“Mathematics, a universal language that enables understanding of the world, is an integral part of the curriculum.”
It’s equally brilliant to see accurate mathematical vocabulary being prioritised as a driver to reduce the attainment gap:
“A proactive approach to helping children to acquire everyday language used to describe quantity, shape and time would also benefit disadvantaged pupils, who are more likely to misunderstand instruction and activities.”
And that language is seen as an key representation in its own right. With successful vocabulary acquisition needing to be cumulatively sequenced in a well-connected curriculum. This is evident through a dedicated section headed: “Maths facts, vocabulary and symbols at the start of a sequence” which places the responsibility on the teacher to “engineer the best possible start for pupils by closing the school-entry gap in knowledge of the early mathematical code: facts, concepts, vocabulary and symbols."
“In the primary phases, pupils’ experience of problem-solving often involves solving word problems. The first barrier to overcome is language.”
Yes! Fantastic to read about the difficulties that can arise when interpreting language within word problems. Converting between different representations is really challenging for pupils (another nod to the overlooked ‘maths giant’ - Duval, from previous blogs). However, it’s disappointing because it feels to us that the review then goes on to focus only on developing pupils reading skills as a solution: “Pupils therefore need to be proficient readers at the required level”.
Of course reading is vitally important but the role in which dialogue plays in mathematical understanding (including engaging with problems) feels undervalued. Here’s Robin Alexander, an internationally acclaimed and influential ‘maths giant’, who has published widely on a range on topics from policy to pedagogy, defining dialogue:
‘achieving common understanding through structured, cumulative questioning and discussion which guide and prompt, reduce choices, minimise risk and error, and expedite “handover‟ of concepts and principles’
Robin Alexander (2004)
Pertinent when we are all aiming towards “conjecturing” environment encouraged by our own National Curriculum.
The EEF research review found that:
Alexander et al. (2010) argue that dialogic teaching is crucial to advancing learning. Effective discussion is likely to be part of collaborative approaches to learning. This will include elements of listening, reflection, evaluation, and self-regulation (Kyriacou & Issitt, 2008). Discussing mathematics can help to make learners’ thinking visible and enable ideas to be critiqued (Walshaw & Anthony, 2008).
(Hodgen et al. 2018, page 46).
It is disappointing to see that a quick search of the term ‘talk’ across the entire research review yields no results. No references to talk in the maths classroom. Books, research, articles, webinars – you name it, many maths giants have dedicated their entire careers to talk. Robin Alexander’s work on ‘Dialogic teaching’ (see above), Neil Mercer’s ‘types of talk’ and Clare Lee’s on ‘Language for Learning Mathematics’ all lend themselves nicely to the review’s focus on solving problems too.
“It is important that pupils use mathematical language themselves. […] Pupils who are able to use mathematical language to express their ideas are able to communicate with one another and their teacher, they are able to both build and share meanings of words and expressions, and ultimately learn maths more effectively.”
Clare Lee (2006)
Instead, the review chooses to focus on the following recommendation: “Studies have also shown that the ideal environment for periods of independent work is one that is not just quiet but is in fact near silent”
This is surprising as the National Curriculum is very clear on the importance of talk in maths learning: ‘The national curriculum for mathematics reflects the importance of spoken language in pupils’ development across the whole curriculum – cognitively, socially and linguistically. The quality and variety of language that pupils hear and speak are key factors in developing their mathematical vocabulary and presenting a mathematical justification, argument or proof. They must be assisted in making their thinking clear to themselves as well as others, and teachers should ensure that pupils build secure foundations by using discussion to probe and remedy their misconceptions.’
Although we feel quiet environments can help pupils focus, just as each child is unique, each class is unique too. So, we feel teachers are best placed to decide the volume of their own classrooms during independent work, a volume which that suits the needs of their specific pupils.
It’s a shame, as we interpreted the review as only advocating a classroom environment of ‘near silent’. This shortcoming misses the opportunity of promoting the NC’s requirement of using talk to assist pupils ‘in making their thinking clear’. Askew’s work on ‘private talk’ and ‘public conversation’ (a ‘maths giant’ referred to in my previous blog on representations) would have been a helpful inclusion here. Opportunities to engage in ‘private talk’ can help pupils articulate and refine their thinking during in ‘secure setting’ of independent work to ‘rehearse ideas that they might share more widely’.
The review claims a core theme is how to prevent struggling pupils from falling further behind their peers. Why is talk not a central part of its messaging?
“One in three children who struggled with language at age five did not reach the expected standard in maths at age seven” Save the Children report, 2016.
This large scale study took place ‘pre-COVID’ – imagine the picture now, with prolonged and ongoing school disruption nationwide.
Talk is of crucial importance in the maths classroom. All pupils deserve a classroom ethos which encourages and supports meaningful communication. Whilst we can’t change our pupils’ backgrounds, we can support their development of language and subsequent later outcomes.
In the final instalment, we’ll take a look at the review’s stance on mathematical thinking.
Askew, M. (2016) Private Talk Public Conversation (article) From Mike@mikeaskew.net on NCETM EY Website.
Clare Lee, 2006. Language for Learning Mathematics
Duval, R. 2006. A Cognitive Analysis of the Problems of Comprehension in a Learning of Mathematics. Educational Studies in Mathematics. 61: 103-131.
EEF Guidance Report: Improving Mathematics in Key Stages Two and Three. (November 2017)
Hodgen, J., Foster, C., Marks, R., & Brown, M. (2018). Evidence for Review of Mathematics Teaching: Improving Mathematics in Key Stages Two and Three: Evidence Review. London: Education Endowment Foundation, accessed at: https://educationendowmentfoundation.org.uk/evidence-summaries/evidencereviews/improving-mathematics-in-key-stages-two-and-three/
Mercer, N. (1995) The Guided Construction of Knowledge: talk amongst teachers and learners. Clevedon: Multilingual Matters
Robin Alexander, 2004. Towards Dialogic Teaching.
Save the Children (2016) Early Language Development and Children’s Primary School Attainment in English and Maths: New Research Findings, accessed at https://www.savethechildren.org.uk/content/dam/global/reports/education-and-child-protection/early_language_development_briefing_paper.pdf