ian ross autumn 2015. to develop an understanding of early counting and calculating to understand...
TRANSCRIPT
![Page 1: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/1.jpg)
Ian RossAutumn 2015
![Page 2: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/2.jpg)
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.
![Page 3: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/3.jpg)
Make 99
Choose tens or units7 Throws onlyAddition only
3
![Page 4: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/4.jpg)
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
![Page 5: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/5.jpg)
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 =
![Page 6: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/6.jpg)
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?
![Page 7: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/7.jpg)
7
5
![Page 8: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/8.jpg)
8
“a visual tactile resource which allows children to manipulate, notice and explore patterns - making connections between images and number.”
![Page 9: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/9.jpg)
9
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?
![Page 10: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/10.jpg)
10
Using the tiles…How many different ways can you make
What about
Making towers of ten…how many different ways can you find?
![Page 11: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/11.jpg)
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?
![Page 12: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/12.jpg)
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?
![Page 13: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/13.jpg)
Inquiry: investigation, playing with a problem – PLAYING
Reasoning: ordering, systematising, organising – FINDING PATTERNS
Concept formation: clarifying, extending – JUSTIFYING
Translation: interpretation, generalisation, extending concepts - GENERALISING
![Page 14: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/14.jpg)
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
![Page 15: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/15.jpg)
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.
![Page 16: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/16.jpg)
16
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.
![Page 17: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/17.jpg)
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.
![Page 18: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/18.jpg)
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!
![Page 19: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/19.jpg)
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?
![Page 20: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/20.jpg)
Patterns in the environment Copy Repeat Continue Extend
![Page 21: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/21.jpg)
![Page 22: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/22.jpg)
![Page 23: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/23.jpg)
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!
![Page 24: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/24.jpg)
1. Log onto www.NCETM.org and register
![Page 25: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/25.jpg)
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.
![Page 26: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/26.jpg)
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)
![Page 27: Ian Ross Autumn 2015. To develop an understanding of early counting and calculating To understand how models and images are used within early maths](https://reader034.vdocuments.mx/reader034/viewer/2022051621/5697bfc31a28abf838ca5a48/html5/thumbnails/27.jpg)