Talk for learning Session 3
Aims of the session To reflect on the use of talk in the mathematics lesson in the context of the Williams Review To become familiar with recent research into different characteristics of effective talk in the classroom To consider how these characteristics might be developed to enhance children’s mathematical understanding To work collaboratively to plan a guided group session incorporating talk for learning
Williams Report 2008 “Talking mathematics should not be seen simply as a rehearsal in class of the vocabulary of mathematics, novel and important though that may be for the young learner. It should extend to high-quality 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 ofmathematical ideas and applications.”
Odd one out 1 4 19 25
Describe this group of numbers 12, 2, 6, 18, 9, 3, 4, 1, 2
Effective features of talk (EPPI) Going beyond ‘Initiate, Response, Feedback’ Focusing attention on mathematics rather than ‘getting the answer right’ Working collaboratively with pupils Transformative listening Scaffolding Enhancing pupils’ self-knowledge about using dialogue as a learning experience Encouraging high quality pupil dialogue Inclusive teaching (Full report = http://eppi.ioe.ac.uk/cms/LinkClick.aspx?fileticket=8eLz2pqykKw%3d&tabid=2368&mid=4383&language=en-US)
A says to B, "If you gave me one of your books, I would have as many as you." B replies, "If you gave one of your books, I would have twice as many as you." The question, of course, is "How many books do A and B each have?" • Thinking about the above problem: • Language of the problem – what makes it difficult? • The strategy to solve it – where is the mathematics in the • problem? • The description of the solution – what does it focus on and • how does it work? • Language of the teacher – the child – the mathematics
Going Beyond ‘Initiate, Response, Feedback’ (IRF) “Some teachers go beyond the typical use of IRF which involves asking pupils to answer closed questions and then giving them some evaluative feedback. Some teachers use more open-ended questions and follow-up questions, and asking pupils to explain the method they had used.”
Talk Prompts What can you work out? (From the information given) If you know that, what else do you know? Can you tell me what your thinking is? Shall we test that? Does it work? Do you still think that is …..? Do you agree that ………….? Why is that bit important? So, what must it be?
High-quality pupil dialogue “Teachers can respond in an encouraging manner to pupils’ contributions. There is a need for teachers to be accepting towards pupils’ contributions, to encourage pupils to develop their contributions further and indeed, to allow the direction of a lesson to follow the pupil’s contribution. Being accepting towards pupils’ contributions may enhance the quality of the discourse, but may also create a tension for the teacher in wanting to direct pupils’ attention towards mathematically acceptable strategies.”
Is it sometimes, always or never true? The difference between any two odd numbers is an even number. If you add three consecutive numbers together, the answer is always even. The sum of four even numbers is divisible by 4.
Giving a good explanation: Has a logical sequence or order - may begin with explanation ‘stem’ e.g. I know that…because… Uses appropriate and accurate technical vocabulary Speech is clear and confident May initially seek clarification from the questioner Responds accurately to the question Uses pictures, diagrams, apparatus to support and clarify
Scaffolding “Teachers can use dialogue to scaffold pupils’ thinking and understanding. Scaffolding is when the teacher provides support (or scaffolds) to help the pupil’s learning and this helps pupils build on prior knowledge. Different types of scaffolding can be used by teachers, for example the teacher focusing pupils’ attention during a class discussion on key features and merits of particular strategies suggested by pupils for solving a challenging problem. Another example was to discuss with pupils a deliberate mistake in dialogue to stimulate the quality of pupils’ mathematical thinking.”
Tom’s problem Tom collects stamps. One day he counted his stamps. He said “When I count the stamps by two I have one left over. When I count the stamps by three, I have one left over. When I count by five I have none left over.” How many stamps has Tom got?
Key Messages Effective dialogue: Provides regular opportunities for all children and adults to talk about mathematics in order to challenge mathematical ideas to refine thinking to confirm understanding Involves listening and responding to one another’s ideas to build on and secure learning Develops and shares models of how mathematical language can be used accurately Links to and between practical, written and all other forms of mathematical communication Is an integral part of effective mathematics learning
What makes a good guided session in mathematics? • A focus on developing use of mathematical language to explain • and reason • Opportunities for children and teachers to engage in sustained • mathematical dialogue • Informed by and creating opportunities for assessment including • active observation to gain information and take action • Purposeful selection of groups informed by the focus of the learning • Use models and images that support aspects of learning and • thinking these children find difficult • Promote a ‘can do’ approach to problem solving and enquiry within • a self-supporting group • Review the presentation, accuracy and efficiency of methods • avoiding any sense a method is right or wrong • An integral part of quality-first mathematics teaching
Guided group session incorporating talk for learning What is the learning objective? Which group of children will be involved? What is the role of the teacher in the guided group session? Which of the 8 characteristics of effective dialogue will be incorporated in the session? How will collaborative talk be encouraged? What questions will the teacher ask? What are the expectations of the talk that will be used and developed? How will the children be supported when they run into difficulties? How will they be encouraged to persevere?
The teacher’s role is multifold: To ask questions to support the children in developing their methods for finding a solution without modelling ‘the way’ of tackling this To help the children to articulate their way of tackling the problem To help the children to see how alternative methods work so they can begin to decide which is more efficient and why To enable children to set associated problems on which they can use their methods to see if they work and refine them where appropriate To assess the skills the children have in tackling problems like this and use this information to determine the next steps in teaching
How will you further develop the characteristics of effective dialogue in your teaching sessions?
Session 4 Plenary
Feedback from Day 1 interim task – Overcoming barriers How did you adapt and develop the materials to personalise them to the identified children’s learning needs? What impact did the use of the materials have on children’s learning? What was the role of your collaborative partner in developing this activity in the classroom and evaluating impact?
Over the course of the two days and interim task you have: explored assessment for learning in mathematics, including APP processes and tools developed knowledge of the Overcoming barriers materials planned and carried out collaborative CPD based on using these materials to support a guided group session used developing knowledge of the APP materials, including standardising judgements and moderation, to identify areas of development for children explored talk for learning and guided group work in more depth with a view to planning a further in-school guided session
Next steps – points to consider What steps do you now need to take to further develop the use of APP processes and tools within your own practice and to support the moderation of assessments within your school? How might you build on the interim task to work with a colleague to further implement the use of Overcoming barriers materials as one tool in supporting guided group work? How might you use actions identified during the talk for learning session to enhance guided group work and wider classroom practice? What further support, internal and external to the school, will you need to carry out these actions?
Finally… Developing dialogic teaching through puppet use Mathematics and science focus 12 schools, 2 teachers per school Thursday 21st May = 1 day puppet training from Stuart Naylor and free puppets/resources per participant (school to pay supply, but training is free) Lesson study to develop the use of puppets back in school (funded) Friday 19th June (am) = Feedback and evaluation session (funded) NB: The 2 training sessions will be at The Angelus Centre.