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Globally, education authorities are placing increasing emphasis on the development of literacy and numeracy in primary and secondary schools. Mathematics in particular has developed into a sophisticated and complex body of knowledge and has applications in almost all areas of human activities. It is becoming increasingly difficult to live a normal life without making use of mathematics of some kind. It is felt therefore that everyone should study mathematics up to a certain level of schooling. In view of this, mathematics has been made an important core subject in the Primary and Lower and Upper Secondary school curriculum in Brunei Darussalam and all pupils are required to study it.
In the New Education System for the 21st Century, better known as the SPN-21, learners are expected to achieve the following learning outcomes in Mathematics:
develop learning skills, concepts, understanding, and attitudes to cope confidently with the mathematics of everyday life;
stimulate the interest of learners in learning mathematics and foster good learning habits;
understand and develop mathematical thinking and reasoning skills through solving mathematical problems;
develop learners' ability to interpret and communicate clearly and precisely mathematical ideas both orally and in writing and to read and comprehend a mathematical text;
provide a foundation for learners who may continue their studies in mathematics or other disciplines where mathematical concepts are essential; and
develop an appreciation of the nature of mathematics and mathematical processes.
SPN21, basically, is aimed at improving students' success rates in schools and enhance their marketability upon their entry in the job market, which would, hopefully translate in improved chances in life. In order to achieve the learning outcomes, collaboration from all parties concerned is very much needed. Teachers, as facilitators, should be equipped with the required knowledge and skills which facilitate to the students' achievements and to better prepare learners with the skills of the 21st century.
Study on students' performance in Brunei examinations clearly show that both primary and lower secondary pupils are drilled into learning and applying mathematical rules without understanding how the rule evolved and why it works (MOE,2008). Appropriate practice plays an important role in the teaching and learning of mathematics at all levels of schooling and is connected to mathematical thinking through reasoning, communicating, and problem solving. It reminds students that mathematics is well-structured (organised, filled with patterns, and predictable) and that the power of algorithms resides in their applicability as a tool for routine tasks and in the process of solving mathematics problems.
In order to become fluent in calculation, students must demonstrate efficient and accurate methods, supported by number operations and operational sense. Students should be provided with opportunities to develop and discuss invented algorithms helps to enhance number and operation sense. When students are engaged in development of computational methods or in recording, explaining, and critiquing one another's strategies, they can learn about efficiency, validity and generalizability.
The Research Framework
1.2.1 Problem Statement
Fractions are first introduced to pupils in Year 2 in Brunei mathematics curriculum. The curriculum keeps revisiting the topic of fractions in a spiral way at different depth. In secondary education, the topic of fraction is still being revisited and taught. In O Level Mathematics students are expected to be able to perform calculations by suitable methods, with and without a calculating aid in involving fractional operations.
Despite being taught from primary to secondary levels of education, the students still find fractions difficult and it was reported that many teachers needed to review the previous fraction concepts in each grade level (Kamii, 1994; Robitaille,1992)
Research on students' ability to perform operations on fraction had shown disappointing poor results (Idris & Narayanan,2011). A survey on topics students find most difficult in school in Malaysia, revealed that fraction was listed as one of the most difficult topic at the primary and secondary level mathematics (Kim, 2003). However a study in China reveals that students in China are good at recognizing forms of representation of problems and equivalent fractions, their competency of computation on fraction is good, but their understanding of fraction has some deficiencies.(Su,nd)
In this study, the researcher will be looking at the students' difficulty in operations of addition and subtraction of fractions and explore alternative ways which might be useful to teachers. The key issue in the study will be addressing the students' difficulties by looking at their understanding of fraction- teaching with justifications and with the use of appropriate learning aids. The knowledge is then strengthened with the use of a game. To summarize the lesson, a video song on addition and subtraction of fraction is played.
Throughout the researcher's teaching years, most common problems observed are those concerning with fractions. Students are unable to perform operations with fractions properly and correctly which lead to poor performances in the topic. Study found out that promoting conceptual understanding of fractions leads to beneficial gains in higher level mathematics. Recognizing the importance of the topic, it is important for teachers to ensure that students have a firm grasp on the concepts of fractions.
The study will be of great value to the researcher and Mathematics teachers, in order to improve the teaching of this topic specifically and the teaching of mathematics as a whole. The study will also be beneficial to the students' learning as the teachers would know and understand what the students' difficulties are and teaching methods that will be employed to address such learning difficulties.
The purpose of the study is to investigate the difficulties faced by students of Year 7 on the fractions particularly in addition and subtraction. The study also aims to find out to what extent students have understood the nature of fractions. Specifically the study would seek to answer the following research questions.
What is knowledge level of Year 7 students in fractions and what aspects of fractions do Year 7 students find most difficult?
How would conceptual understanding of fractions help students operate with fractions?
To what extent is remediation effective in addressing students' difficulties with fraction?
To what extent will teachers' content knowledge and pedagogical skills in teaching fractions help students become confident in dealing with fractional problems?
1.3 Significance of the study
The study findings will significantly inform teachers about the impact of their work on pupils learning outcomes on fractions. The study findings might also motivate teachers to understand which of their practices might have been more or less effective. Teaching for understanding, as being emphasized in the SPN-21 framework, is one of the key components in this study. Firm grasp of the conceptual understanding of the equivalent fraction, will help students to understand how fraction work. Students can better visualize and understand the value of a fraction. Students will have fewer problems in the future when they are introduced to fraction operations and algorithms (especially when adding and subtracting with unlike denominators).
The study findings will also provide valuable information for students and teachers that understanding the nature of fraction has influence on the development of mathematical thinking. Fluency in understanding fractions is also essential to achieve success in algebra.
1.4 Scope and Limitation of the Research
The study is looking at students' perspective on their learning of fractions in the mathematics curriculum. Students' knowledge on the topic will be tested and analysed. The result will give the indication to the researcher as to which area need the most attention in the remediation process. Achievement tests and confidence scale test are administered on the topic being studied, which is Fraction. According to a study that investigates the relationship between fraction proficiency and success in algebra, success in manipulating and performing basic operations on common fractions has led to positive performance in algebraic reasoning (Brown & Quinn, 2006). Suffice to say, promoting conceptual understanding of fractions leads to beneficial gains in higher level mathematics.
The other limitations in this study are:
The study is only focusing on students' difficulties in addition and subtraction of fractions, as understanding and knowing how to do addition and subtraction is essential in multiplication and division. Furthermore, many research findings cited that common difficulties are in addition and subtraction. The time to conduct the study is also limited so the researcher can only look at a small part of the curriculum.
Gender issues is not examined in the study as the sample is gender bias, that is the school chosen is restricted to female enrolment. The result cannot be generalized to the whole year 7 population throughout the country, the pattern may provide the basis for further study with a wider sample.
1.5 Structure of the Research Study
The study is presented in five chapters. Chapter 1 has introduced the nature of the study, its aims, rationale and the problem statement. Chapter 2 reviews the relevant literature related to the study and will explore the overview of the topic and theories that are related and relevant to the study. Chapter 3 will be looking at the methodology used in conducting the study. Chapter 4 is dealing with the discussion of findings, and Chapter 5 is the conclusion from the study is discussed and recommendation for future research is stated.
Mathematics is an important core subject not only in Brunei education system but also in other countries' education system. It is compulsory that all students learn Mathematics up to certain level. In the SPN-21 curriculum framework, teaching and learning are tailored to cater for students need, ability and learning style (MOE, 2008). Fraction is one of the topics which have been taught to students from as early as when they are in Year 2. Students are expected to be able to handle all the sub-constructs of fractions (Kieren, 1995) fluently, which will help them with the other aspects of the topic. Regardless of this, students still find fraction to be one of the difficult topic in Mathematics. Previous research findings on students' difficulties revealed that students were lacking in the conceptual understanding of fractions. Addition and subtraction of fraction is one of the areas of concern which may contribute to the difficulty in handling fractions. This research exercise is specifically looking at the students' difficulty in doing addition and subtraction of fractions in Year 7 students. The finding from this study will be of great importance to the researcher as well as to other mathematics teachers.