REVIEW OF RELATED LITERATURE
A literature review is a body of text that aims to review the critical point of current knowledge including substantive findings as well as a theoretical and methodological contribution to a particular topic.  Literature review is a search and evaluation of the available literature in our chosen topic area. Literature review helps the investigator to survey the literature in the chosen area of study as well as to synthesize the information into a summary.
It also helps the investigator to critically analyze the information gathered by identifying gaps in current knowledge by showing limitations of theories and point of view and by formulating area for further research and reviewing area of controversy. The  literature review seeks to describe, summarize, evaluate, clarify and/or integrate the content of primary reports (Cooper, 1989).The present  study is an attempt to understand the interaction effect of Mathematical Beliefs and Achievement Motivation on Achievement in Mathematics of secondary school students. The review of the literature was classified and presented in the following heads,
•	Theoretical Overview of Mathematical Beliefs
•	Theoretical Overview of Achievement Motivation
•	Studies Related to Mathematical Beliefs
•	Studies Related to Achievement Motivation
•	Studies Related to Achievement in Mathematics

Theoretical Overview of Mathematical Beliefs
	The theoretical framework of Mathematical Beliefs is outlined briefly in this section of the report.
Meaning of Mathematical Beliefs	
	In everyday language, the term “belief” is often used loosely and synonymously with terms such as attitude, disposition, philosophy and value. Because these various concepts are not directly observable and have to be inferred. Due to their overlapping nature, it is not easy to produce a precise definition of beliefs.  Beliefs about mathematics is a notion, which effects learning and teaching of students and thereby effects on the success of them directly or indirectly as having importance in mathematics teaching and learning process (Cobb, 1986; Kloosterman, 1991; Kloosterman & Cougan, 1994; Schoenfeld, 1989; Thompson, 1984). The research studies indicated that it is helpful to develop positive belief about mathematics and make sense of what has been learned about mathematics subjects in mathematics teaching (Cobb, 1986; Raymond, 1997; Thompson, 1992). Mathematical beliefs of students, which also determine the perspectives of students with regard to the mathematical world, have great importance for the mathematic applications as well. For example, if students believe that all of the mathematical problems would be solved within five minutes, then this situation has serious amount effect on the time they would allocate for a problem (Schoenfeld, 1992). Many researches that have been performed (Kloosterman, 1991; Kloosterman & Cougan, 1994; Thompson, 1984) have also put forward that the beliefs of students with regard to nature and education of mathematics have effect on their abilities of learning of the mathematics and their mathematics education.
Many researchers have tried to write a clear definition of mathematics beliefs, however, there is a large diversity in the terms used to describe students’ mathematical beliefs. Mathematical beliefs refers to student’s beliefs towards mathematics, belief on mathematical competency and belief about learning context which impacted mathematical performance. (Schuck & Grootenboer, 2004). Op’t Eynde and De Corte (2003) defines mathematics-related beliefs systems as the implicitly or explicitly held subjective conceptions students hold to be true about mathematics education, about themselves as mathematics learners, and about the mathematics class context. These beliefs determine in close interaction with each other and with student’s prior knowledge their mathematical learning and problem-solving activities in class.
 Schoenfeld (1989) states that mathematical beliefs are the ways that students’ conceptions about mathematics shape the ways that they engage in mathematical activities.  Kloosterman (1991) defined mathematics beliefs as the personal assumptions from which students make decisions about the actions they will undertake. These beliefs influence students’ actions in the classroom. Mathematics beliefs refer to the students’ feelings about mathematics, aspects of the classroom, or about themselves as learners of mathematics (Reyes, 1984).
Mathematical beliefs play an important role in enhancing the quality and effectiveness of the teaching and learning of mathematics (Adnan, Zakaria & Maat, 2012). Raymond (1997) notes that past school experiences, early family experiences and the teacher education program have the greatest effect on developing pre-service teachers’ mathematical beliefs. All teachers possess beliefs about their profession, their students, how learning takes place and the subject areas they teach, and their practices should flow from these beliefs . Thus, they transfer their own attitudes and beliefs to their students. As a result of their past experiences, pre-service teachers come to their education courses with deeply rooted anxieties and attitudes about mathematics.
Dimensions of Mathematical Beliefs
One theoretical framework of mathematical beliefs was developed by Grouws, Howald, and Colangelo (1996), which proposed seven dimensions of mathematical beliefs, which can be grouped into four categories: the nature of mathematical knowledge, the character of mathematical activity, the essence of learning mathematics, and the usefulness of mathematics. 
The nature of mathematical knowledge includes the composition, the structure, and the status of mathematical knowledge.  Mathematics might be viewed as isolated facts or as coherent concepts. The poles of this dimension are mathematics as a coherent system and mathematics as a collection of isolated pieces. Mathematics as a coherent system reflects the belief that as one does mathematics one finds meaningful connections between and among concepts,  principles  and skills. The belief is operationalized  by both acting on the above expectation and in resolving conflicts that arise.  In contrast,  mathematics as a collection of isolated pieces reflects the belief that mathematics consists of a variety of independent topics and skills,  thus losing or gaining one piece of information has little effect on the development of another. Conflict is often resolved by putting one's confidence in the most familiar and easily recalled knowledge. Not only are strands such as geometry and algebra considered separate, the roles of proof, construction and problem solving are independent as well. 
The character of mathematical activity consists of doing mathematics and validating ideas in mathematics.  Mathematical activity might be perceived as implementing procedures for results or as making sense of concepts. The poles of this dimension are mathematics as sense-making and mathematics as results. Mathematics as sense-making reflects the belief that the process of doing mathematics activity depends on valuing, exploring, comprehending, and expanding the concepts and principles underlying mathematics. Doing mathematics activity involves thinking and figuring things out. In contrast, mathematics as results reflects the belief that the process of doing mathematics is implementing procedures and finding results.  At most it is acknowledged that mathematicians created such procedures for specific uses and that they understand the underlying principles involved. Doing mathematics involves remembering and carefully following step-by-step procedures. In general, the predetermined existence of an algorithmic process for approaching a mathematical situation outweighs the value attributed to any intuitive insight the student might possess. 
The essence of learning mathematics refers to whether mathematics is to be memorized or is to be understood. The poles of this dimension are learning as constructing and understanding and learning as memorizing. Learning as constructing and understanding represents the belief that one creates new knowledge by fitting things with past experiences. The learner feels a need to be involved actively in experiences and resolve any conflicts with previous knowledge that arise. In contrast, learning as memorizing represents the belief that learning mathematics is a process of mentally storing what one has been taught; that is, the learner is a passive receiver who records existing knowledge. Learning well means to be able to quickly and accurately recall needed information. 
The usefulness of mathematics pertains to whether mathematics has value in everyday life. The poles of this dimension are mathematics as a useful endeavor and mathematics as a school subject with little value in everyday life of future work. Each dimension spans a continuum that ranges from what is described as naïve beliefs to sophisticated beliefs. The beliefs are regarded as relatively independent, so that individuals can possess both naïve and sophisticated beliefs simultaneously. The preceding dimensions are not necessarily independent and a strong position held on one dimension may predict a position on other dimensions. Nevertheless, it is helpful to consider each of these dimensions separately in identifying the range of important conceptions about mathematics. Each dimension has the potential to affect student learning and mathematical behavior.
Analyzing the connections between mathematics-related Op’t Eynde and De Corte’s (2003) proposed triangular model that breaks mathematics-related beliefs into three sub-categories: beliefs about the self (as a mathematics learner), beliefs about mathematics education  and beliefs about classroom context. Op’t Eynde and De Corte (2003) describes mathematics education beliefs as containing students’ beliefs about mathematics, about mathematical learning and problem solving, and their beliefs about mathematical teaching. Students’ beliefs about self refer to their intrinsic goal orientation beliefs related to mathematics,  extrinsic goal orientation beliefs, task value beliefs,  control beliefs  and self-efficacy beliefs.  Finally  classroom context beliefs include beliefs about the role and functioning of their teacher,  beliefs about the role and functioning of the students in their own class  and beliefs about the socio-mathematical norms and practices in their class.
Op’t Eynde and  De Corte (2003) included within this framework of beliefs are three different types of mathematics beliefs that are held by students.  These beliefs are beliefs about mathematics education, beliefs about the self, and beliefs about the social context. The first type of mathematics-related beliefs discussed is the students’ belief about mathematics education.  This refers to the beliefs that students have about the nature of mathematics (Op’t Eynde & De Corte, 2003).  For example, this would include students’ beliefs that mathematics is difficult or based on a set of rules.  It also contains the students’ perception of the usefulness of mathematics outside the classroom.   
The second type of belief that Op`t Eynde and De Corte.(2003) present is the students’ belief about the self.  Within this category, they include four subcategories, which are self-efficacy beliefs, control beliefs, task-value beliefs, and goal orientation beliefs.  Self-efficacy beliefs focus on the students’ perceived level of success and failure in learning mathematics (Pajares & Miller, 1994).  An example of this would be a student who is confident that he or she understands the difficult material within a specific mathematics unit (Op’t Eynd & De Corte, 2003).  
Control beliefs are the student’s beliefs that he or she can accomplish a certain task.  An example is a belief that if they study in appropriate ways, then they will be able to learn the material (Op’t Eynde & De Corte, 2003).  Task-value beliefs focus on the reasons why a student engages in learning and problem-solving.  An example of a task-value belief is the belief that it is important to learn the material in a mathematics class (Op’t Eynde & De Corte, 2003).  This would also include the belief that the student knows why it is important to learn mathematics. 
Goal orientation beliefs include the reasons why a student tries to succeed in a course. An example of a goal orientation belief is a student who believes the ultimate goal in a mathematics course is trying to understand the content as thoroughly as possible versus a student who believes the ultimate goal is to get a passing grade even if he or she doesn’t understand the course material (Op’t Eynde & De Corte, 2003). 
The third type of belief included in the definitions of students’ mathematics-related beliefs are the beliefs about the social context of the classroom (Op’t Eynde & De Corte, 2003).  These beliefs refer to the students’ views and perceptions of the classroom norms that guide teacher and student behavior in that specific classroom.  This type of belief includes the perceived social norms that exist in the classroom.  This would include the students’ beliefs about the role of the teacher and the role of the student in the mathematics classroom. The beliefs about aspects of classroom culture that relate to mathematics activity fall into this category.  An example of a belief about the social context would be the belief about what counts as an acceptable answer or explanation in their classroom. 
 	As mentioned above, there are three categories of mathematical beliefs that students may hold (Op’t Eynde & De Corte, 2003).  Within these three categories are many different sub categories of beliefs. These beliefs are the students’ beliefs about mathematics education and the students’ beliefs about the self in relation to doing mathematics. Students’ beliefs about mathematics education can reflect their opinion on what mathematics is like and how the student approaches mathematical problems and tasks (Op’t Eynde & De Corte, 2003).  For example, students often believe that mathematics problems only have one right answer and that there is only one way to solve those problems (Schoenfeld, 1992).  Some students believe that the only way to be successful in mathematics is to memorize the procedures and apply them mechanically and without conceptual understanding.  Often students believe that mathematics problems should be able to be solved in five minutes or less.  Another belief that students hold is that the mathematics learned in school has nothing to do with the mathematics used in the real world.   
Students’ beliefs about mathematics can affect the way in which they approach mathematics problems (Op’t Eynde & De Corte, 2003), and thus affect the transfer process that occurs during problem-solving.  For example, a student who views mathematics as a body of true facts and procedures to learn and apply will approach mathematics differently than the student who sees the subject grounded in problem-solving and meaning-making. The student who believes that mathematics is about memorizing procedures or formulas may begin the solution process by looking for a procedure or formula that will help them find the solution.  In contrast, the student who believes that mathematics is about solving the problem and sense-making may begin the solution process by identifying important quantities and relationships between quantities in the problem  and then devise multiple ways to solve the problem.  Because students’ mathematical beliefs can affect the problem-solving process,  it seems reasonable to conclude that students’ mathematical beliefs might also indirectly affect the transfer process, which takes place during problem-solving. 
According to Op’t Eynde and De Corte (2003)  the analysis of the nature and the structure of beliefs and belief systems points to the social context, the self and the object in the world that the beliefs relate to, as constitutive for the development and functioning of these systems. They suggest a triangular representation of students’ mathematics-related belief system. In other words, students’ mathematics-related belief systems are characterized by their beliefs about mathematics education, beliefs about self  and beliefs about the class context (Op’t Eynde & De Corte, 2003). The triangular model of students’ mathematics-related belief systems is given in Figure 1

Figure 1. Triangular model of students’ mathematics-related belief systems
McLeod (1992) categorizes student’s beliefs into four categories related to the object of belief: beliefs about mathematics, beliefs about self, beliefs about mathematics teaching, and beliefs about the context in which mathematics education occurs. The student’s cognitive actions are impacted by both consciously and unconsciously held beliefs about the task they are working on (mathematics), the social environment where the task is taking place (context), and the student’s self-perceptions in relation to the task (self).
Ernest (1991) outlined a developmental sequence of five different mathematics-related belief systems that are hypothesized to be found amongst teachers: authoritarian, utilitarian, mathematics centred, progressive, and socially aware. Ernest’s (1991) contribution showed that it is possible to relate these attitudinal representations to conceptions on the theory of mathematics, learning mathematics, teaching mathematics, and assessment in mathematics, as well as identifying beliefs on the aims of mathematics education. According to Ernest (1991), the most important of these categories is the teacher’s philosophy of mathematics, which might vary from absolutist to social-constructivist values. Teachers’ theories of learning and teaching are said to relate to approaches used in class and are fundamental because they define the teacher’s perception of the learner’s role as active or passive, dependent or autonomous, or as receiver or creator of knowledge. 
In turn, Kuhs and Ball (1986) characterised three different and dominant conceptions of the ideal teaching and learning of mathematics. The first is the learner-focused view that stresses the learner’s construction of mathematical knowledge through social interaction. The second is the content-focused view with an emphasis on conceptual understanding. The third is the content-focused approach with an emphasis on performance which values performance as the key goal whose attainment depends on the mastery of rules and procedures. Furthermore, Renne (1992) proposed a purpose of schooling/knowledge matrix to conceptualise four different teachers’ conceptions of teaching and learning mathematics. Two groups of teachers are identified in the purpose of schooling category, namely, school-knowledge oriented and child development oriented. Teachers within the school knowledge group believe that teaching is an act of passing information on to others while learning involves the process of reproducing that information. At the same time, school-knowledge oriented teachers place great emphasis on the syllabus and curricular guidelines to guide their instruction. In turn, child development oriented teachers are more likely to consider children’s needs and characteristics as the primary factors in instructional decision making. The second category in the matrix relates teachers’ beliefs to the way teachers perceive knowledge itself. School knowledge oriented teachers design activities that emphasise acquisition of knowledge in terms of “what” is going to be learned. As such, this type of knowledge is concerned more with rules, procedures, and drill. This type of knowledge is very fragmentary because it does not help the learner relate isolated pieces of knowledge to the whole framework. In contrast, child development oriented teachers are more concerned with learning of mathematical concepts within an interrelated knowledge structure that is holistic and meaningful. 
Measurement of Mathematical Beliefs
Hendy, Schorschinsky and Wade (2014) developed three psychometrically tested scales as guided by expectancy-value theory, self-efficacy theory, and health belief model. In this study they used a 5-point rating scale to indicate a variety of math beliefs. Factor analyses produced a 10-item Math Value Scale with 2 subscales (Class Devaluation, No Future Value), a 7-item single-dimension Math Confidence Scale, and an 11-item Math Barriers Scale with 2 subscales (Math Anxiety, Discouraging Words). Hierarchical multiple regression revealed that high levels of the newly discovered class devaluation belief (guided by expectancy-value theory) were most consistently associated with poor math behaviors in college students, with high math anxiety (guided by health belief model) and low math confidence (guided by self-efficacy theory) also found to be significant. 
Yuniarti and Pang (2014) conducted a study the relationship between mathematical beliefs and mathematics anxiety among pre service elementary school teachers in east borneo, Indonesia.The questionnaire used in this study consists of three sections. Section A presents sixteen items with five point Likert scales to investigate pre service elementary school teachers’ mathematical beliefs. The items were adopted from Mathematical Beliefs Questionnaire. Section B presents twenty seven items with five point Likert-scales to investigate the level of mathematics anxiety among pre service elementary school teachers. The items were adopted from the Revised-Mathematics Anxiety Survey. The last section of the questionnaire consists of five items to obtain the information about gender, age, ethnicity, year of study and secondary school major. 
Briley (2012) developed Mathematics Teaching Efficacy Beliefs Instrument (MTEBI) consists of 21 items, which are organized into two subscales: the Personal Mathematics Teaching Efficacy (PMTE) subscale and the Mathematics Teaching Outcome Expectancy (MTOE) subscale.  These subscales correspond to the two dimensions of teacher efficacy.  The PMTE subscale consists of 13 items that relate to a pre-service teacher’s belief in his or her capability to teach mathematics effectively.  The MTOE subscale includes 8 items that relate to a pre-service teacher’s belief that effective mathematics teaching can result in student learning.  The items are rated on a 5-point Likert-format scale ranging from Strongly Disagree (1) to Strongly Agree (5).  Higher scores on the PMTE subscale indicate stronger personal mathematics teaching efficacy, whereas higher scores on the MTOE subscale indicate greater expectations of student learning of mathematics.  The Cronbach alpha for scores pertaining to the entire MTEBI was 0.81.  The Cronbach alpha was 0.87 for the PMTE subscale scores and 0.67 for the MTOE subscale scores.
Zakaria and Musiran (2010) developed a Mathematical Beliefs Questionaire which contains 23 items.The participants’ responded to the Likert-type questions range from 1(including strong disargument) to 4 (indicating strong agreement). However for items 21 -23 the responses are 1 (not important) to 3 (very important). A higher score indicated a belief consistent with the constructivist approach.The Mathematical Beliefs Questionaire has three dimensions, beliefs about the nature of Mathematics, beliefs about teaching Mathematics, and beliefs about learning Mathematics.Cronbach alpha reliability index for beliefs about the nature of Mathematics is 0.74, beliefs about the learning of Mathematics is  0.71.
Theoretical Overview of Achievement Motivation
	This section deals with the theorectical overview of Achievement Motivation.
Meaning of Achievement Motivation
Motivation has become one of the major domain of psychology and  education. It is the stimulus to action resulting from an individual’s desire to reach established goals or purpose. Psychologists define motivation as an internal process that activates, guide and maintain behaviour overtime. Motivation may vary both on intensity and direction. Different psychologists have defined motivation in different ways.
Feather (1963) defined motivation as a relatively stable personality disposition which may have an innate basis but is more likely the product of early learning of approaching or avoiding stimuli.
The concept of motivation occupies a prominent place in many learning situations. In the modern world, the concerns for excellence in academic performance has increased more than ever before because of the ever increasing competitions as well as by the pressure put on the individual by the modern socio culture. The educational system that we have at present is an attempt to meet the requirements of the individual. But inspite of all our effort and educational input children are unable to show educational performance up to the level that is expected of their age or grade in the school. The reason may be many and varied.  But it has been observed that in addition to other factors there is usually a lack of sufficient motivation for the students, teachers, parents and other involved in the teaching learning process. The situation which evokes achievement motivation, the condition in which achievement behaviour will ensure all allied factors which effect both achievement motivation and achievement have become the fundamental issue in motivational and educational research studies.
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.  McClelland (1961) has emphasized that, for the motive to achieve to be aroused in performance awesome activity, the individual must consider himself responsible for the outcome (success or failure), there must be explicit knowledge of results so that the individual knows when he was succeeded and there must be some degree of risk concerning the possibility of success.
Achievement motivation is defined as the combination of psychological force which initiates, directs and sustains behaviour towards the successful attainment of some goals which provides a sense of significance (Good, 1973).
According to Mukherjee (1965), Achievement motivation is that behaviour which shows an effort to do one’s best; to do better than other or in general to accomplish something to one’s satisfaction.
According to Murray (1938), achievement motivation  referred 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 standard of excellence. It is conceived as desired to accomplish something difficult. The desire is accompanied by action, that is, the individual makes intense, prolonged and repeated effort to accomplish something difficult. According to Murray’s (1938) conception, personality is the idea of a hierarchy of configuration of basic psychogenic needs or motive. His view was that a need could be around from within by internal visceral processes or from without by the effect on the person of the immediate situation. He listed numerous needs, out of which need for affiliation, need for achievement, needs for nurturing, etc, have given more attention. The need energizes activity on the part of the organisms and maintains its activity to the organisms alters the unsatisfying situation.
Atkinson (1964) in his theory specified that achievement motivation is a special case of intrinsic motivation which differentiates out of the basic motivational propensity of need to feel component and self determining in relation to the environment. The motive for success is simply one’s need to match some standard of excellence.  Probability of success is one’s expectancy of achieving the goal and it is related to both a person’s ability difficulty of the task. According to him, there are basically two types of people and each will act in an achievement oriented fashion under different condition. They are the person for whom the need to achieve is greater than the fear of failure and person for whom the fear of failure is greater than the need to achieve. Each of the individuals is motivated by the desire to achieve certain pleasant affect, with the difference being that it for the former the pleasant is in achieving, where as for the later the pleasant affect is in avoiding the sense of failure.
Achievement motivation is referred to as the need for achievement. It is an important determinant of aspiration, effect and persistance will be evaluated in relation to the same standard of excellence. The factors of motivation and ability are the prime ingredients in academic and intellectual accomplishment. According to McClelland and Atkinson (1953), the goal of achievement oriented activity is to succeed to perform well in relation to a standard of excellence or in comparison with others who are competitors. Achievement Motivation is a high level of intellectual curiosity which differ in their strength of motive to active in various activities,  differ in the challenge they pose and the opportunity they offer. Thus both personality and the environmental factors must be considered in accounting for the strengths of motive to achieve in a particular challenge in a the particular situation.
Achievement Motivation Theory
Achievement motivation theory was put forward and refined by a group of researchers Murray (1938), Atkinson and McClelland (1961) over the years. According to this theory, an individual’s motivation to achieve something in life or the dire need to achieve a specific goal is governed by various internal factors such as willingness, determination, punctuality, personal drive along with numerous external factors (also known as environmental factors) such as pressures, expectations, targets, etc., set by relevant organizations, members of the family or the society. A person’s need to achieve something and the reason behind his/her overall motivation to achieve a certain goal, according to the Achievement Motivation Theory, more often than not, comes from within and is strongly related to the individuals need for power and affiliation. Achievement motivation theory is all about how the needs of an individual change over a period of time with changes in his experience. The theory also explains what effects an individual’s need for achievement, power, and affiliation have on their behavior. McClelland  and Atkinson (1953) has stated that every individual’s motivation is driven by the need of these factors, irrespective of age,  gender,  race or culture one belongs to. According to McClelland (1961) Achievement motivation consists of the following components. Components of Achievement Theory of Motivation presented in Table 1

Table 1
Components of Achievement Theory of Motivation
Sl. No.	Dominating factor (components) of motivation	Characteristic of the person	
1.	Achievement	•	Are high performers
•	Believe in excellence
•	Have a strong mind setting to accomplish the given 
     task
•	Calculates risk of the task beforehand
•	Demands regular feedback from the superiors.
•	Prefers working alone to group works
•	Appreciates accomplishment rather than rewards 
     (tangible or intangible)	
2.	Power	•	Have the desire to control and influence others
•	Are argumentative, competitive and assertive in nature
•	Enjoys status and recognition
•	Are likely to feel frustration under uncontrollable  
     situations	
3.	Affiliation	•	Desires to feel belongingness and relatedness
•	Seeks love, affection, and recognition
•	Are likely to agree on whatever his coworkers have to say
•	Fears rejection
•	Prefers collaboration to competition
•	Tends to avoid high risk and uncertainty
•	Prefers group works to working alone	

Many schools have developed mission statements that refer to educating students  so that they become life-long learners. The people who continue to learn throughout  their lives must actively make decisions and take actions to develop their education; that is,  they have no teachers handing out deadlines or grades.  It can be said that intrinsic motivation plays a vital part in an individual's choice to take on challenges and keep working on them until completion.  In order to develop adults with these characteristics,  teachers need to focus a large part of their teaching on developing this  important characteristic. This literature review addresses three areas related to intrinsic motivation. The first area discusses why intrinsic motivation is important  and describes the behaviors of intrinsically motivated individuals. The second area examines the development of the use of rewards in schools  and how rewards affect  intrinsic motivation and the achievement of students. The third area stresses  educational practices that are designed to promote intrinsic motivation. In addition, the differences in the treatment of children with learning disabilities is examined and discussed. 
	Teachers typically describe good students as hardworking,  interested, and   motivated (Spaulding, 1992).  Motivation is a word heard over and   over again as crucial to a child's learning and is often heard as being a major problem in schools today. Two types of motivation, intrinsic and extrinsic motivation, have been  identified by Deci (1971; 1972).  Deci describes an intrinsically motivated person as one who engages in an activity for the activity itself;  the reward being the activity.  A  child who cleans his room for the purpose of displaying his baseball card collection is  said to be intrinsically motivated.  Extrinsic motivation occurs when a person completes an activity because it leads to the receipt of an external reward.  A child who is promised a trip to the movies after cleaning his room is said to be extrinsically  motivated.  While the majority of rewards given in school can be thought of as extrinsic  motivators,  children learn the most when guided by intrinsic motivation.  Children  who are intrinsically motivated display a number of behaviors that allow them to  perform accordingly with their academic abilities  (Spaulding, 1992).  For example,  children who are intrinsically motivated become deeply involved in the task at hand and experience a feeling of enjoyment (Amabile and Gitomer, 1984) and seek out challenges with the intention of conquering them (Adelman and Taylor, 1990). According to DeCharms (1972),  an intrinsically motivated person feels that he can try  to produce a change in the environment, and feels confident that the change will  occur.  Children seen demonstrating these characteristics in the classroom would be characterized as motivated,  good students. Children with learning disabilities also benefit from intrinsic motivation.  These children tend to work longer and harder on tasks than extrinsically motivated children  with learning disabilities (Haywood, 1968)  and have been shown to establish critical internal systems of self-reward and mastery goals (Harter, 1978).  Children exhibiting  high levels of intrinsic motivation can achieve at levels that are higher than predicted  by psychological testing (Harter, 1983).  The development of intrinsic motivation is indeed crucial to the learning of children with and without learning disabilities.
Studies Related to Mathematical Beliefs
	Hughes, Auslander Stinson and Fortner (2019) investigated the relationships among practicing  elementary teachers’ (N = 153) beliefs about mathematics and its teaching and learning, mathematics anxiety and instructional practices in mathematics. The findings revealed that those with beliefs oriented towards a problem solving view of mathematics reported more standards – based teaching .  The findings also revealed that beliefs having the strogest relationship with practices than the mathematics anxitey.
	Prendergast,  Breen,  Bray,  Faulkner,  Carroll,  Quinn and Carr (2018) investigated  secondary students (n = 975) beliefs about mathematical problem solving. The analysis of data revealed that students who were further through their secondary education had a stronger belief that not all problems could be solved by applying routine procedures. In contrast, the same  students held less positive beliefs than their younger counterparts that they could solve time consuming problems and that conceptual understanding was important. The analysis also indicated that gender had a significant impact on belief in mathematical problem solving.
Ren and Smith (2018)  conducted a study on  teacher characteristics and contextual factors as links to early primary teachers’ mathematical beliefs and attitudes. The results of the study showed that the various teacher characteristics and contextual factors are related to early primary teachers' beliefs about mathematics teaching and learning and teachers' attitudes toward their own learning of mathematics. The sample of the study comprised of  396 early primary teachers . The results showed significant relationships between teachers' mathematical knowledge for teaching and teacher-centered beliefs, motivation in learning mathematics, and anxiety toward learning mathematics and the potential role of teachers' mathematical knowledge for teaching in improving teachers' mathematical beliefs and attitudes.
Zandra (2017) conducted  a study on connections between secondary mathematics teachers' beliefs and their selection of tasks for English language learner. The results indicated that the tasks teachers select impact students' opportunities to learn mathematics and teachers' beliefs influence their choice of tasks. Through the qualitative analysis of surveys, interviews and classroom artifacts from three secondary mathematics teacher. The findings suggested a need to critically examine the potential impact of seemingly benign teaching practices and the beliefs underlying them. 
Gafoor and Kurukkan (2016) analyzed secondary school students’ beliefs concerning mathematics and mathematis learning.The results of the study indicated that most of the students perceive mathematics as difficult and boring, possess beliefs like mathematics is not in their reach, only people with high intelligence can learn mathematics and also ability to learn the same is an inborn ability.
Kamalimoghaddam, Tarmizi, Ayub and Jaafar (2016) examined the direct and indirect effects of mathematics beliefs on mathematics achievement by mediating mathematics self-efficacy. The results showed that students who held strong beliefs on mathematics, had higher self-efficacy in mathematics and these led to high mathematics achievement. The study also indicated that students’ mathematics beliefs had a poor and no significant direct effect on their mathematics achievement.
Kang (2016) conducted a study on socio-mathematical norms and the teacher’s mathematical belief of Korean in-service elementary teacher.  The beliefs of the teacher regarding their students' learning in mathematics are an essential factor due to their importance in developing a desirable mathematics classroom culture. The purpose of this study is to find the relationship between the construction of socio-mathematical norms in classroom mathematical culture and teachers' beliefs. The results revealed that the mathematical belief of the elementary school teacher was reflected in the decision making for mathematics instruction, and greatly influenced the purpose, contents, and methods of the mathematics class, which contributed to creating socio-mathematical norms, or repeated patterns appearing between the teacher and students.            
Adams (2014) conducted a study on the effect of students' mathematical beliefs on knowledge transfer among 2000 junior high classroom students. The findings of this study showed that students’  beliefs about mathematics education had an effect on the general transfer process as a whole and on specific steps in the transfer process . It also showed that influence of the students’ self-efficacy’s on the transfer process is mediated by their  mathematics beliefs. 
Kristen (2014) developed a study on "The Effect of Students' Mathematical Beliefs on Knowledge Transfer". This study examined how students’ mathematical beliefs, specifically beliefs about mathematics education and selfefficacy, affect the transfer process. Data were collected from three middle school students. These data were collected through in-class observations, students’ written work  and student interviews. The analysis of this data has shown that students’ beliefs about mathematics education can affect specific steps in the transfer process as well as the transfer process in general. 
Yuniarti and  Pang (2014) examined the relationship between mathematical beliefs and mathematics anxiety among pre-service elementary school teachers in East Borneo, Indonesia.  The study was conducted on a sample of 374 elementary school teachers from the elementary school teacher education departments in public universities in East Borneo. The findings showed  that there is no significant relationship between beliefs about the nature of mathematics and mathematics anxiety and between beliefs about mathematics teaching and mathematics anxiety. Furthermore, there is a negative significant relationship between mathematical beliefs and mathematics anxiety among pre-service elementary school teachers when combining the dimensions of mathematical beliefs. In other words, a higher mathematical belief is associated with lower mathematics anxiety.
Haciomeroglu (2013) conducted a study on mathematics anxiety and mathematical beliefs: among elementary pre-service teachers. Three hundred-one pre-service teachers enrolled in the elementary teacher education program were administered two surveys to measure mathematics anxiety and mathematical beliefs. Results of the study revealed that there were significant differences between the third year and fourth-year pre-service teachers regarding their mathematics anxiety and mathematical beliefs. They held strong beliefs about teaching and learning mathematics that were aligned with the teacher education program. The results suggested that the pre-service teachers who held stronger beliefs and felt less anxious were more confident about their abilities to teach mathematics effectively. Thus, the significant relationship between mathematics anxiety and mathematical beliefs should be acknowledged.
Saran  and Gujarati (2012) explored how preservice elementary teachers change their negative beliefs toward mathematics into positive ones after taking a mathematics methods course that follows the concrete-pictorial-abstract (CPA) instructional method. It is also explored that the  relationship between those beliefs and sociomathematical authority, by administering surveys, using reflective narratives  and informally interviewing 145 preservice teachers who are preparing to work in urban classrooms during two academic years. The study investigated changes in sociomathematical beliefs and mathematical identities. Findings of the study  revealed that most of the preservice teachers changed their mathematical identities and beliefs about teaching mathematics in positive ways to be more in accordance with reform-oriented practices. 
Stiegelmeyer  (2012) conducted a study on  the relationship between mathematical knowledge of numbers and operations and mathematics beliefs of prospective  teachers. This study surveyed 82 preservice elementary teachers using items from an instrument designed to predict student achievement based on a teacher's mathematics knowledge for teaching (MKT) in numbers and operations concepts.There is  no relationship was found between the number of MKT items answered correctly and math mythsand a  weak, negative correlation was found between participants' numbers and operations survey section scores and math anxiety. Preservice elementary teachers who reported higher math anxiety levels had lower scores on the numbers and operations survey section. 
Briley (2012) conducted a study on the relationships among mathematics teaching efficacy, mathematics self-efficacy, and mathematical beliefs for elementary pre-service teachers. The results indicated that the  pre-service teachers who reported stronger beliefs in their capabilities to teach mathematics effectively were more likely to possess more sophisticated beliefs as well as were more likely to have more confidence in solving mathematics problems. Mathematical beliefs also had a statistically significant effect on mathematics teaching efficacy and on mathematics self- efficacy. Thus, the significant relationship between mathematical beliefs and mathematics teaching efficacy should be acknowledged by mathematics teacher educators. 
Zakaria and Musiran (2010) conducted a study on beliefs about the nature of mathematics, mathematics teaching and learning among trainee teachers. The participants of the study were 100 trainee teachers. The findings of the study indicated that the beliefs of trainee teachers about the nature of mathematics, mathematics teaching and learning are positive. i.e., towards constructivism approach.
	Physick (2010) conducted a study on exploring mathematics-related belief systems. The purpose of study  is to explore student’s mathematics-related beliefs systems and the use of a mathematics-related belief questionnaire (MRBQ) to measure such systems. 73 students from three Mathematics XI classes are used as subjects for the study. The result of the study support the existence of three subcategories of mathematics-related beliefs that include beliefs about self, mathematics the object, and the context in which they learn mathematics. An analysis of the correlations among the factors suggests a core set of beliefs with strong interconnections that might be used to categorize student’s mathematical dispositions and which may be connected to achievement in mathematics.
	Tarmizi and Tarmizi (2010) conducted a study on analysis of mathematical beliefs of Malaysian secondary school students. The study focused on the affective issues related to mathematics learning and instruction and specifically on mathematical beliefs, attitudes or values. 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, to name a few. The purpose of this study was to examine mathematics-related beliefs of secondary school students namely, students' beliefs in their mathematical competency and students beliefs on their mathematics teachers attribute in mathematics teaching. A total of 430 secondary students participated in the survey. Findings indicated an overall significant effect on students' beliefs in mathematical competency, with three significant predictors namely, students' beliefs on teachers attribute to mathematics teaching, grades in mathematics and gender.
Briley, Thompson and Iran-nejad (2009) conducted a study on  mathematical beliefs, self-regulation  and achievement by University students in remedial mathematics courses. Research in the Schools among ninety-four students completed 2 surveys to measure mathematical beliefs and active,  dynamic and multiple-source self-regulation. The  findings of the study revealed  that the relationship between achievement, either in mathematics or in academics in general, and both sophisticated mathematical beliefs and multiple-source self-regulation.
Mason and Scrivani (2004) conducted a study on enhancing students' mathematical beliefs: which aimed at ascertaining students' beliefs about mathematics and mathematical learning, as well as developing those beliefs and related variables by changing the classroom learning environment. Eighty-six fifth graders were involved, divided into two groups: one in the innovative learning environment (N=46) and the other in the traditional (N=40). The findings provided  evidence that the intervention contributed more than traditional teaching to developing students' mathematical beliefs, as well as to improve their performance in solving usual and unusual word problems.
Studies Related to Achievement Motivation
	Rani and Reddy (2019) examined the gender related differences and differences across academic majors on achievement motivation among adolescent students (n = 80). The results of the study indicated that significant difference exist between the achievement motivation of sciences and arts stream students and achievement motivation among male and female college students.
Kholisiyah,  Rukayah and Indriayu (2018) conducted a study on   achievement motivation  analysis of  outstanding students in learning writing at primary schools. This study aimed to describe achievement motivation on outstanding students in learning to write at the fifth-grade primary schools students. The research method used is descriptive qualitative. Subjects in this study were 18 achieving students. The data were collected through questionnaire,  interview  and observation. The results of this study indicated that the achievement motivation on outstanding students in learning writing is good, this happens because of several factors that support outstanding students in learning writing have good achievement motivation.
      	Ramaprabou and  Dash (2018) conducted a study on the effect of academic stress on achievement motivation among college students, to find out the effect of academic stress on achievement motivation of college students. 50 college students of various professional, arts and science colleges functioning in and around Puducherry were approached at random to collect data using a purposive sampling method. The findings revealed that moderate stress leads to high achievement motivation. 
Adegboyega (2018) conducted a study on the influence of achievement motivation on Nigerian undergraduates' attitude towards examination. This study investigated the influence of achievement motivation on Nigerian undergraduates' attitude towards examination. A descriptive survey of the correlational type was employed for the study. One thousand, five hundred and thirty-six (1,536) undergraduates in Nigeria were drawn using purposive and stratified sampling techniques. Achievement Motivation Scale (AMS) and Attitude Towards Examination Scale  (ATES) were the instruments used to collect relevant data. The findings revealed that the majority of Nigerian undergraduates have a high level of achievement motivation and  also revealed that majority of Nigerian undergraduates have a positive attitude towards examination. The findings also revealed that gender, age, level of study, university and family type had a significant positive influence on undergraduates' achievement motivation and attitude towards examination in Nigeria. 
        	Yilmaz and  Kaygin (2018) conducted  a study on the relationship between lifelong learning tendency and achievement motivation.  The aim of the study was to reveal the relationship between lifelong learning tendency and achievement motivation. The sample for the study consisted of 570 prospective teachers attending a pedagogical formation course at two universities in Turkey in 2016. Relational screening model was used in the study and the data were collected through Achievement Focused Motivation Scale and Lifelong Learning Tendency Scale. The findings indicated that, there is a low, positive correlation between prospective teachers' achievement motivation and lifelong learning tendency.  As for the correlation between lifelong learning tendency and the sub-dimensions of achievement motivation, lifelong learning tendency has a significant correlation with the expansion of objective,  self-consciousness  and internal effect . 
Turki,  Jdaitawi  and Sheta  (2018) conducted a study on fostering positive adjustment behavior in relation to  social connectedness, achievement motivation and emotional-social learning among male and female university students. This study analyzed the differences in achievement motivation and emotional-social learning levels between the genders. The sample comprised of 240 university students, both male and female.  Findings of  the study revealed that  the relationship between the study variables does not significantly differ between genders. Emotional-social learning is significant in terms of predicting the adjustment. Furthermore, gender differences were noted in terms of emotional-social learning levels, but not in terms of achievement motivation and social connectedness. 
Asrat (2017)  studied the relationship between students' attitudes towards school,  values of education,  achievement motivation and academic achievement in Gondar secondary schools,  Ethiopia.  The sample consisted of 362 students selected by using a systematic sampling technique were taken from grade 9 students. The results of the study revealed that the  that principals, supervisors,  teachers,  parents and educational practitioners should give attention to students' attitude towards school, values of education and achievement motivation in secondary schools and during instruction besides the cognitive factors. The result is that students’ attitudes towards school, values of education and achievement motivation were positive and significant in secondary school students.
 	Han and Lu (2017) conducted a study on correlation among achievement motivation, goal-setting and L2 learning strategy in EFL context. The results showed that compensation and metacognitive strategies are reported as being used the most frequently, followed by cognitive and effective strategies, while the three least frequently used individual strategies involve  use words differently, start L2 conversation, and ask for native's help. Concerning the relationship between achievement motivation and strategy use, the motive to achieve success (Ms) is positively and significantly correlated with four of the six types of learning strategies, i.e. cognitive, metacognitive, affective and social strategies.
	Indira and Kumar (2016) analyzed the career maturity and achievement motivation among higher secondary school students with hearing impairment. The results revealed that majority of the higher secondary school students with hearing impairment had average level of achievement motivation and career maturity. The results also indicated that there exists no significant difference between boys and girls in the level of achievement motivation.
	Yan (2016) conducted a study on a study on the relationship between college students' boredom tendency and attribution style as well as achievement motivation. Results of the study showed that the boredom tendency is closely related to the attribution style and achievement motivation, and plays a partial mediating role in the relationship between attribution style and achievement motivation.
Dewia, Bundua and Tahmira (2016) conducted a study on the influence of the antecedent variable on the teachers' performance through achievement motivation in senior high schools. It was quantitative research with 130 respondents using Structural Equation Model Analysis AMOS 18. The study found that the antecedent variable in the form of emotional intelligence and competence had a positive and significant effect directly on teacher performance and the teachers' competence becomes important in supporting the teaching profession and providing convenience for teachers in the teaching and learning process effectively to improve the performance of teachers through achievement motivation.
Arundhati, Setyosari, Susilo  and  Sihkabuden (2016) conducted a study on the influence of strategy of learning and achievement motivation of learning achievement class VIII students of state junior high school. The instrument used in this study was two-fold instruments to measure moderator variable (achievement motivation) and instruments to measure the dependent variable (the learning achievement). The findings revealed  that there is a difference of learning achievement between groups of learners that learned with problem-based learning strategy with a group of learners that learned with the learning strategy discussions. There is a difference in learning achievement between groups of learners who have high achievement motivation with a group of learners who have low achievement motivation. There is an interaction between the two strategies using problem-based learning and discussion, as well as achievement motivation on learning achievement.
Sarangi (2015) conducted a study on achievement motivation of the high school students. The sample of 200 students, studying in class IX of ten government high schools of Goalpara District of Assam was used. It was found that there was no significant difference between tribal-non tribal and boy-girl students but urban students have shown high achievement motivation than the rural students and the relationship between achievement motivation and academic achievement, it was observed that there was no significant relationship between achievement motivation and academic achievement of tribal, boy and rural students but there was a significant relationship between the achievement motivation and academic achievement of non-tribal, girl and urban students.
              Ebadi and Shakoorzadeh (2015) investigated the academic procrastination prevalence and its relationship with academic self-regulation and achievement motivation among high-school students in Tehran City. The sample included 624 high school students (312 Boys & 312 Girls) from different areas and regions that selected using random cluster-multistage sampling method. Procrastination Assessment Scale-Student, Self-Regulated Learning Strategies questionnaire and Achievement Motivation Test  were used in this study. The results of academic procrastination prevalence using descriptive statistic showed that over half of students nearly always or always procrastinate. The results also showed that boys and girls procrastinate at the same rate, in general and boys more than girls procrastinate only on preparing academic tasks. The results  of regression analysis  showed that academic self-regulation and achievement motivation predict academic procrastination significantly.
 	Yaman, Dundar and Ayvaz (2015) conducted a study on  achievement motivation of primary mathematics education teacher candidates according to their cognitive styles and motivation styles. The results  revealed  that  there exists significant relation between achievement motivations of teacher candidates according to their cognitive styles and motivation styles or not. Both comparative and correlational survey methods were used to determine cognitive styles, motivation styles and achievement motivation of the teacher candidates and to investigate the relationship between these variables. Findings also revealed that achievement motivations of the teacher candidates did not differ significantly in terms of gender and cognitive styles. 
	Jung (2015) investigated the relationships between ethnically diverse US high school students' (N=331) perceptions of their parents' or classroom's motivating factors and their achievement motivation in their math class, connecting achievement goal orientation and self-determination theories. An additional hypothesis was supported that students with different ethnic backgrounds (i.e., students of European, Asian, and Latino descent) differed in how their perceptions of their parents' motivating variables were related to their own achievement motivations, but not the relationships between students' self-regulated motivations and achievement goal orientations. 
Albion (2013) explored  level of social adaptation and its relationship with the achievement motivation of the secondary school students in Jordan. The  sample consisted of 495 secondary school students in the province of Jerash. The results, indicated  that the level of social adaptation and achievement motivation among secondary school students in the province of Jerash were high, and also showed the presence of a statistically significant positive relationship between the social adaptation and the achievement motivation among the secondary school students in the province of Jerash too.
Studies Related to Achievement in Mathematics
Nalline and Arthur (2019) explored  the effects of metacognitive strategies and content-specific feedback on student achievement in high school mathematics. Participants consisted of a convenience sample of students in honors geometry. For both the posttest and retention test, students in the experimental group significantly out performed the students in the comparison group. 
	Lawrence, Arul and Saileella (2019) conducted a study on self-regulation of higher secondary students in relation to achievement in mathematics. A sample of 300 first year higher secondary students studying during the academic year 2018-19 was selected by using simple random sampling technique from Tirunelveli district, Tamil Nadu. Data were collected with the help of Self-Regulation Scale constructed by Saileela (2013). The findings showed that there is a positive relationship between self-regulation and achievement in mathematics of higher secondary students.
A meta analysis conducted by Turgut  and  Turgut (2018) on  the effects of cooperative learning on mathematics achievement in Turkey. The result  revealed that the effects of cooperative learning on mathematics achievement is moderate and positive.
 	Ugo and Obasi (2018) studied the predicting growth rate of students' achievement in mathematics using mathematical growth model. The results indicated that the  Students' mathematics achievements in secondary school have an influential effect on their performance in university and their future careers. The results also  indicated  that the predicted growth rate of students' achievement in mathematics is approximately increased by 25.3% per year. This showed  a weak upward trend in the predicted rate of achievement at credit level and consequently indicated unsteady sustainability in mathematics achievement as well as economic growth. It is recommended among others that there should be an investigation into factors responsible for the weak and unsteady achievement growth in WAEC general mathematics in Nigeria. 
Faisal and Jasmine (2018) conducted a study on linking homework to achievement in mathematics of 8th-grade Arab students. Results of analysis showed that the majority of Arab students spend less time doing homework (less than 60 minutes) and do not need to take homework every day to strengthen their knowledge and get better scores in mathematics. Two-level analyses revealed that different associations were seen in most of the Arab students  between homework time, homework frequency, computer use, and internet use in doing homework with achievement in mathematics. 
The study conducted by Ching, Jinxin and  Cecilia (2017) explored  the cross-lagged association of achievements in mathematics and languages. The sample comprised 48,547 third-grade, unbalanced bilingual students who were measured three times over six years: in 2007 (in Grade 3), 2010 (Grade 6) and 2013 (Grade 9). The multilevel cross-lagged analysis found prior achievement in a subject was the strongest predictor of achievement in that subject three years later. Furthermore, the cross-subject bidirectional prediction was found among achievements in mathematics, Chinese language, and English language for students from Grade 3 to Grade 6 and from Grade 6 to Grade 9.
Geethanjali and Jibi (2016) explored the relationship between attitude towards mathematics and achievement in mathematics of high school students of malappuram districts.The results of the study revealed that the relationship between attitude towards mathematics and achievement in mathematics of high school students is significant, high and positive. The results also showed that girls shows more achievement in mathematics than boys.
Oyegok, Oyelabi and  Nnaji (2016) conducted a study on mathemaphobia and teaching learning materials as correlates of pupils achievement in mathematics. Correlation design was adopted in the study. The study conducted among 1,080 students and 48 mathematics teachers who were randomly selected. Three instruments (Students Mathemaphobia Questionnaires (SMQ), Teaching-learning Materials Inventory (TMI) and Mathematics Achievement Test) were used for data collection. The results of the study showed a linear relationship between the predictors and the criterion. The combination of predictor variables and students achievement in basic mathematics yielded multiple correlations of 0.574 with students' achievement in basic mathematics.
Alordiah, Akpadaka and Oviogbodu (2015) investigated the influence of gender, school location, and socio-economic status (SES) on students' academic achievement in mathematics. The study was an ex-post factor design in which the variables were not manipulated nor controlled. The results of the study showed that students have an average achievement in mathematics. The result also showed that male students performed better than female students, urban students performed better than rural students and students of parents with high SES performed better than students of parents with low SES. One of the recommendations was that teachers should put into consideration the disparities that exist between male/female, urban/rural, and low SES/high SES when teaching mathematics.
Vivian and Yukiko (2015) conducted a study to understanding student achievement in mathematics and science among  Trinidad and Tobago students. Findings revealed that schools account for a substantial amount of variation in students' mathematics and science performances. School socio economic status (SES) had a significant effect on student achievement and suggest the important role of school context in understanding student performance in Trinidad and Tobago and the Caribbean.
The study conducted by Ajai and  Imoko (2015) assessed gender differences in mathematics achievement and retention by using Problem-Based Learning (PBL). The results  revealed that male and female students taught algebra using PBL did not significantly differ in achievement and retention scores, thereby revealing that male and female students are capable of competing and collaborating in mathematics. The finding showed that performance is a function of orientation, not gender. The study recommended the use of PBL by mathematics teachers to overcome the male image of mathematics and enhance students’ (male and female) achievement and retention.
Enu, Danso and  Awortwe (2015) conducted a study  to  find out whether group size has any effects on students’ mathematics achievement in small group settings. Two third year classes of the 2011 / 2012 academic year were selected from two schools in the Central Region of Ghana for the study. The two classes constituted the control and experimental groups respectively and consisted of 50 students in the control group and 47 in the experimental group. The results of the study showed no significant difference in the mean scores of mathematics achievement among the three subgroups of the experimental group.
Ebrahim and Ahmadreza (2015) conducted a study on mathematics achievement in high- and low-achieving secondary school students. Two-level hierarchical linear modelling was applied in this study. The results indicated that of the total variance in mathematics achievement, were due to school differences in the high- and low-achieving schools, respectively. Controlling for the school-level factors, the better-performing students were those with a higher level of confidence in learning mathematics in both samples. After controlling for the student-level factors, inadequacies in school resources and school type yielded the strongest link to achievement in the high- and low-achieving schools, respectively.
	Awofala (2014) investigated the effect of a personalised print-based instruction versus a non-personalised print-based instruction on the attitudes toward mathematics word problems of 350 senior secondary school students .The Attitudes toward Mathematics Word Problem Inventory (ATMWPI) and Achievement in Mathematics Word Problem Test (AMWPT) were used to collect data relating to the dependent measures. The results of the data analyses showed that the personalised instruction students had higher levels of self-confidence, liking, usefulness, and motivation but recorded low level of anxiety regarding mathematics word problems compared with the non-personalised group students.                     
Battey and Leyva (2013) examined how teacher-student relational interactions affect students’ mathematics achievement and learning. The study found that relational interactions explained a significant portion of the variance in mathematics achievement was when  controlling for prior achievement. The author recommended reconceptualization of mathematics instruction as both an academic and social mechanism affecting equitable opportunities. 
Conclusion
The review of related studies helped the investigator to gather extensive information and gave a wide perception of the present problem. It is evident that most of the research studies in mathematical beliefs are done outside the country. Few numbers of studies of mathematical beliefs are conducted in the Kerala context. The review of related studies revealed that mathematical beliefs have a prominent role in students learning.  A number of studies related to achievement in mathematics and achievement motivation are done in the Kerala context, but no one had dealt with the study on interaction effect of mathematical beliefs and achievement motivation on achievement in mathematics of secondary school students in Kerala. Many of the studies are related to teacher’s mathematical beliefs.  Most of other studies are correlate with mathematical belief, mathematical anxiety, self efficacy etc. Hence the investigator felt that it was worthwhile to undertake  a study to analyze the interaction effect of Mathematical Beliefs and Achievement Motivation on Achievement in Mathematics of Secondary School Students.