ian ross autumn 2015. to develop an understanding of early counting and calculating to understand...

Ian RossAutumn 2015

To develop an understanding of early counting and calculating

To understand how models and images are used within early maths

To develop skills of self audit in subject knowledge and pedagogy.

Make 99

Choose tens or units7 Throws onlyAddition only

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An understanding of pattern The ability to reason and describe Knowledge of basic number The ability to generalise and hypothesise

Early maths gives us the foundations for later understanding

What issues did you have with counting like this?

What about this? Dog +fish = Red – house=

Or for you really bright sparks Dog x brown =

Read the article ‘Counting Principles’ This is from the work of Gelman and Gallistel in the 1970s.

Talk to the person next to you-

What are the counting principles? What order do you think they are learnt in? What have you seen so far in school about

counting? Do the children get to practice counting daily?

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“a visual tactile resource which allows children to manipulate, notice and explore patterns - making connections between images and number.”

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Can you order the tiles What do you recognise? How do you think this will support

children’s understanding of number and the number system?

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Using the tiles…How many different ways can you make

What about

Making towers of ten…how many different ways can you find?

NRich and NCETM are two very useful websites. In your pack is an article by Jenny Way on why number sense is important and ways of teaching it.

How does Numicon help children develop number sense?

What is the problem with only using Numicon to teach number sense?

Every Foundation Stage and KS1 classroom should have a set of core models and images that support mathematics.

From your experience what models and images have you seen?

How do these support understanding in maths?

Inquiry: investigation, playing with a problem – PLAYING

Reasoning: ordering, systematising, organising – FINDING PATTERNS

Concept formation: clarifying, extending – JUSTIFYING

Translation: interpretation, generalisation, extending concepts - GENERALISING

Hands-on learning is still important – provide appropriate practical equipment for children to use and manipulate

Seeing mathematics through models and images supports learning – help children to see how mathematics works and can be represented through physical objects

Talking mathematics clarifies and refines thinking – give children the vocabulary and language of mathematics; provide activities and time for them to discuss mathematics, using this language.

Make mathematics interesting – share your interest in mathematics with the children.

Learning from mistakes should build up children’s confidence – look out for mistakes and encourage children to recognise that making mistakes is something everyone does.

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Take turns to play. Cross out and circle. E.g 4 + 6 = 10 Next person starts at 10.

Game 1 – work competitively so that your opponent can’t go.

Game 2 – work cooperatively to cover all the numbers.

The national curriculum for mathematics aims to ensure that all pupils:

1.become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.

2.can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

Why do children need to be fluent? To the person without number sense, arithmetic is a

bewildering territory in which any deviation from the known path may rapidly lead to being totally lost. Dowker (1992)

List as a table what you believe fluency is about!

Numbers as pictures Can you investigate all the numbers to 20. Which make squares, which make rectangles and which make sticks?

What areas of maths are you learning here?What strategies, models and knowledge do you need to tackle this problem?

Patterns in the environment Copy Repeat Continue Extend

School coordinators have worked on developing a calculation policy based on the requirements in the revised curriculum. Before children can develop a standard algorithm approach to calculation they need a good understanding of number and what it does. You need to get hold of it, read it and inwardly digest it!

1. Log onto www.NCETM.org and register

2. Complete the self audit tool for FS and KS1

3. Start with the content knowledge and then the specific pedagogy.

4. When all is complete print screen onto a word document name and date it and send to – Annwen, your tutor and your mentor.

Week One – observe maths lessons (look for models and images, practical apparatus, counting, questioning, vocabulary)

Week Two – plan with the teacher a series of lessons (Think about the steps children need to take to achieve the big picture)

Week Three – plan with the teacher’s support and be observed in you teaching. (remember to include all the things you were looking for in week1)

Any questions – ian@penninelearning.com

Thank You!