The concept of a number

1. Concept
Whole Numbers

2. Concept: the metaphor or picture one
creates in their head
 Number understanding 0 – 9
Creating a picture in a student‟s mind
about a number.
For example, the number three (3).

3.  According to Jamieson-Proctor (2011), Van
de Walle (2010) & Booker et al
(2004), mathematics instruction, including
the concept of number, should follow a
model of learning from concrete to
abstract.
 Thelanguage model moves through 4
stages: (Jamieson-Proctor, 2011)
 Children‟s Language
 Materials Language
 Mathematical Language
 Symbolic Language

4.  Booker, et al (2004) add at this early stage of concept
development the focus of instruction needs to be with
materials and patterns that allow insight into the
number; rather than concentrating on the recognition
and writing of the symbol „3‟ itself. This reinforces the
idea of the language model.
 Children start off learning about the number three
with language and objects that are familiar to
them, counting to recognise what three toys are. They
then move to use their notion of three to group
objects into three, firstly with toys and than more
mathematical materials. Finally students move to
more mathematical language of sorting and
matching to manipulate the objects.

5. Using the Language model, the table below gives a brief overview
of the teaching sequence to develop the concept of a number 0-
9, for example 3.
Language Materials Language Record
stage
Children's Language Familiar items to the „find me three of the
child – toys e.g. dolls, same thing‟ or “find me
cars, fruit e.g. bananas, three dolls”
apples etc
Materials Language Counters, paddlepop “Can you give me a
sticks, unifix blocks group of three
Pictorial only
counters” or
“sort those paddle pop
sticks into groups of
three”
Mathematics Language Counters, paddle pop Sort, match or set of
sticks, unifix blocks, MAB three
blocks,
Symbolic Language
none needed As above

6.  To provide full meaning of the number e.g
„three‟, students need to understand what is meant
when we say „three‟.
 This includes giving children opportunities to encounter
'three' in different situations - three people, three
sticks, three pencils, three balls, etc.
 Using the same material again and again when
teaching about numbers restricts children's experience
and prevents them from generalising that 'three' refers
to collection of any three objects (Indira Gandhi
National Open University [IGNOU], 2012).
 The next slide shows an example of a child who has
had restrictive experiences with the concept of three.

7. Four year old Sally was reciting number names, some of them in order
and others randomly. The child's aunt sitting nearby asked her "Can
you write 'three' ?"
Sally said "yes" and wrote the following:
When the aunt asked what had she drawn alongside, the child
replied 'flowers'. On asking her why she had drawn them, she replied
that: "This is the way three is written in the book". When her aunt said:
"If I draw three ducks here, will they be „three'?" Sally replied: "No they
will not. "

8.  The previous slide demonstrates that Sally‟s concept of
the number three is about „three flowers‟ rather than
the notion that three is a collection of a set number of
objects.
 To move Sally beyond this understanding a teacher
needs to begin to demonstrate a generalisation of
three so Sally can change her concept of three. This
can be achieved through singing songs using 3,
reading stories that contain 3, allowing children to
make groups of 3 either with themselves or objects.

9.  To reinforce the number concept being learned for the
day or week the teacher could use the number 3
throughout the day. Choosing 3 stories to read, asking
for 3 volunteers to help out, use physical exercise to
practice 3, e.g. 3 star jumps.