(image: Julie Herlihy)
Two recent events sparked this blog. Firstly, watching the launch video of the NCETM’s Reception and KS1 ‘Mastering number’ programme, where three approaches to teaching maths are characterised:
And secondly, an email question from a teacher about whether or not dedicated time each day was appropriate or effective for children learning mathematics in the EYFS - should there be a short ‘formal’ maths lesson each day in EYFS?
Mathematics research is clear, that there must be a balance in the EYFS between what Clements and Sarama (2021) call "high-quality instruction in math and high-quality free play” (Anthony and Walshaw 2007, Downton et al 2020). This is because high-quality teaching both helps children learn and raises adults’ awareness of, and ability to make use of, the maths potential of other, everyday activities:
“… and - this is important - such math promotes higher quality play. Really? Yes: children in classrooms with stronger emphasis on math were more likely to be engaged at a higher-quality level during free choice (play) time.”
(Clements and Sarama 2021: 373)
So, this is obvious, isn’t it? If we prioritise and value something, quality rises. But now to the word ‘formal’. Adult-led teaching is indispensable for effective mathematics learning, but this should be unpressurised and playful, to avoid the development of maths anxiety (DEANS for Impact 2019). Adult-initiated interactions with groups of children, small and large, need not be ’telling shops’, but instead be playful and truly interactive, taking children’s ideas onboard. This is true for all ages of learner, or we risk re-cycling all the same problems associated with maths teaching – disassociation, lack of interest, anxiety. Research doesn’t indicate any sort of timing or whether there should be whole- or larger-group sessions. In the end, what matters is that I am clear about why I am doing what I do; a lot of children’s time is wasted on the carpet.
Exploration
Adult-led sessions and free play (exploration) work together. Whitebread’s research has consistently demonstrated superior learning and motivation arising from playful approaches to learning with young children (Whitebread, Basilio, Kuvalja and Verma 2012). I would go further and argue there needs to be such a balance at all stages of learning/school. I have written more about this here: https://info125328.wixsite.com/website/post/roller-skating-or-tidying-which-is-mathematics-to-be . All children of all ages need both a safe environment and time to make sense of the ideas we share with them, the teaching we do, and in order to make connections with their own ideas. Time to make sense on their own, with friends, to redo something, to practice: time for exploration. Frequency of mathematical experiences in a wide range of contexts is important (What Works Clearing House 2013) and what is often called ‘continuous provision’, in particular, can offer space for children to make sense of what they are being taught, to reinforce ideas and to do so independently. Moreover, through sensitive interaction with children whilst they explore, we can build young children’s mathematical understanding further as well as supporting the development of the statutory EYFS Characteristics of Effective Teaching and Learning (DfE 2020). Exploration provides children opportunities to become engaged, to have and explore their own ideas, plan and make decisions about how to approach a task, etc. This shouldn’t finish at the end of Reception.
Dedicated maths sessions
(image: Maeve Birdsall)
In the launch video for the NCETM’s ‘Mastering number’ programme, which consists of daily dedicated maths sessions for year groups R to Y2, it is the following approach to teaching that is prioritised over others:
“The attention of all is focused on the one mathematical relationship and distractions are reduced.”
I don’t have a problem with the focussing of children’s attention, indeed it is hard to think of an effective teaching situation where this doesn’t occur. I don’t have a problem with this being the emphasis for the programme’s short teacher-led maths sessions (although I have yet to see the materials to see if these are effective and appropriate for the age range 4-7). However, this video is saying something else, it is saying the other two approaches described on the slide are ineffective. Regarding what they call “an open approach” (there is no definition of what this is) the statement is:
“One of the downsides of this approach is that we get lots of ideas all at once, which can be for some children, be overload and all they want to think about is their own idea. They haven’t got the space in order to learn new ideas.” (NCETM 2021)
Unpicking this statement:
“We get lots of ideas all at once”: Isn’t this just what we want? Isn’t this the way we assess and respond to all our - unique – children? Isn’t this exactly how children become involved in the maths? Isn’t it our job to manage this, sift these ideas, value these and choose those to pursue now, which later? Isn’t that the stuff of teaching? Isn’t us listening to what children are thinking and how they are making connections and reasoning the most important thing we do when we teach?
“…and all they want to think about is their own idea. They haven’t got the space in order to learn new ideas.”
We don’t stop children’s ideas by focussing on one, children will still want to think about their own idea – we all do, don’t we? Imagine yourself in a meeting, listening to someone speaking. We all have our own thoughts. The issue is whether we as teachers invite and use these. I would argue that it is my job, in working towards understanding, to hear and build on these ideas, linking them with the mathematical relationship(s) I am focussing on in my teaching. We all have something to bring to the maths. To imply these young children’s ideas (under 7 years of age and under statutory school-age in many jurisdictions) are not worth listening to is sending a very damaging message about mathematics, that, in the words of Anita Straker:
“There is a danger that mathematics is seen by children as something in which they learn about other people’s ideas, particularly yours,
and it has nothing to do with them.”
(Anita Straker 1993:10)
Have we learnt nothing since 1993?
“… which can be for some children, be overload”: Where is the evidence that listening to the ideas of others is “overload”? What is overload in this sense? Where is the acknowledgement that others’ ideas can feed into a rich, sustained, joint conversations that lifts all children’s thinking? In fact, where is the acknowledgment of the value of children’s talk to advance and develop their thinking at all?
What about the importance of Executive Functioning? (Gilmore & Cragg 2018). There are three aspects to Executive Functioning:
(1) inhibitory control
(2) working memory,
(3) attention shifting and cognitive flexibility.
It is our job to support the development of children’s EF abilities, and we don’t do this by ironing out distractions.
The NCETM appears to be, without research evidence, sending a message that there is one way to teach that is better than any other; teacher directed. This is not OK.
I am aware that many EYFS practitioners and those working in KS1 are fearful of the erosion of the fundamental principle of the Unique Child (DfE 2020) and of time for play in the earlier years. I share that concern, as these are both devalued and misunderstood by both DfE and Ofsted. Adult-initiated episodes are essential in mathematics but this should not make up the entirety of our children’s maths diet. High-quality instruction, the words of Clements and Sarama can be a balance between whole group teaching, teacher-led work with small groups or working with a child 1:1. These need to be playful by nature and tuned into the children’s developmental level and interests, as Clements and Sarama illustrate. Such sessions have to be developed and extended by children in their exploratory play., which in turn feeds into the teaching episodes. Teaching is never an either/or, exploratory and dedicated maths sessions are not binary situations but complex interactions between children and adults. Both require us to listen to our children and hear their ideas.
These ideas are explored further in my book “Playful Mathematics”, to be published by SAGE in the spring of 2022
References:
Anthony, G., and Walshaw, M. (2007). Effective Pedagogy in Mathematics/Pangaram: Best Evidence Synthesis Iteration [BES]. Wellington, New Zealand: New Zealand Ministry of Education
Clements, D. and Sarama, J. (2021). 3rd Edition. Learning and Teaching Early Math: The learning trajectory approach. New York: Routledge
Deans for Impact (2019). The Science of Early Learning: How Young Children Develop Agency, Numeracy and Literacy. Austin, TX: Deans for Impact.
Downton A., MacDonald A., Cheeseman J., Russo J., McChesney J. (2020). Mathematics Learning and Education from Birth to Eight Years. In: Way J., Attard C., Anderson J., Bobis J., McMaster H., Cartwright K. (eds) Research in Mathematics Education in Australasia 2016 –2019. Singapore: Springer
Gilmore, C., and Cragg, L. (2018). The role of executive function skills in the development of children’s mathematical competencies. In A. Henik & W. Fias (Eds.), Heterogeneity of function in numerical cognition (pp. 263–286). Elsevier Academic Press.
Straker, A. (1993). Talking Points in Mathematics. Cambridge: CUP
WWC (What Works Clearing House) (2013). Teaching Math to Young Children. Available at: https://ies.ed.gov/ncee/wwc/PracticeGuide/18
Whitebread, D., Basilio, M., Kuvalja, M. and Verma, M. (2012). The Importance of Play: A report on the value of children’s play with a series of policy recommendations. Brussels: Toy Industries of Europe (TIE). Available at: http://www.csap.cam.ac.uk/media/uploads/files/1/david-whitebread---importance-of-play-report.pdf