“The progress and the improvement of Mathematics
are linked to the prosperity of the state”
-	Nepolean

Education is a deliberate and conscious activity on the part of civilized societies to help their members lead a socially meaningful and happy life. Education is a liberating force. It is also democratizing force, cutting the barriers of caste and class, smoothing out inequalities imposed by birth and other circumstances. Education is the main tool to develop the innate potentialities of an individual. Education is the pillar of a developed and a powerful country besides being the most important element for growth and prosperity of the nation, most important areas of the service sector as it provides the required knowledge and skill to do any work. The knowledge aim of education emphasises that education should aim to enhance the ability of learners to access, assess, adopt and apply knowledge. Education must develop capacity of the students to acquire the relevant knowledge that will gurantee the ability to remain up to date in the changing environment. In order to satisfy the knowledge aim of education, a wide variety of subjects are provided at all stages of education. Among the various subjects, Mathematics is an important subject at pre primary, primary and secondary stages of education as it develops logical and analytical thinking of individuals.
In the present social set up, mathematics is more important for the common man. In this age of rates, taxes, insurance, premia, savings and interests, rent and propaganda; only a person with good mathematical background can be reasonably sure that he is getting his due. Mathematics played an important role in various subjects. Mathematics is one of the greatest of all sciences. It is basic to the understanding of every science. It enters into every walk of life. Mathematics is known as the science of all sciences and art of all arts. So mathematics cannot separate from our daily life.
Mathematics education in school is more emphasized as it improves concept development, fosters higher cognitive abilities and skills. Mathematics is a very useful subject for most vocations and higher specialized course of learning. Mathematics has become a compulsory subject in the school curriculum because of its manifold value to the individual as well as to society. The place of mathematics in school curriculum is thus clearly a central one. In this world of science and technology, mathematics education for all is considered an absolute necessity. Mathematics is the mirror of civilization. Shut out mathematics from daily life and all civilization comes to a standstill. In this technologically developed world, nobody can live a single day without mathematics. Therefore, we can say that mathematics is much important as food, air, and water. Mathematics is intimately involved in every moment of every one's life. Even Nepolean said, “The progress and the improvement of Mathematics are linked to the prosperity of the state”. Mathematics is just like an engine of a train, which carries the whole life delightfully.
The modern cyber era is full of competition and in this age, everyone has developed a quality of education to compare with others to achieve life goals. Education, the foremost weapon for social reform, is now forced to change. In the present educational system, more and more importance is given to the performance in their academic and related activities. The country needs, effective and productive citizens who display scientific and constructive thinking and attitudes in all walks of life. This is possible, to a great extent, with carefully devised educational curricula, especially, on the school Mathematics programme. Education Commission (1964-66) has recommended that “proper foundation in the knowledge of mathematics should be laid at the school”. According to the Education Commission (1964-66), “the advent of automation and cybernetics in the country marks the beginning of the new scientific industrial revolution and makes it all the imperative to devote special attention to the study of mathematics”. Mathematics is a fundamental science subject, which is taught all over the world as an individual’s building foundation from pre-schooling age. Mathematics is the only subject which is known either by literate as well as illiterate. Mathematics is a barrier to success in schools for many students. It is noticed as a difficult subject to master due to its figurative and abstract nature. A student who is futile in mastering mathematics skills loses opportunities to enroll in a broad range of courses, thus limiting career choice.
Mathematics is logical. Logic is the essence of mathematics. Mathematics draws necessary conclusions from explicitly stated assumptions. The student must study a number of axiomatic systems. These may not be deep, but they must be logically correct. He/she must understand the nature of proof, which helps the students to develop critical and creative thinking as well as problem solving ability. Mathematics deals with deep structures. The student must build up an ambition to study deep structures and derive pleasure out of them. The primary aim of teaching mathematics is to enable the student to develop understanding and skills related to mathematical concepts, principles, formulas, and operations and to develop abilities to apply them to problem solving situation.
At the same time, successful problem-solving in mathematics requires students to be able to select and use task-appropriate cognitive strategies for understanding, representing and solving problems. Student’s beliefs about the nature of knowledge and learning influence the strategies they use for several purposes such as learning, developing the confidence, humanizing the critical and creative thinking, improving the problem solving methods and more diversify the self–regulated learning, which in turns affects their academic achievement in mathematics (Foong & Perry, 1998). Mathematics is aroused from different kinds of problems. When a solution is developed for a problem whether it is in engineering, medical, astronomy, academies, architecture or commerce, etc., the problem should be precisely stated and solution system should be represented in an easily understandable form then only others can learn it easily and implement, adopt or customize where ever it is needed. Mathematics is a precise yet easy to understand language. In which the experts can interpret the happening and phenomenon in and around them. 
Achievement motivation is one of the crucial psychological factors determining future academic and occupational success. Therefore, general and professional education should be completed with training focused on psychological skills useful and desirable in everyday life. Formation of students’ competence without practicing and developing needed psychological components will not let educate the graduates comprehensively and might result in their failure on the labor market. In mathematics classrooms, students learn valuable concepts that help them to be successful in their mathematics careers throughout their lives. This success includes success in the current classes they are taking, success in future mathematics classes, and success outside the context of schooling.
Need and Significance of the Study
Research on teaching and learning mathematics has a long history throughout the world. Studies in the area of mathematics education in one form or another seemed to be deeply rooted in centuries. But scientific research in this area is comparatively new, even in developing countries like India. Scandura (1967) remarked that at the end of the first half of the 19th century, it was a hard time for those of us doing basic research on mathematics learning. For few researchers seemed to believe that such complex issues as mathematics learning and mathematical creativity could be studied in a scientifically viable way. Gradually in order to meet the changing and challenging needs of the society, the necessity of research in mathematics teaching and learning in a scientific way was felt by the mathematics educators, social scientists, and psychologists. They become interested in investigating the problems related to more general issues of complex mathematical learning such as problem solving, thinking and instructional processes and pupil’s accomplishment in mathematics in the schools and colleges. The investigators have gone on and on in identifying the factorial variables which will be more promising in determining pupil’s success and failure in mathematics. Pupil’s like and dislike in mathematics, pupil’s tendency to lose interest or gain interest in mathematics, parent’s or guardian’s interest towards mathematics, age old myth and belief that mathematics is a very tough discipline, there is nothing new in mathematics, etc. (Breiteig, Grevholm & Kislenko, 2005). Gender difference of the pupils’ in achievement, interest, and attitude towards mathematics as well as the socio-cultural impact on the pupil’s attitude and performance were studied. The research studies indicated that there has been an increased interest in the role of affective factors in the teaching and learning of mathematics, these affective factors included mathematics-related beliefs such as students’ mathematical beliefs towards mathematics, beliefs on mathematical competency, motivational beliefs, beliefs about learning context, beliefs about social context which impacted mathematical performance, etc. (Schuck & Grootenboer, 2004; Leder & Forgasz, 2006). Adnan, Zakaria and Maat (2012) indicated that the overall teachers mathematical beliefs are high, the teachers conceptual knowledge is good, while mathematical experience is moderate. They also provided the suggestions for better understanding of mathematical beliefs, conceptual knowledge and mathematical experience, particularly within the context of teaching and learning of mathematics. These studies have made a contribution to our understanding of factors related to mathematical ability, interest, problems in teaching and learning mathematics and provide large dividends in the form of considerable improvement in mathematics education, where the problem of mathematics teaching and learning appears to be a universal problem of the century.
 As a practicing teacher for the last 15 years, the researcher felt that there are certain factors that affect achievement in mathematics among secondary school students. Student’s beliefs and achievement motivation towards mathematics teaching and learning play an important role in mathematics education. The learning outcomes of students are strongly related to their beliefs about the nature of mathematics, beliefs about mathematics education, beliefs about the self, beliefs about the social context, beliefs about the nature of knowledge and the process of knowing, beliefs about learning context, beliefs about mathematical education (belief about mathematics as a subject, belief about mathematical learning and problem solving). belief about the self (self-efficacy beliefs, control beliefs, task-value belief, and goal orientation beliefs), mathematics classroom experience, student’s perceived confidence, student’s perceived influence of emotions, the interest of students in mathematics and student’s personality and self-concepts, etc.
Student’s beliefs about mathematics and mathematics learning can have a substantial impact on their interest in mathematics, their enjoyment of mathematics, and their motivation in mathematical class. Studies on student’s mathematical beliefs about the discipline of mathematics, beliefs about themselves as learners have also been clearly underlined in recent years (Schunk & Grootenboer; 2004). Significantly student’s beliefs in their ability to solve time consuming mathematics problems, the importance of increasing their mathematical ability and usefulness of mathematics in everyday life, were all assumed to be related to the achievement motivation to learn to solve mathematical problems. The immature mathematical belief and in appropriate achievement motivation have a strong impact on student’s critical thinking, problem solving performance, and their approach to learning through innovative skills and engagement with mathematics.
  	Achievement motivation refers to a motive to achieve some standards of accomplishment or proficiency, fuses with most of the needs namely for power, superiority and out coming insecurity. Achievement motivation also referred to as the need for achievement is an important determinant of aspiration, effort, and persistence when an individual expects that one’s performance will be rated against some standards of excellence. It is conceived as a desire to accomplish something difficult. The desire is accomplish by action that is the individual makes intense, prolonged and repeated effort to accomplish something difficult. McClelland (1961) proposed a motivational theory, in which he focused attention on the variations of achievement motivation. He argues that individual difference exists in achievement motivation and might represent differences in the strength of a relatively general and stable disposition to achieve that is acquired early in life. The study conducted by Singh (2011) indicated that achievement motivation is a subjective and internal psychological drive, enabling individuals to pursue work they perceive to be valuable and promoting them to reach their goals. Achievement motivation is also a mentality to compete and compare with others. 
  	Numerous research studies have been explored to understand the effects of different variables relating to creativity, mathematical intelligence and student’s achievement. Several studies have analyzed the effects of students’ mathematical beliefs and critical thinking on mathematics achievement and self-regulated strategies on motivation. The study conducted by Tarmizi and Tarmizi (2010) indicated that there has been an increased interest in the role of affective factors in the teaching and learning of mathematics. These affective factors included mathematics-related beliefs such as students’ beliefs towards mathematics, beliefs on mathematical competency, motivational beliefs, beliefs about learning context, beliefs about social context, which impacted mathematical performance, to name a few. Findings also indicated an overall significant effect on students’ beliefs in mathematical competency, with three significant predictors namely, students’ beliefs on teachers attitude to mathematics teaching, grades in mathematics and gender. Amari, Motlag, Zalani, and Parhon (2011) explored the correlation between academic motivation and academic achievement among Tehran University students. The results of the study indicated that there exist a positive and significant correlation between academic motivation and academic achievement. Furthermore, subscales of task, effort, competition, social concern within eight subscales had a significant relationship with academic achievement.
 While conducting the review of the literature, in mathematical beliefs and achievement motivation, it was evident that relationship studies of both the variables on achievement are carried out by various researchers. But it is not possible to find out a study which explored the interaction effect of mathematical beliefs and achievement motivation on achievement in mathematics. Thus, the present study is intended to augment the body of research related to student’s beliefs about mathematics and achievement motivation on achievement in mathematics. The fortitude of the present study is to understand how the application of relatively simple student's mathematical beliefs and achievement motivation in mathematics effect secondary school student’s ability on achievement in mathematics. 
Statement of the Problem
	The study is entitled as; “INTERACTION EFFECT OF MATHEMATICAL BELIEFS AND ACHIEVEMENT MOTIVATION ON ACHIEVEMENT IN MATHEMATICS OF SECONDARY SCHOOL STUDENTS”
Definition of Key Terms
 Interaction effect
For the present study, the term interaction effect stands for the statistical process to see whether the effect of a variable is different for different levels of other variables as studied by the technique of Two-way ANOVA.
 Mathematical Beliefs
 Mathematical Beliefs refer to student’s beliefs towards mathematics, belief on mathematical competency and belief about learning context which impacted mathematical performance (Schuck & Grootenboer, 2004).
 For the present study Mathematical Belief refers to student’s beliefs about mathematical education such as belief about mathematics as a subject, belief about mathematics teaching and learning, belief related to use of mathematics in daily life and belief about competence in mathematics as measured by using Mathematical Beliefs Inventory.
 Achievement Motivation
Achievement Motivation is “the combination of psychological forces which initiate, direct and sustains the behavior of an individual and leading to the successful attainment of a goal which provides a sense of significance.” (Good, 1973). 
Achievement Motivation used in this study denotes readiness among the learners in relation to mathematics to fulfill a planned objective as measured by Scale of Achievement Motivation in Mathematics.
 Achievement in Mathematics
Achievement in Mathematics is an indicator of a student’s performance in mathematics based on the results of a formal or informal assessment (Blankstein, 1959). Achievement in Mathematics indicates the extent to which the learner has internalized the related learning material. 
For the present study, Achievement in Mathematics is operationally defined as the score obtained by the students in the Mathematics test conducted by the school for the first term examination.
 Secondary School Students
The secondary school students refer to those students studying in standard VIII, IX, and X of recognized high schools who follow Kerala state syllabus.
For the present study, secondary school students refer to those students studying in standard IX of various schools in Kozhikode and Malappuram districts who follow Kerala state syllabus 
Variables of the Study
The independent and dependent variables selected for the present study are : 
 Independent Variable
The independent variables used in the study are :
Mathematical Beliefs
Achievement Motivation 
 Dependent Variable
The dependent variable used in the study is ‘Achievement in Mathematics’.
Objectives of the Study
The objectives of the study are:
•	To find out whether there exist any significant difference in the Mathematical Beliefs of secondary school students for the subgroups based on 
o	Gender
o	Socio-Economic Status
•	To find out whether there exist any significant difference in Achievement Motivation of secondary school students for the subgroups based on 
o	Gender
o	Socio-Economic Status
•	To find out whether there exist any significant difference in Achievement in Mathematics of secondary school students for the subgroups based on 
o	Gender
o	Socio-Economic Status
•	To study the main effect and interaction effect of Mathematical Belief and Achievement Motivation on Achievement in Mathematics of secondary school students for the total sample 
Hypotheses of the Study
The study was carried out to test the following hypotheses:
•	There exist significant gender difference in the mean scores of Mathematical Beliefs of secondary school students.
•	There exist significant difference in the mean scores of Mathematical Beliefs of secondary school students with respect to their Socio-Economic Status.
•	There exist significant gender difference in the mean scores of Achievement Motivation of secondary school students.
•	There exist significant difference in the mean scores of Achievement Motivation of secondary school students with respect to their Socio-Economic Status.
•	There exist significant gender difference in the mean scores of Achievement in Mathematics of secondary school students.
•	There exist significant difference in the mean scores of Achievement in Mathematics of secondary school students with respect to their socio-economic status.
•	There exist significant main effect of the independent variables namely: Mathematical Beliefs and Achievement Motivation on the dependent variable, Achievement in Mathematics of secondary school students for the total sample.
•	There exist significant interaction effect of the independent variables namely: Mathematical Beliefs and Achievement Motivation on the dependent variable, Achievement in Mathematics of secondary school students for the total sample
Methodology
The study is intended to investigate the interaction effect of Mathematical Beliefs and Achievement Motivation on Achievement in Mathematics among secondary school students. The investigator used survey method for collecting the required data. A precise description of the sample, tools and statistical techniques used for the study are described below.
Sample 
The population considered for the study comprised of secondary school students in Kerala state who follow Kerala State syllabus. The present study was conducted on a sample of 600 secondary school students of IX standard selected from secondary schools of Kozhikode and Malappuram districts of Kerala State. Stratified sampling technique was used by giving due representation to gender and socio-economic status of secondary school students. 
Tools Used for Data Collection
	The tools used for the purpose of collecting relevant information are 
•	Mathematical Beliefs Inventory (Ganisha & Niranjana, 2019)
•	Scale of Achievement Motivation in Mathematics (Vijayakumari & Sumangala, 2000)
 Statistical Techniques Used
For the purpose of analyzing the collected data following statistical techniques are used.
•	Descriptive statistics.
•	Test of significance of difference between means of large independent sample (t-test)
•	One – way ANOVA
•	Two way ANOVA with 2 x 3 Factorial Design
 Data Collection Procedure
For collecting the required data from the selected sample, the investigator sought permission from various heads of secondary schools of Kozhikode and Malappuram districts of Kerala State. After getting permission, the data were collected from the selected secondary schools of each district. The investigator administered the tools to secondary school students of standard IX by providing necessary directions to the students to fill the response sheet. The scores of achievement test in mathematics were collected from the concerned class teachers.
Scope and Limitations of the Study
The study was intend to investigate the interaction effect of Mathematical Beliefs and Achievement Motivation on Achievement in Mathematics of secondary school students. Appropriate and standardized tools were employed to measure the variables. The investigator developed Mathematical Beliefs Inventory with the help of a supervising teacher. The study was conducted on a sample of 600 secondary school students of various schools of Kozhikode and Malappuram districts of Kerala state. The results of the study will enable the investigator to understand whether there exist any significant difference in Mathematical Beliefs, Achievement Motivation and Achievement in Mathematics among secondary school students for the selected sample with respect to gender and Socio Economic Status. It also helps to understand the main effect and interaction effect of Mathematical Beliefs and Achievement Motivation on Achievement in Mathematics of secondary school students. The investigator hopes the result derived from the study would be reliable, valid and dependable. It helps the teachers and curriculum developers to design the curriculum and plan teaching-learning of mathematics according to the mathematical beliefs and achievement motivation of the students. 
The investigator tried to make the study as successful as possible but certain limitations have crept to the study.
•	The sample selected for the study is not a state wide sample. Due to the time limitations, it was confined only to two districts of Kerala state. i.e, Kozhikode and Malappuram.
•	Only those students who follow Kerala state syllabus were considered. 
•	Only those students studying in studying in IX standard were considered as secondary school students.
•	Other variables which may have influence on Achievement in Mathematics was not considered.
Organization of the Report
The whole report is presented in five chapters.
Chapter I
The first chapter presents a brief introduction of the problem, need and significance of the study, statement of the problem, definition of key terms, variables of the study, objectives of the study, hypotheses of the study, methodology, scope and limitations of the study.
Chapter II
The second chapter gives a theoretical overview of Mathematical Beliefs and Achievement Motivation. It also provides the summary of related studies of Mathematical Beliefs, Achievement Motivation and Achievement in Mathematics.
Chapter III
The third chapter describes methodology of the study in detail with the description of variables, objectives, hypotheses, tools employed for data collection, sample selected, data collection procedure and statistical techniques used for the analysis.
Chapter IV
 The fourth chapter includes the details of the analysis of data and its discussion as per the objectives of the study.
Chapter V
The fifth chapter contains the description regarding the study in retrospect, major findings, conclusion, educational implications and suggestions for further research.