Attitudes and believes towards mathematics are influenced by instructional practice. Research in various institutions has revealed that learners tend to develop their attitudes and believes about mathematics with the way their teachers present the information to them in the classroom. This can be looked at from different perspectives. First of all, it is important to note that the beliefs and attitudes of the teacher towards mathematics would often determine the kind of approach or action taken by the teacher in the classroom. Morrisey (2006).
Studies that have been undertaken on pre-service teachers indicate that teachers act as important mediators between the knowledge and the learners. Their conceptions about mathematics would therefore influence the effectiveness of their instructional practice in the classroom situation. Researchers have expressed mixed reactions concerning the relationship between beliefs and instructional practice but there is a general agreement amongst the majority that indeed action towards mathematics in the classroom is influenced by the attitude and believes of the system of the teacher.
It has been found through research that teachers who hold the position that mathematics should be absolute often utilize a teacher-centered instructional approach in their instructional practice. Such teachers would teach mathematics as a set of universal rules that ought to be memorized by the learners. In their instruction, such teachers would deliver mathematics in the classroom as a linear entity where numerical data is played with using pen and paper. Their objectives mainly focus on making the learners master the content in mathematics. (Cooney et al, 1998)
As indicated by Morrisey(2006),the constructivists on the other hand would tend to adopt a strategy towards enhancing teacher- student interaction in the classroom environment. With such a strategy in the classroom, the mathematics teacher resides around and makes sure that the students fully participate in the acquisition of mathematical knowledge. Problem solving tends to be emphasized by the teachers who holds the belief that mathematics should be constructive. Most of their action in class revolves around certain problems with which the learners are expected to use reasoning and critical thinking skills to come up with solutions.
Findings from studies in various countries have indicated that the instructional practice of the teacher is often a combination of educational trends, personal constructions and believes and attitudes towards mathematics. Studies that were carried out in Singapore mention that majority of teachers were conscious about their attitudes and believes about mathematics and that the conceptions influenced the way they taught mathematics in the classroom. The effectiveness of instructional practice in class is largely dependent on the beliefs and attitudes of the teacher towards mathematics. (Cooney et al, 1998)
The relation between achievement and beliefs towards mathematics
Believes about mathematics influence the achievement in this subject. From a preservice teacher’s perspective, the level of achievement in mathematics is often related to what an individual believes. Low achievement in some student teachers has often been characterized by feeling that mathematics is a difficult subject. (Cooney et al, 1998)
The beliefs of the teachers towards mathematics have a lot to do with the way they understand the mathematical concepts. This would in turn affect their achievements especially is the mathematics tests. Research has also indicated that believes affect the way the teachers would present their content in the classroom. The way the content is presented in classroom is of great important to achievement in terms of the learning objectives. (Wilkins, 2008)Teachers who hold strong beliefs about mathematics tend to achieve their objectives because they use the best approach in delivering the content to the learners.
Conceptions about mathematics begin in the early schooling years. This is marked with disparities between students in terms of low and high achievers in mathematics tests. In studies that have been carried out both in middle and high schools, results have revealed that those students who achieve highly believe that mathematics is a useful subject. On the contrary the low achievers do not have a belief that mathematics is a valuable subject.
Research on the beliefs of student teachers has demonstrated that prospective primary school teachers have beliefs about mathematics that prevent them from teaching children using the correct approaches that can empower them. This can therefore be seen to be undermining the achievement of these teachers in their classrooms. Indeed investigations on classroom behavior have shown beliefs to be contributing significantly and they do affect achievement in the objectives. ( Goulding, 2007).
Negative beliefs about mathematics can be blamed for the poor teaching strategies in classroom situation and consequently the resultant poor results amongst the students. Researchers have therefore concluded that competency and achievement in mathematics are positively correlated with beliefs about mathematics by pre service teachers.
Past experiences and their influence on attitudes towards mathematics
Past experiences have a lot of contribution towards attitudes about mathematics. As it has already been noted, attitudes about mathematics begin in the early years. Research in schools has indicated the existence of students who have positive attitude, those who are neutral and those who have negative attitude towards mathematics. Mathematics seems to be unfriendly to those who have negative attitudes while those with positive attitudes enjoy the subject and even carry it own in future. (Wilkins, 2008)Research studies have indicated that the attitudes about mathematics are carried out by students as they enter teacher training programs.
Negative attitudes towards mathematics have proved to be resistant to change according to experts and they find their way in the classroom as the teachers are posted to their respective schools. Findings on pre-service teachers beliefs have revealed that majority of the student teachers enter teacher training programs with pre-existing belief systems about mathematics. This can be attributed to their past experiences in high school with their teachers and the environment. Research has also established that students who faced difficulties in the process of learning mathematics often have negative attitudes towards the subject even if it is introduced in a different form. Raymond, (1997).
Such people in future end up with the attitude that mathematics is not as useful as other subjects such as art. Quite often those with negative attitude towards mathematics have the opinion that they were not talented and may be that was the reason behind their failure in mathematics during their high school times. Most researchers have considered attitudes about mathematics to have been learnt. In this regard therefore it can be argued that past experiences play a significant role in the learning of the attitudes about mathematics.
Therefore whether a person has a positive or negative attitude towards mathematics, this is influenced by the type of experience he or she was subjected to during the early and middle years of school. The experiences people go through in the early schooling years are later manifested in future in form of beliefs and attitudes towards mathematics. (Ruffell et al ,1998)
Self esteem and the influence on attitude
The attitude held by an individual is as a result of a combination of factors that come into play as an individual goes through various experiences. An individual’s personality can be reflected in the self esteem. Self esteem is therefore a very important component that contributes towards self attitudes. Research studies have indicated that individuals having low self esteem often end up with negative attitudes towards some things in life.
According to Ozgun-Koca et al (2006),having a negative attitude towards mathematics can result from a student having low self esteem. In such situations even when tasks in mathematics might be easier, the mere fact that the students considers him or herself not to be competent compared top others, can translate itself in having a negative attitude towards the subject. It has been found that most of the low archivers in mathematics lack confidence in themselves and hence their low self esteem. On the other hand, people with high self esteem have adequate confidence to encounter and conquer various challenges in life. They therefore would have positive attitude towards learning mathematics. (Morrisey, 2006).
Research has indicated that as individuals grow there can be suststancial change in attitude towards some things in life. In early stages of schooling some individual have low self esteem but as they grow up they overcome it and end up with high self esteem. This change is also reflected in their attitudes especially to subjects such as mathematics. Going through failure experiences can also result in low self esteem in an individual. This can in turn influence the attitude of the concerned individual towards mathematics. Marzano, (2009).
In most cases people who have continued to experience failure in mathematical test would tend to develop low self esteem and can consequently have a negative attitude towards mathematics. Pre service teachers who fail in mathematical tests and have esteem related disorders can have problems with their attitude towards teaching mathematics. Low self esteem can therefore be blamed fro the negative attitudes in some teachers and hence their failure to achieve the required impact on their learners in the classroom. An individual’s self esteem is therefore an important components that determines the type of attitude towards the learning and teaching of mathematics. (Wilkins, 2008)
Lack of knowledge and attitude
A person’s lack of knowledge has a lot to do with the attitude towards mathematics and life in general. It is common knowledge that life has things that we all look forward to having or seeing in future. Without such motivation life would not be worth and perhaps people would not be waiting for the future. People have a desire to wait for the future because of the knowledge they have acquired and have. It is the knowledge that has shaped their attitudes towards some things in life. Morrisey, 2006).
On the other hand people without knowledge of some things would tend not to have specified attitudes based on their lack of knowledge on the reality in the things they are exposed to. Research on knowledge and individual attitudes has revealed that people who have adequate knowledge about some subjects such as mathematics have a positive attitude. On the other hand those with little knowledge about mathematics especially those who are in middle and high school level have negative attitudes towards mathematics. (Goulding, 2007)
According to Marzano,(2009) ,lack of knowledge can be viewed as an obstacle towards discovering the truth and reality about a phenomenon. In this light, the lack of knowledge in mathematics can be considered to be a hindrance towards understanding how simple and manageable the subject is. People who lack knowledge in mathematics can be said to be in the dark in as far as the simplicity of the subject is concerned.
Research has indicated that students tend to have negative attitudes towards mathematics because of their lack of knowledge. On the part of preservice teachers, it is also worth noting that teachers who are not trained might find it difficult to effectively teach mathematics in class. Consequently they might also develop negative perceptions and attitudes towards mathematics. This can all be attributed to their lack of adequate knowledge in the subject area.
All in all it is important to mention that owning wide knowledge about mathematics is very important of preservice teacher training. This is important in the sense that teachers aught to have adequate knowledge in the subject area so that they can impart positively in terms of attitudes to the learners. (Goulding, 2007)
Learners require a good foundation in terms of knowledge to develop positive attitudes about mathematics. If the teachers do not meet the knowledge demands then they are likely to be challenged by the bright ones who have positive attitudes while the low achievers develop negative attitudes towards the subject. The attitude of an individual towards mathematics can therefore be said to be a reflection of the state or level of knowledge in his or her passion.( Morrisey, 2006).
The relation between attitude and belief
According to Morrisey, (2006), beliefs refer to the expression of knowledge or opinion about a given subject in life. People hold different believes on mathematics based on their understanding or experiences they have gone through in the course of interacting with the subject. Attitude refers to the conceptions that people show towards different subjects in life. Attitudes have been known to be acquired through the learning process and they often lead to an action by the concerned people. Attitudes can either be positive or negative towards a given subject like the case of mathematics. (Wilkins, 2008)
Attitudes have a relation with beliefs in the sense that attitude often follow believes of people. If an individual believes that mathematics is an easy subject, this is followed by developing a positive attitude towards mathematics. On the other hand when an individual holds the belief that mathematics is difficult and needs a talent, then what follows is the development of a negative attitude towards mathematics.
In the light of this therefore one can conclude that beliefs and attitudes are closely related as they follow one another in the behavior of people. Ozgun-Koca et al (2006).Beliefs and attitudes all function to influence the behavior of people towards the subject in question. When pre service teachers hold beliefs and attitudes towards mathematics, their behavior is greatly influenced by the two components.
These two aspects are all dependent on the knowledge of the person concerned. It is through knowledge about the subject that an individual can develop beliefs and attitudes towards the subject. Beliefs and attitudes are also influenced by the environment in which an individual would find him or herself and the experience that result which leads to a specific behavior towards the subject. Beliefs and attitudes especially concerning mathematics can be said to be closely related because they determine the behavior of both teacher and learner. (Morrisey, 2006)
In conclusion it is fundamental to state that attitudes and beliefs are a very essential part of teaching and learning mathematics. Teachers acquire beliefs and attitudes towards mathematics from their experiences during school and in the teacher training programs.
The attitudes and beliefs held by preservice teachers have an impact on the achievement especially of the children they teach in class. Through the knowledge they gain in the course of their studies, the teachers can develop their attitudes towards mathematics which tend to influence their behavior towards the subject. Knowledge plays a very significant role in determining the beliefs and attitudes of individuals towards mathematics as a subject. The preservice teachers aught to have positive attitudes towards mathematics to be effective in their instructional practice in class.
The mode of instruction in the classroom setting has a lot of influence on the attitude and behavior of learners towards mathematics. Beliefs and attitudes go hand in hand and influence the behavior of both teachers and students towards mathematics. Therefore the right attitudes and beliefs should be cultivated by the preservice teachers to ensure that they have a positive impact on the learners by empowering them.
Cooney, T. J., Shealy, B. E., & Arvold, B. (1998). Conceptualizing Belief Structures of Preservice Secondary Mathematics Teachers. Journal for Research in Mathematics Education. 29(3). p. 306-333.
Morrisey, J. T. (2006). Changing Beliefs: Teaching and Learning Mathematics in Constructivist Preservice Classrooms. Science Education. 65(2). p. 157 – 177.
Goulding, M. (2007). Mathematical Subject Knowledge in Primary Teacher Training – A View from England and Wales. Seminar report on Conceptualising and theorising mathematical knowledge in teaching (Cambridge). p. 1-11. Web.
Marzano, R. (2009). Designing & teaching learning goals & objectives. Bloomington, IN: Marzano Research Laboratory. Web.
Mellado, V. (1998). The Classroom Practice of Preservice Teachers and Their Conceptions of Teaching and Learning Science. Science Education, 82(2). p. 197-214.
Morrisey, J. T. (2006). Changing Beliefs: Teaching and Learning Mathematics in Constructivist Preservice Classrooms. Science Education. 65(2). p. 157 – 177.
Ozgun-Koca, S. A. & Sen, A. L. (2006). The Beliefs and Perceptions of Pre-Service Teachers Enrolled in a Subject-Area Dominant Teacher Education Program about “Effective Education”. Teaching and teacher education, 22 (7) p. 946-.960.
Raymond, A. M. (1997). Inconsistency between a Beginning Elementary School Teacher’s Mathematics Beliefs and Teaching Practice. Journal for Research in Mathematics Education. 28(5). p. 550- 576.
Ruffell, M., Mason, J. & Allen, B. (1998). Studying Attitude to Mathematics. Educational Studies in Mathematics. 35(1). p.1-18. Web.
Wilkins, J. L. (2008). The Relationship among Elementary Teachers’ Content Knowledge, Attitudes, Beliefs, and Practices. Journal of mathematics teacher education. 11 (2). p. 139-164.