2. Big Ideas
Skills children need to know include determining, matching, sorting, comparing, ordering, and patterning by
using attributes. Attributes can be determined by using all five senses. This has changed my understanding
because I determine most attribute by sight. Therefore I must teach children to use all five, rather than focusing
too much on sight.
Cardinal number is the total of a group, ordinal number is the correct order of numbers & nominal numbers,
which are number plates and house numbers. Children need to develop an understanding of these numbers.
There is a difference between counting and reciting numbers. Some children come to school with the numbers
1-10 memorised, but do not actually understand the value of those numbers. This has changed my
understanding of how children come to school with number knowledge. I must set assessment and activities to
determine whether or not children are able to count to ten, or if its just their memory.
3. Critical concepts, skills, and strategies of Early
Number for children to use
Skills children need to know are determining, matching, sorting, comparing, ordering, and patterning by using
attributes. Attributes can be determined by using all five senses. Children may experiment with objects, testing their
attributes before making conclusions (Rey et al., 2012).
Children need to understand the concept of cardinal principle, an understanding the last number counted is the
amount (Rey et al., 2012).
Children need to understand the concept of order irrelevance, an understanding that it does not matter if counted
left, right, up or down (Rey et al., 2012).
Children need to understand the concept of stable order, than numbers have an order. 1..2..3 not 2..1..3 (Rey et al.,
2012).
Children need to understand the concept of one to one correspondence, the ability to assign one number value to
one object counted (Reys et al., 2012). For example one counter cannot represent two numbers.
Children can recognise groups of up to 4. Separating objects into groups of a number can be a precursor to
counting, and is a skill.
A strategy for children is using concrete materials and memory to practice counting (Reys et al., 2012).
Counting Principles (ORIGO ONE, 2016a) | https://www.youtube.com/watch?v=r4z5j6Oni9M
4. Early number links to the Australian Curriculum
Foundation– Number and Algebra - Number and place value - ACMNA002
Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond (ACARA,
2016).
Elaborations
understanding that each object must be counted only once, that the arrangement of objects does not affect
how many there are, and that the last number counted answers the ‘how many’ question
using scenarios to help students recognise that other cultures count in a variety of ways, such as the
Wotjoballum number systems
Scootle resources for ACMNA002
Number Trains is a resource that allows students to organise numbers by their value, teaching ordinal numbers
(“Number Trains”, n.d.).
Access: http://www.scootle.edu.au/ec/viewing/L2317/index.html
5. Pre-number Language Model
This language model can assist educators to select
appropriate language and resources for developing
mathematical knowledge (Jamieson & Proctor, n.d.).
Pre/early number should be working towards the
concept of numbers.
For example matching attributes can be explained as
Verbal
Symbolic
Concrete/
Visual
Real world -
familiar object
Substituted Object –
E.g. Counters
2. Materials
Language
3. Mathematics Language
1. Student
Language
Language Example
Student Language
That cat is the same as that
cat.
Materials
Language
That counter is the same to
that counter.
Mathematics
Language
That object is similar/equal too
that object.
6. Teaching strategies
Idea Classification – One way of investigating attributes using sight in foundation year can be by playing ‘Guess
Who’. Children must compare faces to an attribute and determine whether or not that person has the attribute or
not. This determining happens in rapid succession as children observe each character. Scaffolding may be used to
help children identify attributes of ‘Guess Who’ that maybe overlooked, such as people wearing earrings and
freckles (Woolfolk & Margett, 2013).
Before using ‘Guess Who’, I would suggest using shapes from an attribute set. The video below demonstrates how a
teacher would use the shapes to teach classification of attributes (Kisi KidsTV, 2013).
https://www.youtube.com/watch?v=5bip0bcFlgo
Counting – Teaching children to count often requires the use of concrete materials or diagrams in tandem with one
to one correspondence, and memory of number knowledge (Reys et al., 2012). One strategy is for children to
organise counters into groups of numbers, matching the value to concrete representations (Reys et al., 2012).
Idea: Get the children to build towers out of Lego. The first tower is 1 block high, the next is 2 blocks high, and so
forth. This will allow the children to manipulate groups of numbers as they count while also visually showing that 3
> 2 > 1 and so forth.
7. Early Number teaching resources
Several videos exist online to help children count
Some comical videos include the use of wrong numbers, which children can correct in class (The Magic Bag, 1979). |
http://splash.abc.net.au/home#!/media/522409/help-the-referee-count-to-ten
Some videos are songs which focus heavily on repetition of a single number, providing real life examples (Seasame
Workshop, 2016). The video focuses on ten | http://splash.abc.net.au/home#!/media/1626912/ten-tiny-turtles
Manipulatives teachers can use include:
Attribute blocks to learn about attributes (Reys et al., 2012).
Deck of Cards to learn about attributes and numbers (Reys et al., 2012).
Counters such as marbles (Reys et al., 2012).
Matching card sets for learning about attributes (Reys et al., 2012).
Caldwell patterns to learn number names and values.
8. Misconceptions of Early Number
When children start to count they may count the same
object twice, overlooking the one-to-one
correspondence principle (Reys et al., 2012). Children
may count an object twice if they are attempting to read
to fast, therefore I would slow the child down as they
count (Reys et al., 2012).
After slowing the counting process down and the child
has difficulty counting with one-to-one correspondence,
manipulatives would be introduced (ORIGO ONE, 2016b).
Placing nine objects into a container, the child would one
by one pull out an object as they count (ORIGO ONE,
2016b).
I would then take this a step further and have the child
place the objects on a Caldwell pattern, getting them to
tell me how many objects are there.
9. Synthesis of Chapter 7
Number sense development is a life long process, with pre-number as the first stage, focusing on classification and
patterning (Rey et al., 2012).
Classification is an essential skill for children to develop, and is used across the curriculum. By using classification children
develop thinking skills, through observation. Attribute blocks can help children develop classification skills (Rey et al.,
2012).
Patterns require problem-solving skills to investigate sequencing, and use imagination to create and visualise patterns that
are based on several attributes (Rey et al., 2012).
A number does not vary when physically altered. Children may believe that the arrangement or configuration of blocks can
change the quantity, therefore developing conservation is crucial (Rey et al., 2012).
Group recognition helps develop addition and subtraction skills, removing the burden of counting small quantities
(subitising) (Rey et al., 2012).
Young children may say unconventional sequences while learning. They must learn each object is counted and assigned
one value and name (Rey et al., 2012). The stable-order rule also needs to be learned, and can be done so by one to one
correspondence (Rey et al., 2012).
Learning the numbers sequence and names should come before writing them (Rey et al., 2012).
10. References
ACARA. (2016). Mathematics. Australian Curriculum. Retrieved from http://www.australiancurriculum. edu.au/mathematics/curriculum/f-
10?layout=1
Jamieson-Proctor, R., & Larkin, K. "Mathematics as a Language”: A Theoretical Framework for Scaffolding Students’ Mathematical
Understanding.
Kisi KidsMathTV. (2013). Patterns & Classification lesson with objects, For kindergarten & 1st grade kids [video]. Retrieved from
https://www.youtube.com/watch?v=5bip0bcFlgo
Number Trains. Scootle. Retrieved from http://www.scootle.edu.au/ec/viewing/L2317/index.html
ORIGO ONE. (2016a, April 18). Introducing the Counting Principles [videio]. Retrieved from https://www.youtube.com/watch?v
=r4z5j6Oni9M
ORIGO ONE. (2016b, April 25). Teaching the One-to-One Counting Principle [video]. Retrieved from https://www
.youtube.com/watch?v=dvyLUpE6o7A
Reys, R., Lindquist, M., Lambdin, D., Smith, N., Rogers, A., & Falle, J. et al. (2012). Helping children learn mathematics. Milton: Wiley.
Seasame Workshop. (2016). Ten Tiny Turtles [video]. Retrieved from http://splash.abc.net.au/home#!/media/1626912/ten-tiny- turtles
The Magic Bag. (1979). Help the referee count to ten [video]. Retrieved from http://splash.abc.net.au/home#!/ media/522409/
Woolfolk, A., & Margetts, K. (2013). Educational psychology. (3rd ed.). NSW: Pearson.
