Mathematics Year 4 and 6 Day 3 May 2010

Mathematics Year 4 and 6 Day 3 Pyramid visualisation and negotiating meaning Feedback from interim task Structures to promote mathematical dialogue 10.30pm Refresh Continue mathematical dialogue Steps to success in Mathematics Lunch

Now close your eyes

4 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

5 Visualise a pyramid. Talk to a partner and discuss what is the same about the pyramids and what is different. Negotiating Meaning - Pyramids

6 Are there different types of pyramid?

Can you visualise different pyramids with the following criteria: A pyramid with an odd number of faces A pyramid where no face is a quadrilateral A pyramid with 12 edges A pyramid where all faces are the same shape A pyramid with an odd number of edges.

Pentagonal pyramidSquare based pyramid Octagonal pyramid

9 Common misconceptions about pyramids A pyramid always has a square base Base is always a regular polygon Base is Irregular Base is Regular Irregular Pyramid Regular Pyramid

10 Common misconceptions about pyramids Base is always horizontal Triangular faces cannot be vertical The apex is always above the centre of the base Right PyramidOblique Pyramid

11 Summary Ability to visualise representations, pictures or images then adapt/change them is an important tool in reasoning in mathematics. Children need extensive practical experience of looking at creating and handling shapes. Visualisation usually takes place after the children have had tactile experiences to draw on.

Remember the progression in visualisation poster.

Why does visualisation help? step into a problem model a problem to plan ahead Visualisation can help you to:

think, pair and share Feedback from the school based tasks Reflect on the guided group work you have done with your children. Remember some of the strategies we discussed to make guided group work effective: Grouping pupils thoughtfully Using layered questions and probing understanding at appropriate times Modelling precise use of mathematical language Setting up dialogue so children learn from each other Using models and images to support and scaffold children’s thinking and experiences. Reflect by yourself on the key questions and the note sheet. Describe your thoughts and experiences to your partner. When you are ready join up with another pair and share key successes all together.

Key Questions for Guided Reasoning Feedback What guided reasoning activities have you tried? How did the models, images or apparatus support the children’s thinking? Which of the strategies did you use to successfully develop the children’s thinking? What was the impact of working in a guided group context for you and the children? Have you developed your own shape guided reasoning idea that you can share? think, pair and share

Feedback from BwD teachers re: guided reasoning I discovered that the children were really poor at working systematically and organising their thinking. I heard children saying “ I can see a pattern!” then describing it. Some more able children (Year 2) were able to make simple hypothesis like “ You always have to put 5 in the middle.” When the children were really familiar with the ‘image’ (like the mobile phone grid and coins) it was easy to speed up their reasoning and help them make connections. I loved the quality of the assessment information I got from the guided reasoning group. I was able to respond quickly to the children’s needs and move them on. think, pair and share

Feedback from the school based tasks Some possible benefits from working in a guided group context: Improved assessment opportunities Activities tailored tightly to the needs of the group and individuals All children actively involved The flexibility to adapt the activity according to the children’s responses Children’s confidence high in a small group Opportunities for sustained dialogue

Other ideas to explore to promote communication and reasoning in mathematics True or false?

Other ideas to explore to promote communication and reasoning in mathematics

BARRIER GAME Describe to your partner how to draw your shape. Can they describe the properties of the shape?

Other ideas to explore to promote communication and reasoning in mathematics Look back at the speaking and listening posters.

Promoting mathematical dialogue Jigsaw (from the group discussion poster) Give everyone in the group a number between 1 and 6. This is your home table. Like numbers join together on a designated table. Task 1: Go to your designated table and create a set of clue cards using the prompt cards. Task 2: Return to your home table and share your clue cards with the rest of the group.

Promoting mathematical dialogue Telephone conversation (from the listening poster) Sit back to back. One of you has two graphs. The person with the graphs has to tell the other person information so that they can present it in the venn diagram. It is a conversation so questions can be asked.

Promoting mathematical dialogue Co-operative Learning Strategies Dr. S Kagan Ideas based on Learning Pyramid- we learn by doing and talking. Everyone in the group must be valued and take part. The Pies principles must be followed.

Promoting mathematical dialogue Positive interdependence Individual accountability Equal Participation Simultaneous interaction Structure + Content = Activity

Promoting mathematical dialogue Hogs and Logs (like Word Tennis) Kagan What do you know about the number 26?

Promoting mathematical dialogue Find the Fib Dr, S Kagan 11 is the missing number 1.(16 + Δ) – (12 + 6) = 9 2.(32 – Δ) + (4 x 12) = 69 3.(21 + Δ) - (2 x 14) = 8

Promoting mathematical dialogue Find the Fib Dr, S Kagan 1.A square has 4 straight sides 2.A square has 2 lines of symmetry 3.Two same size squares next to each other can make a rectangle.

Promoting mathematical dialogue Talking Chips Kagan Everyone has 2 chips. You can only speak when you put in a chip. You cannot continue the discussion when your chips have gone, but you can query another person. Sarah has 3 rods. One is 3 cms long, one is 4 cms long and one is 9cms long. She says she can use the rods together or side by side to make all the lengths between 1 cm and 16cms. Is she correct?

Promoting mathematical dialogue Stand up! Hand up! Pair up! Everyone takes part. You ask 1 person 1 question only. You ask nicely if they will answer your question! The answerer signs their name to show they have answered the question. You can coach your partner to help them understand and answer the question. You thank each other afterwards before pairing up with someone else.

Promoting mathematical dialogue Co-operative Learning Strategies Dr. S Kagan Co-operative Learning Dr. S. Kagan ISBN

Negotiating Meaning in Mathematics Mathematical word or phrase Where do you see this word in everyday life? Mathematical symbols (if there are any): What other mathematical words is it related to? Describe what your word or phrase means: Use your word or phrase in a statement:Picture or diagram:

Think of a range of activities you can use with your class to develop speaking and listening in mathematics.

37 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

What next with communication…. Use the notes on dialogue prompt sheet to reflect on questions and actions you may wish to follow up in school. Think about the role of the teacher/adults and the strategies we can use to promote dialogue and reasoning to develop mathematics.

Steps to success in mathematics: Securing progress for all children