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Developing Talk



Talk in mathematics should not be seen simply as a rehearsal in class of the vocabulary of mathematics… It should extend to highquality discussion that develops children’s logic, reasoning and deduction skills, and underpins all mathematical learning activity. The ultimate goal is to develop mathematical understanding – comprehension of mathematical ideas and applications.
The Williams Report (2008)
A highquality mathematics education [therefore] provides a foundation for understanding the world; the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject
National Curriculum for England 09/2013
Creating opportunities for thinking, talking, engaging and enjoying mathematics can be explored in any number of ways but in order to make it manageable for school staff to review and enhance their practice it is helpful to consider the following three separate yet interrelated strands:
Strand 1
The nature of the tasks and challenges in mathematics lessons – do they ‘demand’ engagement and talk.
Strand 2
The kinds of interactions that take place in mathematics lessons particularly the prompts available to teachers to extend pupils’ thinking (reasoning) and talk.
Strand 3
How mathematics lessons can be organised in order to support pupilpupil and pupiladult maths talk.
To begin with, it is more effective to explore your classroom practice within each strand separately so that you can give sufficient time to trying out and discussing alternative ideas and approaches within the context of your own school setting. The ultimate aim is to reintegrate each strand in order to enhance your planning and teaching for talk. Some of the resources used on the project to develop talk in mathematics can be found under Teacher Resources.
Working collaboratively with one or more colleagues will not only help to inform your own practice but will also help you to make a significant contribution towards whole school development. The teachers on the Maths Talk project gained additional insights into developing talk in the classroom by reading relevant research literature and theoretical perspectives. At the same time, the teachers’ professional knowledge and creativity remained central to the process of reviewing classroom practice as did the consideration that the project teachers were working with young learners at the beginning of their journey in understanding, appreciating, applying and enjoying mathematics.
Strand 1
The nature of the tasks and challenges in mathematics lessons: planning for engagement and talk
The varied objectives of teaching cannot be achieved through a single approach or technique. Instead, teachers need a repertoire of approaches from which they can select on the basis of fitness for purpose in relation to the learner, the subject matter and the opportunities and constraints of the context.
Robin Alexander (2008)
Planning for maths talk at Key Stage 1 involves a balance of introducing and rehearsing new ideas, skills and vocabulary at the same time as challenging the children to reason and apply their developing expertise and understanding of mathematics in order to solve problems. On the Maths Talk project, the need for the children to rehearse, use, and apply key facts, skills and concepts was linked to the idea of planning for playful practice to ensure that children had multiple opportunities to:
 become secure (fluent) in the basic ‘atoms’ of mathematical learning;
 share their thinking at the same time as exploring new mathematical vocabulary including the vocabulary for mathematical reasoning;
 establish ‘good work habits’ – persisting, being independent, developing flexibility and looking for alternatives, being systematic, checking;
 develop positive 'can do' attitudes and high levels of engagement;
 use and apply mathematics to solve problems
Planning playful practice (1) : games and cooperative ‘pieces of the puzzle’
Including games, cooperative ‘pieces of the puzzle’ and other ‘playful’ tasks in your mathematics lesson planning ‘demands’ (in the nicest possible way) that children reason and talk to each other and in a highlyfocused way. On the project, we chose games and puzzles:
 that would provide flexibility for teachers in terms of i) slotting in maths content appropriate to the class and ii) could be organised in different ways e.g. children working as a whole class; small groups, pairs, trios;
 where the framing of the task would be easily accessible to the children; would very quickly be familiar enough for the focus to be firmly fixed on the maths content, and would still engage the children when revisited (for rehearsal of key ideas and to aid fluency);
 that would prompt children’s reasoning and exchange of ideas.
You will need to use your mathematics subject knowledge to fit the most appropriate maths content into some of the starting points for your class. Some helpful resources can be found here and here. As the children work through the starting points, you may have to think on your feet when the children’s answers take you by surprise – but stay with it! A very popular, easily adapted starting point amongst the project teachers is inviting children to a Number Picnic (page 15 ATM publication Little People, Big Maths www.atm.org.uk). The children have to discover (reason) the unknown ‘rule’ in order to know if they can join the picnic or not and then provide an explanation of why they think they can join the picnic. As one project teacher said, “The children always request to play the ‘game’ and have become excellent at offering suggestions for rules half way through. Their vocabulary has improved particularly for children with English as an additional language as I can model language structures, for example, ‘it could be... because...’”.
More guidance on the principles underlying a selection of starting points and resources for games and cooperative pieces of the puzzle can be found here and here
Planning playful practice (2) : props and stories
Props and stories are highly motivating for young children who readily engage with the maths in fantasy ‘realworld’ problems and the ‘wow’ factor of sharing their thinking whilst handling larger (or smaller) than life props. Engaging children with using and applying their maths in this way provides teachers with the opportunity to observe, listen and assess children’s discussions which in turn informs the next steps in planning. Teachers of younger children will be adept at putting together props for role play areas to nurture children’s imaginative play and learning and recent research by Helen Williams found here and here provides insight into the use of role play in mathematics teaching and learning across the primary age phase from 511 years.
Stories can help to shape the focus for a role play area or a set of props, or simply be used in their own right as a stimulus for exploring and talking about maths. Choosing the most apt book involves considering the accessibility of the storyline (the story should be engaging in its own right) and whether there is a selfevident link to a topic within the maths curriculum.
Just one or two pages from a story (and sometimes just the front cover!) can set the scene for children to use and apply their maths, compare their ideas and report back on their results – either verbally or in written format perhaps tabulating their results. In this approach to teaching maths, the role of the teacher is to judiciously integrate teaching interactions or demonstrations at appropriate intervals in order to take the children’s learning forward. As children become more familiar with maths lessons centred on problems or investigations from stories or props, they can begin to generate their own questions to investigate.
A list of stories with potential for maths talk can be found in the Teachers Resources section. Although many of the stories are written for younger children, most of the underlying ideas can be used and adapted with KS 2 children who enjoy the humour in many of the texts. For all age ranges it is also possible to exploit elements of nonfiction texts for maths talk and investigations. For example, one Yr 5 project teacher used the storyline of the Ice Trap, Shackleton’s Incredible Expedition by Meredith Hooper and M.P. Robertson, as the basis for creating her own cooperative pieces of the puzzle investigation for her class linked to work on fractions.
Strand 2
Extending the kinds of interactions that take place in mathematics lessons: creating talk habits
At the outset of the Maths Talk project we reviewed the longstanding and seminal work of Alexander, Barnes and Mercer in order to inform our thinking. Our reviews can be found here and here. One of our main project aims was to enhance the quality of interactions in mathematics lessons between teacherpupil and also pupilpupil with a particular emphasis on extending pupils’ thinking (reasoning) and mathematical talk. We wanted to counter the prevalence of the IRF (teacher initiateschild respondsteacher feeds back) in mathematics teaching and shift the balance of talk in maths lessons in favour of higher quality pupil talk. In order to create more opportunities for pupils to share their thinking the project teachers completed a structured listening (monitoring) exercise originally put together by Ian Sugarman for Shropshire Education Authority located here . A reworked version of the monitoring task can be found in the NNS Professional Development materials Book 5. You could equally well play a reasoning game with one child and listen to their reasoning behind the strategies they adopt as the purpose of completing this kind of exercise is to be reminded of how to:
...be genuinely interested not only in what learners are thinking but in how they are thinking, in what connections they are making and not making. Genuine interest in the learners produces a positive effect on learners, for in addition to feeling that they are receiving genuine attention, you can escape the use of questions to control and disturb negatively.
John Mason (2010)
We can work on listening to and building on answers and getting children to do the same. We can reflect on the feedback we provide. We can reassess the balance of drawing out (questioning) and putting in (exposition). We can consider how ideas can not merely be exchanged in an encouraging and supportive climate but also built upon.
Robin Alexander (2005)
Recreating talk habits for teachers and creating maths talk habits amongst children requires taking some deliberate steps to shift the patterns of interactions in the classroom. On our project we explored three different yet equally valid approaches
Approach 1: Pose, pause, pounce and bounce (Ross Morrison McGill blog)
Although originally developed for use with older pupils, this technique was explored by the project KS1 and 2 teachers and was particularly helpful in reminding teachers to allow children sufficient time to think for a moment before sharing their ideas. It’s hard but essential to allow this thinking time and not to jump in with prompts and ‘helpful’ clues too soon!
For pose, pause, pounce and bounce, you do exactly as the prompts say:
Pose a question (or make a statement or show the children an object)
Pause! (let the children think!)
Pounce — in the nicest possible way to ask for a response from an individual or pair (trio) of children and then,
Bounce to other children, either to add to (build upon) the first response or to give their own response.
 ask a friend
 can I have some help please
 can you come back to me
Approach 2: adopt a phrase: fewer questions more invitations?
Making choices about whether and when to use a question or statement or quizzical look as part of your interactions with children is vital to creating purposeful talk habits in maths lessons. The project teachers tried out a range of interactions based on a set of prompts that would allow more space for children to think and reason, at the same time as creating more opportunities for teachers to listen to the children’s thinking.
The exemplifications for ‘adopt a phrase’ listed below have been categorised using four of Alexander’s (2010) dialogic teaching categories:
 encouraging children to think (and think in different ways);
 using questions that invite more than simple recall;
 using phrases and prompts that build upon children’s responses;
 giving feedback that informs and prompts children to take the next step.
adopt a phrase to encourage children to think (and think in different ways)
adopt a phrase to use questions that invite more than simple recall
adopt a phrase that builds upon children’s responses
adopt a phrase to give feedback that informs and prompts children to take the next step (and also encourages!)
Although originally introduced as prompts for the teachers to use, the project teachers found that the children spontaneously started to use the phrases and prompts in their talk pairs or trios as well.
Approach 3: reproposing
Capture something that a child has said (or recorded on paper) and repropose it to them (or to the whole class) word for word  either there and then or, on another occasion. You may want to write it down and share it the next day. You may want to video a group and share the film back with the group or class for discussion. You may like to start a ‘reproposal’ wall of ideas in the classroom.
You can make a start on ‘ reproposing’ by simply echoing back the answer a child has given (keeping as neutral a tone as possible!) which can prompt her/him into giving a more detailed response (explanation). For example,
One of the project teachers was working on place value H T Us with her class. The class watched as K placed bundles of ten straws and then single straws into a box. The task was for the children to find the total number.
Ch: It’s 52
K: 52
Ch: Yes, because I think you did 5 ten bundles and then 2 straws by themselves and 50+2 = 52, see.
The project teacher comments: “Previously, I might have been tempted just to say ‘well done’ when given the [correct] answer ‘52’. When children got the answer correct, reproposing helped them to extend their reasoning. When they had got it wrong it helped them to check and question themselves.
You can read more about the thinking behind repropsal in the following:
Strand 3
Organising mathematics lessons to promote maths talk
Planning to maximise the opportunities for children to discuss and explain their thinking in mathematics lessons not only involves the careful choice of tasks and challenges but also requires careful consideration as to how the children will be organised. Jenni Way provides some guidance for organising groupings for playing games and cooperative puzzles The Talking Counts research project based at Exeter University provides additional insights as well as practical suggestions for maths challenges for KS1 children to work through. Talk Partners feature in many primary classrooms but the Exeter project explored the impact of grouping children in 3s  Talk Trios. The teachers on our Maths Talk project organised their Talk Trios in differing ways and the trios spilled over into other lessons. Two project teachers commented:
 mixed ability trios so that all children can achieve – maths isn’t just for ‘clever’ children;
 children choose their own partners;
 trios in all lessons not just maths;
 occasionally some dominant children in the trios but all the children know that they are expected to join in the talk and to feed back to the class;
 some teacher support to encourage less vocal children to speak for the group;
 can’t see myself returning to talk partners!
Talking Counts takes a close look at encouraging exploratory talk in mathematics lessons
The teachers on our project also thought creatively about organising classroom furniture that supported maths talk in groups:
Sometimes more discussion and problem solving took place when the furniture was removed.
Other devices that younger children clearly enjoyed at the same time as being prompted to share their thinking included explaining ideas to an alien, pretending you are a penguin and discussing your maths problem with a duck! if you are stuck, talk to a duck!