Oracy is a set of skills which allow us to communicate effectively and encompasses learning to talk and learning through talk; both involve speaking and listening. Learning to talk should lead to learning through talk. The aim is for learners to articulate their mathematical thinking, to make it clear to themselves and others, and to make sense of the mathematical thinking of others, developing a relational understanding of the mathematics1. To achieve this, teachers will need to support exploratory talk2, use dialogic teaching3 and ‘orchestrate productive mathematical discussion’4.
Learning to talk includes:
- Establishing the psycho-social conditions which encourage and support exploratory talk; a classroom ethos that supports communities of learners where everyone’s voice is valued, all learners have the potential to influence others and consensus building is central to lessons. This may involve:
- Supporting all learners by addressing/removing feelings and thoughts that act as a barrier, by saying:
- What’s your first thought?
- What could you do? What might work?
- Imagine you are the sort of person who could do this, what would you do?
- What would Batman/Elastigirl do?
- In response to other learners, learners use sentence starters and questions:
- I agree/disagree because…
- I think differently…
- I’m not sure but…
- Can I make a suggestion?
- Can I ask a question?
- Do you mean…?
- Deliberate positioning of both the teacher and the speaker during episodes of both ‘private talk’ and ‘public conversation’5:
- During private talk (in pairs/trios) teachers:
- Provide space for talk without intervening, sitting and noting from a distance
- Move around, listening in to select and sequence contributions for public conversation
- Prime learners so that they can rehearse their thinking before speaking publicly
- During public conversation (large group/whole class)
- Speakers stand up in their place or come to the front so that they are prepared to speak publicly, and other learners know where to focus their attention
- Teachers position themselves across the class from the speaker to encourage projection so that everyone can hear
- Talking about talk, explicitly identifying aspects of talk useful to the group:
- I am listening out for people who…
- Reproposal6: I heard…say…
- Praising talk, distinctly from mathematics: I like the way you started by saying…
- Supporting all learners by addressing/removing feelings and thoughts that act as a barrier, by saying:
- Being supported to articulate thinking in full sentences. This may involve:
- Using sentence starters such as:
- I notice…
- I think…because…
- I know…
- I wonder…
- Repeating well-structured sentences spoken by other learners and adults.
- Attend to precision in repeating before rephrasing. Ask ‘Is that exactly what you said?’
- Creating meaningful sentences employing both mathematical and everyday vocabulary.
- Requiring use of given words and phrases such as:
- Describe the fraction using the word ‘divided’.
- Explain what you notice about the pattern using the word ‘multiple’.
- Being specific and avoiding the use of pronouns:
- Saying ‘The numerator is seven’ rather than ‘It is seven’.
- Requiring use of given words and phrases such as:
- Using sentence starters such as:
Learning through talk includes:
- Establishing the cognitive conditions where there is something mathematically worthwhile to talk about by providing mathematical experiences that provoke thinking. This will involve:
- Teachers providing time and space for children to think and articulate their thinking:
- Allowing thinking time before talking
- Expecting all learners to share their mathematical thinking
- Asking authentic questions7
- Praising thinking distinctly from correctness
- Teachers providing time and space for children to think and articulate their thinking:
- Teacher modelling thinking aloud with careful, precise use of language.
- Exposing, accessing, and understanding mathematical structure. This may involve:
- Careful use of stem sentences, spoken in full by learners, with a focus on mathematical structure such as:
- To find one … of a shape you divide it into … equal parts.
- I have…one tenths. I have… tenths.
- There are … rows of… There are…altogether.
- Repeating
- Drawing attention to a response that exposes something about the mathematics and ask the class or an individual to repeat this response word for word.
- Rephrasing
- Can you explain what Megan said in your own words? Megan, is that what you meant?
- Consensus building8:
- Making sense of the appropriateness of strategies that are presented
- Examining how presented strategies are both meaningful and efficient
- Connecting different strategies presented
- Extracting the general rule that can explain the differences in the presented strategies
- Creating generalisations together such as:
- For unit fractions, the larger the denominator, the smaller the fraction.
- Angles which meet at a point on a straight-line sum to 180 degrees.
- Careful use of stem sentences, spoken in full by learners, with a focus on mathematical structure such as:
- Mathematical questions arising from students. This may involve:
- Clarifying understanding linked to the learner’s responsibility when listening.
- Using sentence starters and shared questions such as:
- Why does…?
- Can I ask a question?
- What do you mean by…?
- Clarifying understanding linked to the learner’s responsibility when speaking:
- Does anyone want to ask me a question?
- Questions prompted by the mathematics:
- Will it always be …?
- Does that always happen?
- What would happen if…?
- Using sentence starters and shared questions such as:
- Clarifying understanding linked to the learner’s responsibility when listening.
Reference notes:
1 Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20-26.
2 Mercer, N. & Dawes, L. (2008) The Value of Exploratory Talk in Exploring Talk in School: Inspired by the Work of Douglas Barnes, Sage Publishing
3 Alexander, R. (2008) Towards Dialogic Teaching: Rethinking Classroom Talk, Dialogos
4 Smith, M. S., & Stein, M. K. (2011). 5 practices for orchestrating productive mathematics discussions. Reston, VA: National Council of Teachers of Mathematics.
5 Askew, M. (n.d.) Private Talk, Public Conversation available online: http://mikeaskew.net/page3/page5/files/Privatetalkpublicconverse.pdf
6 Parker, C. (2001) In Experiencing Reggio Emilia: Implications for pre-school provision, ed. L. Abbott, and C. Nutbrown, OUP.
7 Schaffalitzky, (2022) What makes questions authentic, 428- 2022-02-03 Dialogic Pedagogy
8 Noriyuki Inoue, Tadashi Asada, Natsumi Maeda, Shun Nakamura, (2019) Deconstructing teacher expertise for inquiry-based teaching: Looking into consensus building pedagogy in Japanese classrooms, Teaching and Teacher Education, Volume 77, 366-377
Version 1.6 January 20th 2023