Teaching in the early years
13 10 16
Joe Lockwood
In todays session;
• Understand how children’s mathematical skills develop
• Understand how curriculum subjects including core literacy,
mathematics and science can be developed through cross
curricula links
• Identify a range of appropriate considerations when planning
an early years session
• Understand the necessary health and safety procedures
involved in planning
Problem Solving, Reasoning &
Numeracy
The Importance of Counting
• Counting is a child’s first experience of number and maths
• Learning to count can support understanding of the number
system
• It’s one tool for calculation strategies
• Counting backwards is no more difficult than counting
forwards
• Counting should happen every day regularly (with a real-life
context)
Alphabetland
• The new number names are A, B, C, D, …
• You must not ‘translate’ these number names into the
banned number names one, two, three…
– Count together
– Can you count by yourself?
– Can you count from L to T?
– Can you count back from G?
– Can you count back from P?
– Can you count in Bs?
Alphabetland – Subitising
How many are here?
Children need to practise ‘subitising’ (visual recognition of grouped
patterns) in both regular (eg on a die) and irregular arrangements).
More and less concept
A child has a packet of sweets and eats them all. He
asks for more. You give them 1-2 more sweets. The
child sulks, as they were expecting another packet.
Their understanding of more was more than original
quantity (one whole packet), but you actually gave them
less.
It will take a while for children to fully understand the
concepts of more and less.
Acquiring the language of number
• A good game to play: 10 nice things
– With a partner, choose 10 nice things
– Take turns to roll the die
– You are allowed to ask your partner for the number of
things on your die roll
– Try and keep track of the number of things that you and
your partner have
– The winner is the first to get all the things
The ‘How to Count’Principles
A short video explaining Galman and Gallistel’s (1978) ‘How to
Count’principles, with a little help from Sesame Street……
https://www.youtube.com/watch?v=8PZSOF45NEY
Gelman And Gallistel (1978)
The ‘How to Count’ Principles
• The 1-1 principle
• The stable order principle
(the number system has a regular order. Children are able to count, but
the correct order is not yet definite, eg, 1,2,3,4,5,6,8,9,10)
• The cardinal principle
Gelman And Gallistel (1978)
The ‘What to Count’ Principles
• The abstract principle
• The order-irrelevance principle
Oral Counting - development
• Children will say numbers from a very early age.
• Fuson identified 5 stages in the early development of the word
sequence
– String level – a continuous sound string (rote counting only; no idea of
numerical value)
– Unbreakable list level – separate words, but the sequence can’t be broken
and always starts from 1
– Breakable chain level – child learns to be able to start at any point which is
essential if they are going to be able to count on (ie, has 4+1, they say “4, 5.”
– Numerable chain level – sequence, count and cardinality are merged, so if
you are counting from 3, then 3 is the first number, 4 is the second
number…
– Bi-directional chain – child can say the numbers in either direction and
start at any point
Oral Counting and Counting Objects
Oral Counting
Counting objects
• Recitation
• Rote counting
• Enumeration
• Counting how many
• Counting ‘things’ (though they can
be abstract)
Making connections
Haylock and Cockburn (2008)
Symbols
Language
Pictures
Concrete Experiences
Children cannot be proficient and good users of numbers, until they
have all four areas. If they are not supported by staff and the
environment, children will not become proficient.
Number Sense
Challenges
• Numbers are abstract ideas
• Numerals are arbitrary symbols
– Where do you see numerals that do not relate to their numerical
amount?
• Traffic signs; does a 40 speed sign mean 40 signs/cars etc?
• House number – does it means 33 people live there?
• Children need to understand when numerals relate to
quantity, and when not
Calculating
• Do we have to wait until children are proficient at
counting before we introduce them to calculating?
– Calculating should be taught alongside counting.
– Children can be calculating with amounts larger than they
can count to (more and less)
Early Addition
Skills in early addition
1. Counting all
2. Counting on from the first number
3. Counting on from the larger number
4. Using a known addition fact (eg, 2+3=5)
5. Using a known fact to derive a new fact (eg, 2+3=5, so
2 and 3 more = 5, or 3+2=5)
6. Using knowledge of place value
Addition Skills
• Count all
1,2,3
4,5,6,7,8
3+5=8
Addition Skills
• Count on
3…4,5,6,7,8 (“it’s eight”)
3…
67
5
4
8
Addition Skills
• Counting on from the largest number
3+5=
5…6,7,8 (“eight”)
5…
6 7
8
Calculating
In conclusion:
• Structured imagery can support children in developing
early calculation skills and can support children in
learning to calculate without counting
• Children need to be supported in developing counting
on strategies for themselves
Real-life maths
• Cooking (measuring, timing, temperature)
• Gardening
• DIY (measurements, electrical wattage)
• Shopping (money)
Some issues to consider when using and
applying mathematics
• The activity needs to be real for the individual child
– This will vary from child to child
• The activity needs to motivate the child
• We need to:
–
–
–
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Be clear about the specific mathematics we are teaching
Identify, build on and reinforce existing skills
Help the child to see the mathematics
Be able and help the child make links within the mathematics and across a variety of scenarios
• Don’t forget to make it FUN!!
What do we need to consider when planning for
teaching in the early years?
• Work on your own, list all the things you may need to take into
consideration. One point per post it note – 5 mins
• Work with a partner, share your ideas. Had they considered
different areas? What were the similarities? Can you group the
points into different categories and give them headings? – 5
mins
• Whole group feedback to compile a central list – 5 mins
Task
• Working in groups, you will plan a micro-teach session to deliver
to the rest of the group. You should both make equal
contributions.
• Your session should last approximately 15 minutes
• You will teach the rest of the class about how the curriculum
area you have been given to investigate can be developed
through a cross-curricular approach. This could be general or a
specific example, and could include tasks and activities
• A range of creative materials will be made available for your use