2. Learning outcomes
At the end of this tutorial and self study you should have:
•developed your knowledge of the stages of
development towards acquiring mathematical
concepts, particularly number
•raised your awareness of the mathematics going
on in an early years setting
•helped you devise and encourage relevant
mathematical experiences leading to
mathematical ideas for young children
•Examined some resources and considered their
use in the early years
3. Early Years Mathematics
Margaret Donaldson Children’s Minds 1978
(Fontana)
‘An adults
knowledge of the
general nature of
the subjects
taught to
children when
they first enter
school is apt to
be so well
established that
it blocks the
realisation of
precisely what
the children need
to be helped to
see.’
4. Counting 1 - 19
• I have explored numbers,
understanding that they represent
quantities and I can use them to
count, create sequences and
describe order
MNU 0-02a
5. Early Years Mathematics
Counting
What does it mean?
View video – ‘Twice five plus the wings of a bird’
6. Early Years Mathematics
Counting and Numbers
From the video we can see that a child must
• know the sequence of number names.
• Be able to match one-to-one words with objects being counted
(one-to-one correspondence).
• Be able to identify a set to be counted (or a subset)
• Understand that the last number name in a count gives the
numerical size of the set of objects (ie. the cardinality) of the
set.
• have conservation of number.
• understand the abstract concept of number ie. sets of 4
whatever have the common property of 1, 2, 3, 4.
• can start counting a set in a different place and realise the
number is the same (advanced conservation).
Refer to the concept maps for ‘Number’ and ‘Counting’
7. Early Years Mathematics
Counting and Numbers
Assessment of learners
• Activity – Read and discuss ‘Talk 1’
• Activity – Read and discuss ‘Talk 2’
8. Early Years Mathematics
Children’s Mark Making
Children should explore number situations, count,
begin to calculate, talk about how they worked things
out and record or represent their mathematics in
their own ways
“Learning involves moving progressively from
concrete examples to the use of symbolic
representations.”
Building the curriculum 2 – Active learning, A guide to developing
professional practice, Scottish Government (2010)
Consider:
'Children’s Mathematical Graphics: Understanding the Key Concept’
Carruthers and Worthington (2009)
9. Early Years Mathematics
Children’s Mark Making
Task: Consider the sample recordings in
relation to the key concepts of number and
counting.
• knows the sequence of number names.
• can match one-to-one words with objects being counted
(one-to-one correspondence).
• can identify a set to be counted (or a subset)
• understands that the last number name in a count gives the
numerical size of the set of objects (ie. the cardinality) of
the set.
• has conservation of number.
• understands the abstract concept of number ie. sets of 4
whatever have the common property of 1, 2, 3, 4.
• can start counting a set in a different place and realise the
number is the same (advanced conservation).
What assessments can be made?
10. Introducing place value
I have investigated how whole
numbers are constructed, can
understand the importance of zero
within the system and can use my
knowledge to explain the link
between a digit, its place and its
value.
Responsibility of all
MNU 1-02a
11. Introducing place value
Use unstructured materials to show the number 34
Use semi-structured materials to show 34
Now make 34 using structured materials
How is 34 displayed on an abacus?
Discuss the difference between each of the materials
in terms of helping children develop understanding of
place value.
Online manipulatives - Chip Abacus
Click here for an interactive abacus
13. Using Structured Materia
Children should be given practice in investigating
different ways of partitioning numbers using
blocks:-
234 - 2 hundreds 3 tens 4 units
23 tens 4 units
2 hundreds 43 units
234 units
Activity - Investigate six different ways to make
248
14. A comparison
Activity
Discuss the difference between the
two types of cards.
3
300
60 6
4 4
What do you think is meant by the ‘quantity value’?
15. Place Value Mark-up
Play this game.
What knowledge and understanding does
this activity reinforce?
Editor's Notes
There should be a variety of counting materials on the tables. Discuss and illustrate each of the principles. Spend some time modelling and talking about activities that could be used. Remind students that there are lots of ideas and resources to be found on BB. Give out the concept maps - 'Number' and 'Counting' and suggest that students work together to identify ideas for the blank activities column.
There should be a variety of counting materials on the tables. Discuss and illustrate each of the principles.
Consider: How are you first going to introduce ‘Place value’ (previous input) – bundles of ten, then bundles on PV board, then bundles, board and PV cards, then B,B & digits, towards just digits
Discuss the important role of Place Value
Each table should have different unstructured materials Straws Pennies
