Improving teaching and learning in Mathematics

© Crown copyright 2009

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Improving teaching and learning in Mathematics

Day 2 – Year 1 teachers


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Aim of the CPD programme

To strengthen teaching and learning of mental mathematics.


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Objectives of the CPD programme

• To deepen understanding of the range and depth of mental mathematics

• To explore fit-for-purpose pedagogy to support selecting the most effective approach to teaching and learning for particular learning outcomes and needs

• To explore the negotiation of meaning through the use of practical resources, visualisation, models and images, language and dialogue, writing, jottings, symbols and notation

• To develop strategies to embed the development of reasoning and communication throughout teaching and learning

• To secure understanding of how to embed mental mathematics within planning and teaching to ensure appropriate pitch and progression


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Agenda

9.00 Coffee and Welcome

9.15 Session 1 – Developing mental mathematics

10.30 Morning break

10.45 Session 2 Part 1 – Negotiating meaning

12.15 Lunch

1.00 Session 2 Part 2 – Developing reasoning through dialogue

2.15 Afternoon break

2.30 Session 3 – Integrating mental mathematics into teaching and learning

3.30 Close


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Session 1 – Developing mental mathematics

Aims of the session:• To reflect on the themes and issues addressed during

Day 1 in the light of experience of the interim task• To consider how interim task activities took forwards

children’s mental mathematics • To reflect on the success of teaching approaches and

strategies incorporated into the interim task, including those developed within a guided group context

• To identify how to continue to develop successful teaching approaches and techniques


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Reflecting on the interim task – impact on children

• How did children respond to the activity and were there any surprises?

• How did the activity develop children’s mental mathematics?

• What notes and jottings did children make and what images or resources did they use?

• What did you find out about the children’s mathematical understanding?

• What next steps did you identify for the group and for the children?


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Reflecting on the interim task – use of guided group work to develop mental mathematics

• Which of the strategies did you use? • What other strategies did you use? • What was the impact of working in a guided

group context, both for you and for the children?


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Reflecting on the interim task – next steps

• What have you done differently to take forwards children’s mental mathematics and what impact is this having on children’s learning?

• In the light of this, what approaches or strategies are you going to continue to develop?


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Session 2 Part 1 - Negotiating meaning

Aims of the session:

• To develop familiarity with the term ‘negotiating meaning’

• To extend understanding of the role of negotiating meaning in developing mental mathematics

• To explore the negotiation of meaning through the use of practical resources, visualisation, models and images, language and dialogue, writing, jottings, symbols and notation


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Pyramid property statements

• It has an odd number of faces• No face is a quadrilateral• It has 12 edges• All faces are the same shape• It has an odd number of edges


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Pyramids – common misconceptions

• A pyramid always has a square base• The base is always a regular polygon• The base is always horizontal• The triangular faces cannot be vertical• The apex is always above the centre of the base• A pyramid always has an apex


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Reflecting on the role of practical resources, language and dialogue

• How could the activity have been enhanced or restricted if 3-D shapes or construction equipment had been available throughout?

• How did you refine your understanding of the term pyramid through the activity?

• What role did dialogue play in this?


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Reflecting on the pyramid activity – visualisation

• What visualisation was involved and how did this promote and support the negotiation of meaning?

• What previous practical experience was this visualisation building on?


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Subtraction definition

Subtraction is a process involving the taking away of objects from a given set of objects.


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Subtraction activity

• Read a problem and decide how an understanding of subtraction as taking away provides access to and relates to the problem.

• Using the definition, try to interpret the problem as taking objects away from a set of objects.

• Is this understanding of subtraction enough? Does it help or restrict you in re-interpreting the problem in a way that will help you find the solution?

• How might we change the definition to improve it?


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Subtraction definition

• How would you choose to define subtraction now?

• Is the teaching approach of starting from a definition like this the most appropriate approach?

• How else might we teach subtraction?


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Plenary

• Need opportunities to negotiate meaning in order to clarify, refine and extend understanding of mathematical language, symbols and concepts

• Without these opportunities, children will have an only partial grasp of related concepts

• A variety of resources are essential in negotiating meaning

• Engage in meaningful mathematical dialogue


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Session 2 Part 2 - Developing reasoning through dialogue

Aims of the session• To identify strategies to promote the

development of communication and reasoning• To consider the role of the teacher in promoting

dialogue and reasoning about mental mathematics

• To continue to explore how language and dialogue support the negotiation of meaning


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Dialogue activities• Read through and briefly try out the activities to become

familiar with the type of problem and what it is challenging the children to do.

• Discuss the role of the teacher and the strategies they could use in supporting, promoting and developing children’s dialogue and reasoning.

• Consider the language you would use to promote the learning and any mental mathematics that would be involved in the activity.

• Write brief notes of key points discussed on a copy of Notes on dialogue.


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Key messages

• Mathematical dialogue is crucial in taking forwards children’s understanding of mathematics through negotiating meaning

• The teacher’s role is critical in shaping children’s emerging use of mathematical language

• Teachers need to draw on a wide repertoire of strategies in order to maximize opportunities for meaningful mathematical dialogue and reasoning


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Session 3 - Integrating mental mathematics into teaching and learning

Aims of the session• To consider how to effectively embed mental

mathematics within planning and teaching of every learning sequence

• To identify how to incorporate key points from this CPD into ongoing planning and teaching

• To review key messages from the two days, identify areas for personal development and issues to share with colleagues back in school


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Key messages from the CPD programme• Mental mathematics is broader than mental calculation, it

is fundamental to mathematical learning and should take place every day

• Models, images and visualisation provide powerful tools to secure understanding in mental mathematics

• Dialogue is essential in negotiating meaning, developing reasoning, taking forward mathematical thinking and giving the teacher insights into children’s understanding

• Planning and teaching needs to incorporate a range of appropriate pedagogies and contexts to promote mental mathematics, selecting those that are fit-for-purpose for particular learning expectations and outcomes


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Securing level documents

• How could you use the information and guidance in each section of the double page spread?

• How could you draw on the Securing level documents to support your on-going planning for the whole class or for specific groups?


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Aim and objectives of the CPD programmeAim:• To strengthen teaching and learning of mental mathematics Objectives:• To deepen understanding of the range and depth of mental

mathematics• To explore fit-for-purpose pedagogy to support selecting the most

effective approach to teaching and learning for particular learning outcomes and needs

• To explore to explore the negotiation of meaning through the use of practical resources, visualisation, models and images, language and dialogue, writing, jottings, symbols and notation

• To develop strategies to embed the development of reasoning and communication throughout teaching and learning

• To secure understanding of how to embed mental mathematics within planning and teaching to ensure appropriate pitch and progression


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Improving teaching and learning in Mathematics