# CHAPTER as one of the branch of Mathematics

CHAPTER 1: BACKGROUND OF THE STUDY INTRODUCTIONThe purpose of this research would be to assess students’ performance and attitude towards Algebraic thinking. The areas covered in this chapter will be the statement of problem, the research objectives, the research questions and the significance of study. STATEMENT OF PROBLEM One of the concept that is widely use in Mathematics is algebra. Algebra has traditionally been introduced when it was considered that students have acquired the necessary arithmetic skills. Besides, algebra has usually been developed separately from arithmetic without taking advantage of their strong link (Chow, 2011). Algebra have been introduced as one of the branch of Mathematics in Malaysia.

Learning algebra in Malaysia started from primary level, secondary level and continues until higher education level. The students’ result in algebra in Malaysia according to International Mathematics and Science Study (TIMSS), are showing that our students is still weak and having problem in algebra. As we know in International Mathematics and Science Study (TIMSS), the 30% of the questions are involving algebra.    Many studies conducted show that students from different grades of different schools face challenges, and have common errors and mistakes, in comprehending the concepts of equation and variable also in mathematical interpretation of letters or a variety of notations and in establishment of and solving equations appropriate for problems. It is seen that studies mainly focus on the process of transition from arithmetic to algebra, students’ misconceptions related to algebra, sources of mistakes, and the challenges they face in algebra. The problem that students face in algebra maybe related to their own attitude and perception toward algebra itself. This problem have been identified in Malaysia through the result of TIMSS where Malaysia’s students have a low grade in TIMSS.

Algebra was considered as the factor that Malaysia students have a low achievement. According to Nobre (2009), stated that most students show large difficulties in this area, which results in a lack of motivation and failure in Mathematics.    The failure or misconception in algebra can be related to the attitude of the students’ to algebra. The perceptions of students’ towards algebraic symbol notation also can affect students’ performance in algebra. Learning algebra can make students feel burden because there is a lot of topic in algebra. The topic that need to be learn in algebra are algebraic expansion, equations, variables, linear pattern, word problems and many more.

According to Egodawatte (2011), the students were lack of motivation in learning of algebra. This is may be due to the failure they faced in learning algebra. The students not only unprepared for algebra, they also come to fear and dislike it which is have a negative attitude towards Mathematics and to think of themselves as mathematically weak.

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One of the major reasons for students either continuing in Mathematics or avoiding Mathematics was their own perception about how good they are at Mathematics (Armstrong , 1979). This research is to investigate does students’ attitude and perception towards algebra is related to their performance. Researcher hope that if there is any relationship between attitude and perception of students with their performance in algebra, teachers can find a way to make algebra more interesting and easier to understand. Students also need to be prepared mental and emotionally about algebra, so that they will not think learning algebra is such a burden to them.  RESEARCH OBJECTIVESThe objectives in this research are:1) To determine students’ attitude toward learning algebra between genders.2) To identify the relationship in students’ attitude and perception about notation symbol toward learning algebra with Algebraic Thinking performance. RESEARCH QUESTIONThe research questions in this research are:2) Is there any significance difference in students’ attitude toward learning algebra between genders?3) Is there any correlation between students’ perception about notation symbol toward learning algebra with Algebraic Thinking performance?   4) Is there any significance relationship between students’ attitude and perception about notation symbol toward learning algebra with Algebraic Thinking performance?  SIGNIFICANCE OF STUDYThe significance of this research is to determine whether students’ performance in Algebraic Thinking are related to the attitudes of the students or not. This study also want to study whether students’ perception toward symbol notation in learning algebra is related to their performance in algebra.

The result of this research will be beneficial to the students, teachers and also the one who are responsible in the education system. The result will show us whether the students’ attitudes and perceptions toward symbol notation in learning algebra are the factors that effect the students’ performance in algebra.   The finding of this report will tending the improvement of student in Mathematics carrying into action especially in learning algebra by providing them the precautions from making the common mistakes by the early age of scholarly person. Teacher and school administration need to be supply with a lot of exercises that consist higher order thinking skills and knowledge related to the topic of algebra. As for the teachers, this study can assist them to identify and analyze the attitude and perception of students toward learning algebra. Moreover, this research also can benefit the teacher since it can be used as reference work to enhance their teaching acquisition particularly in Mathematics subject.

CHAPTER 2: LITERATURE REVIEW INTRODUCTIONIn this chapter, the researchers will discuss about the related published information in this research. The researchers consider the problem faced by the students in solving problems in learning algebra and Algebraic Thinking performance. These include about the students’ attitude toward algebra, notation symbol in algebra and Algebraic Thinking. All of the topics chosen will be concluded by the researchers review of this study.

STUDENTS’ ATTITUDE TOWARD ALGEBRAMany researches and studies have been conducted showing the importance of student attitudes towards mathematical learning. According to Papanastasiou (2000) explains that students with positive attitudes towards mathematics will be outstanding. His research also shows that students with positive attitudes toward learning mathematics appear to provide excellent performance in comprehensive education.

The student’ attitude towards problem solving was very encouraging as cited by the Salleh (2004). Students are found to have a high degree of fortitude. They will not stop trying until they get the answer, and will continue to work on the problem until they are able to finish it.

Students with high self-esteem in their mathematical ability can also solve the more difficult problems.   Additionally, students seem to enjoy solving challenging questions, and so are well prepared to try. Interestingly, his study found that there were no differences in attitudes toward problem solving between male and female students. However, Patterson et al. (2003), in their study of attitude toward mathematics, found that male students had a more positive attitude than female. Research on Tapia and Marsh (2000) on college students also shows that male students have a higher positive attitude towards mathematics than female students.

In addition, male students showed higher levels of confidence in the subject.  Isaac (2000) found that there was no significant difference in the achievement of the problem solving between male and female students. However, some studies show that male students are better than female. These performance differences are clear in difficult subjects, such as mathematics and physics. According to Fennema (1985), males do better than females when the task involves cognitive skills used in mathematics. He further stated that starting from high school, male showed better math skills than female students. Usually, male students can solve implied problems and problems that do not require special (Gallagher & Lisi, 1994). Given existing literature, more studies need to be done on attitudes towards problem solving and mathematical problem solving, particularly in level matriculation, and this study should be particularly relevant in subject algebra.

NOTATION SYMBOL IN ALGEBRA Mathematics is one of the most important subjects in order to success in other proficient in our life. In learning mathematics, one of the core components for the students to be mastered is algebra (Yahya & Shahrill, 2015). In algebra literal symbols are used in many ways and students should know on how to interpret it. A few research had stated about the difficulties had been faced by a students in learning algebra (Christou, Vosniadou & Vamvakoussi, 2006). The difficulties that are faced by a student’s involve literal symbols in algebra. Students tend to have misconceptions on a rational numbers such as during interpreted a fractions.

When the students lack of the knowledge about symbols and notation, they will faces a difficulties and problems in order to understand and solve the questions.  The symbolic notations term comes by referring to the symbols of Algebraic mathematical symbols. Its stated that the symbols include signs, symbols, letters and signs equal (Peter & Olaoye, 2013). A person can communicate each other, reflect and also manipulate the mathematical concept by using a symbol of notation. However there are misconceptions that occurred involving the equal sign in algebra. Thus its suggested that students should be more alert on interpreted the equal sign to ensure that the answer is correct.   As we know, algebra are known as the language that are used in mathematics. Students should recognize the meaning of every symbols represent in the questions.

It is because every variable have different meaning.  These misconceptions are a serious thing and it is difficult to change the students thinking. Thus it seems that students are rarely makes mistakes in stating the symbol of notation due to their problematic in the basic knowledge in arithmetic reasoning.      ALGEBRAIC THINKING ‘Algebra for everyone’. That is the goals that had been highlighted by a mathematics education around the world. The development of algebraic reasoning occurred after the development of arithmetic reasoning. The important of algebraic thinking had accepted widely to every country in the world.

There are two thing that are important in order to organized algebraic thinking which are the study of basic algebraic and the improvement of tools in mathematical thinking (Kriegler, 2008). However to developed the students that will think algebraically, it should start from elementary school. As we know, the curriculum that involves in teaching algebra in elementary school is not simple and easy to be changed automatically.

So in order to increased the students ability in thinking algebraically, it required a basic understanding in learning arithmetic topics in early grades (Cai & Knuth, 2011).   As the policy changes, the teaching and learning of the teachers also changed. As we know, students are emphasis to memorize many things and the instruction given by teachers are a direct instruction.

However, due to the reformed of the curriculum which to increase a students to think algebraically in the early stage in elementary school, students are emphasized to have a higher level thinking (Richardson, Berenson & Staley, 2009).  According to National Council of Teachers of Mathematics (NCTM), there are five (5) Content Standards that should be learn by a students in order to be capable to live in everyday life and also in their workplace in the future. The Content Standards are Number and Operations, Algebra, Geometry, Measurement and lastly Data Analysis and Probability. So it is stated in the second Content Standard in NCTM which emphasis a students to learn algebra in the early ages and not only in the middle school or high school. In order to produce a student’s that are capable to think and reason mathematically, Algebra content include a patterns that are formalizing, generalizations and functions. These thing is important because it is suitable with our situations in everyday life and it also give us a knowledge in the future topics (NCTM, 2000).  As to emphasis a students to have higher order thinking skills such as to generalization, they should be mastered in the basic skills at the first stages. However it is not possible to mastered fundamental skills and developed new skills both together.

During learning arithmetic in elementary school, students tend to answer the questions heavily and they do not think about the representation of relations that should be focused due to answer the question. It is because, when students in a frame of doing operating an arithmetic, students only focus on calculating and didn’t see the aspects of relational in operation. Thus to reform a students to thinking algebraically, there are many adjustments should be make by a students and also teachers in order to achieve the standard stated even though those students are excellent in answering the arithmetic reasoning.

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