching and ELGs.
Firstly, it is important that adults working with young children have knowledge of where learning ‘comes from’ and ‘moves to’ in an area of learning. This is to do with knowing about the mathematics and knowing about the development of young children in relation to that mathematics. This is an evidence-informed learning trajectory and there are trajectories of varying degrees of detail available for free, online. A good one to start with is the early years section of the NCETM website: https://www.ncetm.org.uk/in-the-classroom/early-years/
And although not strictly trajectories of learning, the guidance documents organised broadly by age on the ECMG site are also useful: https://earlymaths.org/building-firm-foundations-in-mathematics/ . But the go-to place for a detailed, research-based trajectory for each area of maths is that pulled together by Clements and Sarama and their team, here: https://learningtrajectories.org
You have to sign up, but this is comprehensive, evidenced and is all absolutely free. Why write our own?
A progression document - those that I have seen – are about the children rather than the maths. They are about plugging in the children at the beginning and not moving them ‘on’ until they ‘master’ each step along the (same) journey. They become minimum ‘expectations’ for a year group that are ‘ticked off’ when they are achieved. Here is one for counting:
The problem with a progression like this is that this isn’t how we learn: learning is messy. This is why the Unique Child is enshrined in the statutory EYFS https://www.foundationyears.org.uk/files/2017/03/EYFS_STATUTORY_FRAMEWORK_2017.pdf A progression document such as that above is a false set of steps introduced to lead to, often, an ELG or to link to the KS1 curriculum. A progression document is also no help to me if I am teaching. There is no support and no notion of how one idea might link with and build on another.
On the other hand, a learning trajectory is quite different. It works from a – distant – goal and draws on research into child development and mathematical understanding to build up what children need to be able to do attain that goal.
“Children follow natural developmental progressions in learning and development. Children follow natural developmental progressions in learning math, too, by learning math skills in their own way.” (Clements and Sarama 2021, p3)
The key phrase here is “in their own way’. There are goals but these are coherent and connected ‘big ideas of maths’ that are indicative of future mathematical development. Trajectories are not absolute stages, but rough guides of developmental pathways, they are not lists of everything that children need to learn, but high-quality illustrations of how we might work to support the kind of thinking that children need to develop. And longitudinal research on the use of learning trajectories has found them to be a powerful tool for teaching and learning (Clements and Sarama 2007, 2008).
For example, here is one for counting:
(Clements and Sarama 2021, p5)
The difference is striking. A trajectory supports teaching and learning by helping us understand children’s thinking and thus help children learn deeply by tuning in both our incidental and our planned teaching to this.
This is an essential distinction between teaching and monitoring. I am noticing that folk are spending hours and hours drawing up, and requesting examples of, progression documents for all areas of early learning. My response is, for whom? Will it positively affect my teaching? The children’s mathematical experience and ultimately, their learning? Often not. Having access to a trajectory will however positively enhance my teaching.
So, I am arguing for a refusal to draw up a progression document and to examine any I am shown critically. Who is it written for? If it is for a member of SLT then I have much better things to do that will benefit my children’s learning. If it is “for Ofsted” it is worth pointing out this recent tweet from Ofsted:
What we also have to remember is that although these learning trajectories are organised under mathematical areas or topics, attitudes and processes are as important to develop alongside – and integrated into – all these topics. And that’s why the Characteristics of Effective Learning are so important. Which is probably another blog.
Table taken from Ofsted (2013) Mathematics in school inspection: Information pack for training.
References
Clements, D.H. and Sarama, J. (2007). Effects of a pre-school mathematics curriculum. Summative research on the Building Blocks project. Journal for Research in Mathematics Education, 38 (2)
Clements, D.H. and Sarama, J. (2008). Experimental evaluation of the effects of a research-based pre-school mathematics curriculum. American Educational Research Journal, 45 (2)
If you are really interested in this the recent book referenced in this blog is:
Clements, D.H. and Sarama, J. (2021). Third edition. “Learning and Teaching Early Math: The learning trajectory approach.” New York: Routledge
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