1. INTRODUCTION
Learning pre number concepts is an essential strategy if a child wants to have a
very good understanding of mathematical skills in school! What cognitive philosopher
said about this belief?
This paper will answer this question and issue, where it tries to prove that learning
pre number concepts builds children study of early Mathematics and also the foundation
for learning later skills that learnt in primary and secondary schools. Other than that, this
paper also wants to prove that cognitive learning theories play an integral role in teaching
and learning of early Mathematics.
Before a child knows the symbol of numbers, they are exposed with pre number
experiences such as sorting, comparing, making observations, seeing connections, telling,
discussing ideas, asking and answering questions. According to Troutman (2003), in
developing number sense for children in kindergarten, it began with learning pre number
concepts.
In contrary, the cognitive learning theory like Piaget and Bruner also believed that
learning pre number concepts is one of very important strategies in teaching and learning
early Mathematics skills. Based on the preschool syllabus, the children have to
experience pre number concepts, numbers concepts, numbers operations, subtraction
within 10, the value of money, the concept of time, shape and space, construction and
ICT application.
So, in pursuing the aims in preschool learning, this paper will prove that learning
pre number concepts and the role of cognitive theories are the fundamental of early
Mathematics study.
The pre number concepts
According to our module, there are five prerequisite skills needed in preschool
Mathematics study, they are, develop classification abilities by their physical attributes,
compare the quantities of two sets of objects using one-to-one matching, determine
quantitative relationship including ; as many as, more than and less than, arrange objects
into a sequence according to; size, length, height or width and vice versa, and lastly

2. recognize repeating patterns and create patterns by copying repeating patterns using
objects such as blocks, beads and et cerra.
The cognitive learning theory
Jean Piaget(1896 – 1980) was originally a biologist but moved into the study of the
development of children’s understanding.
His view of how children’s minds work and develop has been successfully
influence children education especially in logical mathematics. His research has a huge
impact on learning study.
His four stages of cognitive development became the most essential guidelines for
teachers. By knowing the stages, teachers and school boards will know the best way to
cater the children’s differences. The four stages are the sensori-motor(0 – 2 years),
preoperational(2 – 7 years), Concrete operational(7 – 11 years) and the formal
operational(11 – 16 years).
Meanwhile, according to Bruner(1960), the child’s cognitive structures mature
with age as a result of which the child can think and organize material in increasingly
complex ways. He was influenced by Piaget and Vigotsky later on. He believed that
there are three stages of cognitive development as the first stage is Enactive(0 – 1 years),
Iconic(1 – 6 years) and the third is Symbolic( 7 years onwards).
Bruner stated that the children of 4 to 6 years old are able to visualize the images
through concrete materials. So, during these periods, it is often very helpful to have
diagrams or illustrations to accompany verbal information.
Therefore, in this paper I will discuss about the teaching of two topics in
preschool syllabus and support it with the ideas of Piaget and Bruner theories, and also
prove how learning pre number concept develop their knowledge on Mathematics skills
through various activities involving the two topics chosen. The two topics are Numbers 1
to 10 and Shapes and Space.

3. THE ROLE OF PRE NUMBER CONCEPTSIN TEACHING TOPICS CHOSEN
WITH SUPPORT FROM PIAGET AND BRUNER
Determine quantitative relationship including „as many as‟, „more than‟ and „less
than‟
The teaching of pre number concepts is very important for pre-school children because
these concepts lay the foundation for children to develop the acquiring of later skills. As
for determining the quantitative relationship including ‘as many as’, ‘more than’ and
‘less than’, this concept is one of the pre-counting activity as an understanding of the
concept of ‘more’, ‘less’ and ‘the same’.
So, it is can be taught in teaching or introducing the Numbers 0 to 10 before the
children learn the numbers itself. The teacher can give the children some colourful
beads, block or straws for have them manipulating it through play and games activities
such as, find the more beads, and compare sets of blocks according to colours and so on.
These activities will motivate them to observe, explore and play actively.
This pre-number concept also is useful in teaching Shape and Space where by
using the same objects, the teacher can ask the children to gather things and put them
together according to its colours, sizes and shapes.
The teaching of the pre-number concept given as above is relaying on the theory
by Piaget(1960a, 1960b, 1964) as it said that children should not be taught certain
concepts until they have reached the appropriate stage cognitive development in
preoperational stage. They are interested in comparing more objects but still restrained
by concrete world.
As for Bruner(1960), he explained that complex ideas can be taught at a
simplified level first, and then move to the more complex levels later on.
Arrange objects into a sequence according to size(small to big), length(short to
long), height(short to tall) or width(thin to thick) and vice versa

4. Teaching Numbers 0 to 10 also can be taught in arranging objects activities according
their sizes, lengths, heights and widths. For example, arrange the cubes from small to big
and at the same time put some beads in the cubes to see the sequence of numbers and the
children do not have to count!
When teaching shapes, this pre-number concept will be very meaningful to the
children as they are able to touch, feel and observe the different shapes. Children like to
play with shapes in different colours through games like fun games, placing objects or
people in different position(over, under, above, below or between).(Arkmann, 2004).
So, different activities can be very enjoyable for children below 7 to learn the early
Mathematics.
In kindergarten year, most 5-year-olds can copy shapes, such as triangles and rectangles
because according to Piaget &Inhelder(1956), at this age, children still draw chimneys at
a 90º angle from the roof, instead of vertically or perpendicular to the ground.
In addition, Bruner suggested that a child capable of learning any material so long as the
instruction appropriately given and told. So, children capable to identify shapes around
them even though they do not know the names of the shapes.
SUGGESTION ACTIVITIES, STRATEGIES AND RESOURCES IN
CORPORATE WITH PRE NUMBER CONCEPT
Teaching Numbers 0 to 10
The children must acquire pre-number concepts in order to develop good number sense.
Here is the suitable activity to determine quantitative relationship including ‘as many as’,
‘more than’ and ‘less than’.
Learning outcome:
By the end of the teaching and learning acitivity, the pupils will be able to:

5. determine quantitative relationship including ‘as many as’, ‘more than’ and ‘less than’.
Materials:
Sets of colourful beads
Sets of different sizes of balls
Containers
Procedures:
1. Determine the quantity of the beads by colours
1.1 The teacher asks the pupils to sit in group of four and do the task give in group.
1.2 Then, the teacher gives a question, ‘look children, which colour of beads has
more?’
1.3 Teacher continues asking questions, ‘how about the red beads, is it lesser than the
green or has equal? Can you match them one to one to explore? Here you go.’
1.4 The pupils respond to the questions.
Teaching pupils in this stage of development according to Piaget should employ
effective questioning about determining quantities.
Topic 2: Shape and Space
Activity: Arranging objects into a sequence according to size(small to big), length(short
to long), height(short to tall) or width(thin to thick) and vice versa
Learning outcome:
By the end of the teaching and learning activity, the pupils will be able to:
Arrange objects into a sequence according to size, length, height and width
Material:
Sets of different sizes of blocks
Sets of different sizes of balls

6. Procedure:
1. Teacher divides the pupils into a group of four and gives the activity to them.
2. Teacher gives the instruction: ‘Children, here are some blocks with different sizes.
Teacher wants all groups try to think of a way to arrange the blocks according to their
sizes from small to big. I give you all 3 minutes to do the task. Here you go!’
3. The pupils do the activities and the teacher observes while they do the task in group.
As mentioned before, Piaget stated that the teacher should gives appropriate questions
to the pupils to motivate them to determining the quantity or characterizing the shapes but
in this activity, the teacher let the pupils to explore and to observe by manipulating the
objects given. It is because children like to manipulate objects in this stage of
development according to Piaget’s Preoperational stage and Bruner’s Iconic stage theory.
IMPLICATION OF LEARNING THEORIES
Piaget
Critics of Piaget’s work argue that his proposed theory does not offer a complete
description of cognitive development(Eggen&Kauchak, 2000). Piaget is criticized for
underestimating the abilities of young children. Even though, Piaget’s theory is useful
and implemented in the field of psychology and education and referred to in children
development(Piaget 1960), but criticized because overestimating the abilities of older
learners, having implications for both learners and teachers.
Other than that, positively Piaget gave impacts on teaching numbers and
quantities where for example, a child may be asked to bring enough cups for everybody
in the class without being explicitly told to count.
Unlike his theory, games are also a good way to acquire understanding of
mathematical principles, so not only the cognitive activity should be given an attention in
teaching Mathematics(Kamii, 1982).

7. Bruner
Bruner’s theory of how children construct knowledge involves three basic modes of
instruction. In their early years, young children rely extensively upon enactive modes of
learning.
Iconic representation normally becomes dominant during the next stage of
childhood years. Children learn to understand what pictures and diagrams are and how to
do arithmetic using numbers and without counting objects
So, an implication of Bruner’s developmental theories is that children should be
provided with study materials, activities, and tools that are matched to and capitalise on
their developing cognitive capabilities. For example, a teacher wanting to help children
learn about dinosours could use all three modes.
Views of other Mathematics teachers
Jerome Lumbidau
Experience: 17 years of experiences teaching Mathematics in Primary schools
School: SK KokolMenggatal, Kota Kinabalu, Sabah, Malaysia
View: “ I agree with Piaget and Bruner in teaching early Mathematics study using pre-
number concepts to give them solid awareness of number sense. They can use the
knowledge in higher level cognitive development later on.”
GardanGuntis
Experience: 17 years in teaching Mathematics in Primary schools
Current School: SK Rangalau Lama, Tuaran, Sabah, Malaysia
View: “ Piaget and Bruner gave an influential and meaningful guidelines on how to
help pupils to be more logical and critical in thinking, I believe that their theories are
helpful for all of us.”
Jacqueline Vun
Experience: 12 years in Primary school
School: SJK(C) ST. James, Kota Kinabalu, Sabah, Malaysia

8. View: “ Yes, we teachers should help the pupils to acquire the pre-number concepts
before they are taught the numbers symbolically, we supposed use a various materials
to give them the opportunity to learn in more convenient and meaningful way of
learning the Mathematics skills. So, it should start from the early stage of cognitive
development. I agree with Piaget.”
So, overall summary of the views and my research on the topic, Piaget and Bruner give
positive impact on our education especially on children cognitive development in regards
with pre-school early Mathematics study. Furthermore, pre-number concept teaching is
also one of the most important things that every Mathematics teacher should re-consider
when giving the skills in school. It should be started at early age to build a solid
character of number sense in a child.
CONCLUSION
It is undeniable that learning pre number concept in preschool level is an essential
fundamental of Mathematics study. The learning experiences reinforce the children’s
ability in acquiring the skills from concrete to complex and it is supported with the
opinions by Piaget and Bruner. Besides, Mathematics teachers views also prove that the
theories are true about the importance of learning of pre number concept.
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9. REFERENCES
KPM.(2011). HuraianKurikulumPraSekolahKebangsaan. BPK
OUM.(2012).HBMT1203 Teaching of Pre-School Mathematics. Seri Kembangan: OUM
Reedal.,E, Kristin.(2010,May). Jean Piaget’s Cognitive Development Theory in
Mathematics Education.The Journalpp 16 – 20
http://ctl.utsc.utoronto.ca/twc/sites/default/files/LitReview.pdf
http://www.youtube.com/watch?v=NA0kaApMGgU&feature=related
www.unce.unr.edu/publications/files/cy/2006/fs0691.pdf