CHAPTER 1

INTRODUCTION

This chapter deals with the background information about the research, its significance in education and the problems involved which are prepared as research questions. The requirement for such research is heightened as there had been no previous study into the development of number sense in primary schools in Brunei Darussalam.

The main aim of this research is to explore the primary pupils’ performance on the development of number sense at the primary four and five in four government schools in Brunei Darussalam. The study will explore the present level of number sense of primary four and five pupils at the four government primary schools. The study will also investigate the differences in performances by school level and school area and looked into the teachers’ perceptions on number sense. The theoretical framework is presented in this chapter to show the variables that will be considered in this study and how these variables will be assessed through the use of the instrumentations developed.

Background of the Research

Brunei’s Education System

Brunei Darussalam has a 7-3-2-2 school system pattern. The pattern represents primary, lower secondary, upper secondary and pre-university levels respectively. The period of primary education is seven years; one year in pre-school, three years in lower primary (primary one to primary three) and three years in upper primary (primary four to primary six). There are two medium of instruction in primary school. In pre-school and lower primary the medium of instruction is Malay but in upper primary the medium of instruction is English except for the subjects such as Malay language, History, Art, Physical Education and Civic. At the end of the year, primary 6 pupils sit for a public examination, Penilaian Sekolah Rendah (PSR) which consists of five subjects to be assessed including Mathematics. Upon passing the examination, the pupils go into the lower secondary level either level 1 or level 2 courses for three years.

At the end of secondary three, students sit for another public examination called Penilaian Menengah Bawah (PMB) or Assessment for Lower Secondary. On passing the examination, the students enter the upper secondary level which takes for two years. At the end of the second year, students sit for Brunei-Cambridge GCE Ordinary level examination.

Those students who pass Brunei-Cambridge GCE Ordinary level examination may advance their study by entering two-year pre-university level (Form six) which leading to the Brunei-Cambridge GCE Advance level examination. Some may decide to go for further studies at local institutions such as Institute Technology Brunei (ITB), Universiti Brunei Darussalam (UBD), technical colleges, vocational schools, nursing colleges or study abroad or they may opt for employment.

Mathematics Education in Brunei Darussalam

Mathematics is one of the most important subjects in the school curriculum in Brunei Darussalam. This can be seen by its appearance in the school timetable especially in primary schools. It is one of the subjects that offered in every public examination in Brunei Darussalam. In fact those pupils who sit for PSR in upper primary schools and did not manage to pass this subject need to repeat examination once again or else cannot proceed to lower secondary level. This shows the importance given to Mathematics in the school curriculum as a core subjects for primary level. Mathematics is an essential basis of individual’s life. Individual requires at least a basic mathematical knowledge in all aspects of life, work and training in Brunei Darussalam.

There was a great concern in Brunei amongst administrators, educators, teachers as well as society at the low performance of students in Mathematics subject at primary and secondary levels (Sarina, 2004). The results of Mathematics subject in public examinations - PSR, PMB, GCE O-level and GCE A-level have not improved. The poor performance has been detected over the years and some efforts have been done by some groups of people especially mathematic teachers. The big challenge for the administrators, educators, teachers and society is to clarify the problem persist. The teachers are the implementers of the curriculum with classroom; therefore they may be the answer to the problems of Mathematics education. They need to provide the best possible techniques of teaching and learning mathematics in the classroom by emphasizing the understanding of the concepts and procedures first and foremost. Students have to understand the concepts and procedures of learning mathematics topics from the beginning they learn mathematics; from pre-school level to secondary level. This has to be done consistently since learning mathematics is a continuous learning process. The students should develop their number sense through the given meaningful activities in the classroom. This draws the attention of the writer to investigate the present level of pupils’ number sense where the absence of number sense in learning mathematics amongst pupils may contributes to the low performances in PSR mathematics.

Number Sense in Brunei’s Schools

Documents calling for reforms in the school mathematics curricula in many industrialised countries in recent years have emphasised the need for teachers to provide instruction that leads to meaningful learning in particular for students to develop number sense (Australian Education Council, 1991; Hong Kong, 2000; National Council of Teachers of Mathematics, 2000; Singapore, 2000). This supports the view of school mathematics as a sense-making experience encompassing a wide range of content, instructional approaches, and evaluation techniques. However, in the past, mathematics classrooms were dominated by instruction and performance of rote procedures “to get right answer.”(Burton, 1993). This continue to happen until now where administrators and parents still give high expectation to mathematics teachers to drill pupils into learning of rules and algorithms in order to get high test scores. Such instructional approach frequently invites the negative effect on the development of mathematical through number sense. Instruction that does not emphasize conceptual understanding of ‘how’ and ‘why’ the rules work but rather emphasize on rules and algorithms can disturb with the development of number sense.

Number sense is a very new terms that almost all mathematic teacher never aware of its existence in mathematics curricula. Although it is new to the language of mathematics curricula, its meaning which emphasises understanding and meaningful learning is commonplace in the literature of mathematics education (Brownell, 1935; Burns, 1994; Hiebert, 1984; Plunkett, 1979; Skemp, 1982). As a teacher, one does not have to settle on an exact definition for number sense, but should aware of its existence. Some teachers do not know what number sense is actually means in the context of learning and teaching of mathematics. What is number sense? Most literature indicated that numbers sense is difficult to define and that it is not a single entity, but rather has many dimensions. Like “common sense”, number sense is a valued but difficult notion to characterise (McIntosh, Reys, Reys, Bana and Farrell, 1997). The NCTM document Curriculum and Evaluation Standards for School Mathematics (2000) defines number sense as the ability to decompose numbers naturally, use the relationships among arithmetic operations to solve problems, understand the base-ten number system, estimate, make sense of numbers, and recognise the relative and absolute magnitude of numbers. The complicated and multifaceted nature of number sense suggests that it cannot be confined to specific textbook strategies. Rather, the development of number sense involves the whole range of activities that fill the whole approach of teaching mathematics. To help pupils to develop this very valuable ability, teachers can provide pupils with experience that encourage them to model and describe numbers in many ways and to apply mathematics understandings in appropriate and efficient ways (Burton, 1993).

The focus of a new mathematics curriculum should be to help children to learn mathematical concepts with understanding and which sequentially to develop number sense. These are challenging times for mathematic teachers of primary schools as well as the pupils. For teachers to provide the best learning environment for their pupils, they must understand individual pupil’s present level of number sense. Teachers need to be able to tackle their own teaching to make sure that their pupils understand mathematical concepts and procedures.

Why is the development of number sense important? When we say that someone has good number sense, we mean that he or she possesses a variety of abilities and understandings that include an awareness of the relationships between numbers, an ability to represent numbers in a variety of ways, a knowledge of the effects of operations, and an ability to interpret and use numbers in real-world counting and measurement situations (Burton, 1993). This simply means that he or she has an ability to understand what numerals mean.

Much has been said about how importance to develop number sense throughout the learning of mathematics as earlier as possible. It is essential that Brunei mathematics teachers should be aware of the existence of each pupil’s number sense and be ready to develop them in the classroom through the entire activities.

Statement of Problem

Mathematic is one of the five subjects that are to be tested for the public examination at the end of Primary school that is (Penilaian Sekolah Rendah, PSR). Parents, administrators and teachers have always given more concern on the performance of mathematics that the candidates had performed. Sainah & Suffolk (1999) pointed out candidates for Brunei Darussalam’s Primary Certificate of Education (PCE) which now refers to Penilaian Sekolah Rendah (PSR) have always performed poorly on the mathematics examinations compared with examinations in other subjects. Poorly performed mathematics subjects in PSR gives more concern among society as it is one of the important subject in the school curriculum. Administrators and parents often push teachers to choose the best classroom instructions for getting high scores in examination. The teachers usually thought that ‘drill and practice’ using past examination papers regards as the best answer to be taken. This often done several months before the examination get going. They are often doing this often based on the belief that the pupils must practice a lot without knowing how and why it works. They are trying to do this under great pressure and leading the pupils to learn rules and algorithms by hard and without understanding wholly why or how the rule works. Such instruction was what Skemp (1987) referred to as instrumental instruction.

Over recent years numerous studies into the teaching and learning of mathematics at all levels in schools in Brunei Darussalam, have drawn attention to how skill-drill, examination-oriented teaching approaches are, year after year, generating poor overall performances on externally-set mathematics examination as mentioned by Zurina (2004). Yet this skill-drill, examination-orientation has become deeply embedded into the psyches of students and teachers (Nannestad, 2002), and continues to manifest itself in powerful, yet largely subconsciously held, didactical contracts between teachers and students. Teachers experienced all these practices and usually lead them to forget encouraging students to use common sense while solving mathematic problems. The students fix themselves to use rules and algorithms all the time when solving easiest to difficult problems.

Classroom teachers’ instructions often push students to learn rules by rote at first and foremost without knowing why and how the rules work. Rote learning of these traditional algorithms does not accentuate the conceptual understanding and may perhaps hinder the development of number sense. Parmjit Singh (2004) believed that students who merely manipulate numbers via algorithm have not learned mathematics. This was further pointed out by Pirie (1988) who said, “An algorithm is not itself knowledge, it is a tool whose use is directed by mathematical knowledge and care must be taken not to confuse evidence of understanding with understanding itself”. Both writers noted that learning and memorizing algorithms alone does not give much input on learning mathematics as fully.

This research used a number sense test adapted from McIntosh et al, 1997. The aim of the test is to assess the pupils’ understanding of numbers and operations and to find out the effect of the teachers’ instruction in the development of number sense. The research will be focused on the general level of number sense possessed by primary four and five pupils in six selected government schools in Tutong district.

Purpose of the Research

Mathematic is one of the most important subjects in primary school in Brunei as it can be seen from the school timetables. There are ten thirty-minute periods for lower primary and nine thirty-minute periods for the upper primary. Mathematics is often required in most profession. Societies too recognize the importance of it in daily skills.

Currently much discussion is occurring within teachers as well as community regarding the low mathematic performance to most primary schools pupils in Brunei. Such comments usually made soon after they obtain the primary public examination, Penilaian Sekolah Rendah (PSR) results. Teaching approaches need to be reviewed from time to time. The role of teachers and pupils has to be examined from time to time too.

Presently, the new primary mathematics curriculum comprised of topics which integrate “number sense” beginning from primary 1 up to primary 6. This idea modification will affect the teacher instruction in the teaching of mathematics.

The new mathematics curriculum aims to provide children with skills and understanding which will enable them to cope confidently with the mathematics of everyday life. The aim of the new curriculum is also to stimulate children’s interest in mathematics and encourage good learning habits, the ability to solve mathematical problems and think clearly and logically; develop the children’s ability to interpret and communicate mathematical ideas. It hopes to help children to appreciate how mathematics can help to interpret the world in which they live, in line with the national aspirations of Malay Islamic Monarchy (MIB). The new curriculum is also hopes to provide a solid foundation for those who may wish to continue studies in mathematics (Curriculum Development Department, 2005). Through these, pupils are expected to appreciate the beauty and importance of mathematics. Hence, the teaching and learning of mathematics, even at the early stages, should attempt to inculcate critical and creative thinking, apart from memorizing rules and algorithms.

Most mathematic teachers believed that pupils must be trained skills first and foremost (Veloo & Ali, 2004). Teachers trying very hard to focus on this need and often resort to drill and practice which leads pupils to learn rules by rote and without knowing why and how the rule works. Teachers’ intention is just that the pupils could get “the right answers” and score high marks towards the end. Rote learning of these traditional paper-and-pencil algorithms possessed by this pupils may not have well-developed number sense in their schema (Veloo & Ali, 2004).

Hence, this research is trying to investigate the general level of number sense possessed by primary four and primary five school pupils in Brunei Darussalam and to explore the significance differences in performance by gender of the pupils in each level. It aims to explore individual primary four and primary five pupil’s present level of number sense and to explore their mathematic teachers’ perceptions towards number sense in the selected schools.

Theoretical Framework

One of the new features of the Primary Mathematics curriculum in Brunei is the teaching of estimation and mental computation. Estimation skills empower us to make quick decisions regarding daily household and financial matters. For example, we need to estimate the quantities and the cost of commodities we consume monthly and set aside a budget for the food consumption of the family (Curriculum Development Department, 2005).

Estimation and mental computation are the elements which associated with the presence of number sense. In the presence of these elements in the new mathematics curriculum form the basis for this research to explore the general level of primary school pupils’ number sense in Brunei Darussalam. It is hypothesised that after exploring pupils’ level of number sense, there will be a significant different in the level of number sense between primary four and primary five, as started early 2006 primary four should be treated with number sense compared to primary five pupils who still dealing with the old primary mathematics curriculum.

Figure 1 provides a sketch of a framework of the research. The researcher will carry out a pilot study, in March 2006. The pilot will be conducted in one of the primary school in Tutong district. The school will not be the selected schools for the main study. In the pilot study, pencil-and-paper number sense test which will be needed for the main study will be trialled and validated. The rewordings to the pencil-and-paper number sense test will be carried out based on the findings of the pilot study. These modifications will provide as useful purposes of facilitating the development and technical validation of the instruments, which will be used in the main study.

Number Sense Test

(NST)

(Pencil-and-paper Test)

For all pupils in 4 schools

Instrument 1

(Modified NST)

Type of

D

C

B

A

School Setting

Interview

Instrument 2

(Interview)

Perceptions Questionnaires

For all MathematicsTeachers in 4 schools

Instrument 3

(Questionnaires)

A

B

D

C

Type of

School Setting

A & B: Urban Schools

C & D: Semi-Urban Schools

Figure 1. Framework of the main study.

Research Questions

The main objective of this research is to investigate the general level of number sense in upper primary pupils. It is hoped that the main study would answer the following research questions:

1. What is the level of number sense possessed by primary 4 school pupils in Tutong district?
2. What is the level of number sense possessed by primary 5 school pupils in Tutong district?
3. Are there any significance differences in performance between primary four and primary five pupils?
4. Are there any significance differences in performance between urban schools and semi-urban schools?
5. What are mathematics teachers’ perceptions of number sense in the selected schools?

Significance of the Research

There were few studies done in Brunei by the officers from Curriculum Development Department, Ministry of Education such as finding the general level of number sense among form 1 and 2 students from two leading secondary schools who scored 5As at the end-of-primary (PSR) examinations in Bandar Seri Begawan and exploring the possible negative effect of instrumental instruction and its influence on the development of number sense among 1200 secondary 1 and 2 students from eighteen secondary schools throughout Brunei Darussalam. But, there is no study has been conducted in Brunei Darussalam in investigating the level of number sense among primary school pupils.

This research has an attempt to investigate the general level of number sense among primary four and primary five pupils in some of government schools in Tutong district, and to find out the perception of teachers teaching mathematics in the selected schools towards number sense. It is hoped that the findings of this research will provide information to school administrators and mathematics teachers regarding the primary pupils’ performance on number sense tasks. It is also hoped that the findings of this study will encourage mathematics teachers to change classroom norms and practices and to integrate relational learning activities that lead to the development of number sense. Hopefully the research will also make mathematics teachers to be aware of the existence of number sense in the mathematics syllabi and which drive them to focus on meaningful learning that leads to the development of number sense.

Mathematics teachers might use the findings of this research to help them in planning their teaching strategies and designing their lesson plans for teaching mathematics topics which hopefully might lead to develop number sense and thus improve their pupils’ mathematics performances. If the pupils have number sense, they would be able to make an estimate, check their own mistakes on mathematics problems, make relationship between numbers, to represent numbers in various ways and to interpret and use numbers in real-world counting and measurement situations The findings might also benefit teachers in preparing themselves to better appreciate students’ thinking strategies in solving any mathematics problems.

Scope and Limitation

There will be few possible limitations of the research, relating to sampling and time constraints for the main study.

Sampling. This research will be to investigate the general level of number sense in primary four and five pupils from the four selected government primary schools. No non government schools will be involved in this research. Primary 6 will be excluded in the research as they are going to sit for the public examination, Penilaian Sekolah Rendah (PSR) in early October this year. The four schools will be selected from Tutong District only comprises two urban and two semi-urban. The number of pupils to be involved in the main study is presently 300 pupils. The author is aware that the actual pupils sample size may differ due to some unpredicted circumstances, for instance, pupils being absent during the tests or interviews, or pupils transferring to other schools. Findings of this study cannot be generalized to other government schools or to the whole pupils’ population in Brunei Darussalam.

The perceptions of teachers teaching mathematics in the selected schools towards number sense will be based on the results from a questionnaire that will be designed for this research. Therefore these perceptions of the mathematic teachers sample in this research cannot be generalized with other mathematic teachers’ perceptions in other schools. The research will not take into accounts of pupils’ abilities, classroom environments, teachers’ qualifications, teaching techniques and approaches used in the schools selected.

Time Constraints. The research will be carried out from July to October 2006 in primary four and primary five classes in four selected government schools. Sample will be small due to time constraints as the study has to be completed within the period of few months allowable for Master of Education degree. The deadline of the completion of the dissertation for the research is at the end of December 2006.

Definition of Terms

The following terms are defined to clarify the meaning of terms in the research:

1. Upper primary pupils: Primary four through 6 of age from 9 to 11.
2. New curriculum: The Brunei new primary schools’ mathematics syllabus introduced in 2005.
3. Development: The progress of number sense in upper primary pupils.
4. Number Sense Test (NST): It is a 40-item paper-and-pencil test on number sense which is used to administer this research. It is adapted from a number sense test published by McIntosh ((McIntosh, Reys, Reys, Bana and Farrell, 1997). There are two types of NST will be used:

NST4 - It is a 40-item paper-and-pencil test on number sense which is used to administer Darjah 4’s pupils.

NST5 - It is a 40-item paper-and-pencil test on number sense which is used to administer Darjah 5’s pupils.

5. Penilaian Sekolah Rendah (PSR): It is a public examination for primary 6 of all government and non-government schools in Brunei.
6. Penilaian Menengah Bawah (PMB): It is a public examination for secondary 3 (the third year of lower secondary) of all government and non-government schools in Brunei.
7. Estimation: To set a value.
8. Urban Schools: Schools that are situated around the town area.
9. Semi-Urban Schools: Schools that are situated faraway from town area.

Summary

In many areas of the mathematics curriculum recent years clearly states that the development of number sense should be in line with the learning and teaching of mathematics in normal classroom environments. Many research findings strongly recommended the development of number sense to make the learning of mathematics is a very meaningful situation and the pupils are expected to appreciate the importance of mathematics and benefits a lot from it.

Veloo and Ali (2004) found out that in general the level of number sense ability among the sample of secondary students in Brunei investigated was low. What will be the level of number sense possessed by primary four and five school pupils in Brunei? It is the purpose of this research to investigate the general level of their number sense.