2:0 This chapter focuses on views of different authors and researchers concerning causes of low performance of students in mathematics at Ordinary level .The literature helped the researcher in trying to resolve the problem by identifying what had been tried and the results of those trials .The literature helped the researcher to identify gaps that need to be in the area of study .The chapter began by discussing the theory that influences the information of causes of poor performance then it went on to review what has been discovered on the sub problems in an attempt to answer the study problem .
2:2 THEORETICAL FRAMEWORKS
In an academic arena the most important event is the success or failure of the learner to learn .Experience of failure in problems designed to test the level of learning is often followed by a na”ve reaction of blaming either lack of ability ,lack of luck or lack of effort of the designed problem .Success is often followed by access to possession of ability ,easiness of task or input of effort in school work .Mathematics is mostly disguised as a subject not for the weak and so this becomes a self-fulfilling prophecy that mathematics is a subject for those with great intellectual ability .A large number of studies seem to gravitate towards the problem of mathematics education in Zimbabwe as illustrated by the poor performance of students who have failed to meet the admission requirements of mathematics faculties .
Mabila (etal) (2006) asserts that, mathematics is one of the most paramount fears of teachers and other mathematics educators globally. It is of paramount importance for teachers to have a theoretical background in order to better understand the behaviours and performance of students and be able to help them .In a study in Lesotho on causal attribution of performance in mathematics ,it was discovered that there is a relationship between causal attribution and performance (Kallenbach and Zaft ,2004 ).The theorem of na”ve psychology was first profounded by Fritz Heider in 1958 and was later developed into a theoretical framework by Weiner and friends in 1972 .The theories of success and failure in education are very important .In this study the theory helped to explain the origins of the students and teachers perceptions of pupils’ performance in mathematics .(Weiner 1992 )observes that, most explanations for success or failure have some characteristics which are , whether the cause of failure is within the person or outside the person ,the second being , whether the cause is seen as stable or unstable . Finally is whether the cause is perceived as controllable or uncontrollable. Thompson (1995 ) postulates that ,a central assumption of the Attribution theory is that people attempt to maintain a positive self-image .Therefore if people do well in an examination they are likely to attribute their success to their own efforts or abilities ,but when they do poorly they believe that failure is due to factors which they have no control .
Basing on this theory, if learners perform badly in mathematics they attribute the cause to other factors other than themselves and in most cases it is the teacher who is given the blame and the teacher acts likewise and blames the students for not putting enough effort in their learning .Oloyede (1996)adds credence to the above sentiments in this study on effects of psychological theories in mathematics teaching when he said that for any mathematics teacher to be academically functional and
effective in the classroom the knowledge of educational psychology should be the basis for new encounter in his or her teaching .The tendency for individuals to consistently make particular kinds of attributions overtime is referred as attribution style. Metalsky and Abramson( 1981 ) This means a self-enhancing style is one that habitually gives credit to hard work for success and attributes failure to lack of effort .
Attribution Theory influences pupils’ perceptions and deals with four explanations for success and failure in, achievement situations, ability effort, task difficulty and luck. The internal attributions are ability and effort to the individual, whilst task difficulty and luck are external to the learner. Ability is taken to be a relatively stable, unaltered state, whilst effort can be altered. One concept that is central to attribution is locus of control (Bandura, 1997) .Locus of control has been defined by Weiner (2000) as a subjective personal belief that the extents to which one’s actions determine outcomes. A student with locus of control believes that success or failure is due to his or her own efforts or disabilities. Locus of control can be either internal or external to the individual .A student with external locus of control always believes that external forces cause his or her failure. On the other hand ,one with internal locus of control also known as self-efficacy believes that one’s behaviour makes a difference (Zimmerman ,1998) .Self efficacy or locus of control can be very important in explaining a student’s school performance if the teacher has knowledge of the theory .
Several researchers have observed that students who are high in internal locus of control have better grades and test scores than students of the same intelligence who are low in internal locus of control .(Shell, (1995 ). According to (Bandura, 1997) observes that studies have established locus of control to be the second most important predicator of student’s achievement. Students who believe that success in school is due to luck, teacher’s effort or other external factors are unlikely to work hard because they have no confidence in their ability. In contrast ,students who that that success and failure are due to their efforts can be expected to work hard provided they are prepared to do so .If pupils believe that hard work results in improved performance they will put more effort and an improved performance will motivate them in future and will not blame external factors for their failure .Salami (1997)also agrees with the above statement when he says ,success that is attributed to good luck is not sustainable ,as failure may occur in the future since luck is unstable .Furthermore it has been observed that students who attribute their performance to luck avoid the front seats but prefer the back seats . In addition attribution to luck has been known to be characterised poor attitude to study, low motivation and low motivation to achieve (Forsth and MacMillan 1981).
Attribution of failure to lack of effort may result in improved success because performance might be improved if more effort is exerted. This is echoed by Rao (2007) who asserts that, when students fail, they are most likely to persist and eventually succeed if they attribute their failure to lack of appropriate effort . Effort is most effective if it is reviewed as the persisting devotion of effective academic time to the task .It is important that when students perceive themselves as unsuccessful they are helped to develop the conviction that they have the ability to succeed in mathematics and they could succeed if they give their best. Attributing mathematics failure to lack of ability may result in low expectance for future success because ability is stable and will not increase greatly and also future performance will show little improvement.
In reality success in a learning situation is a product of the student’s effort( internal factors ) and luck task difficulty ,behaviour of the teachers thus teaching methods and availability of resources (external factors ) .In a classroom situation ,students receive constant feedback concerning their level of performance on academic tasks either relative to others or relative to some norm of acceptability .Bandura (1997) asserts that ,the feedback students receive influences their self-perceptions . Attribution theory can help teachers to understand how students may interpret and use feedback on their mathematics performance be it negative or positive .It has been observed that constant reference to a student as being dull may influence the child’s self-perception that he or she is not good in mathematics and will attribute his or her poor performance to lack of ability hence will not bother making an effort to improve. The theory encourages educators to give feedback that has the greatest motivational value that will positively influence students’ self-perception (MacCown, Driscoll and Roop (1996).
Burstein (1992) in a study that influences mathematics performance found that there is a direct link between students attitudes towards mathematics and the students’ performance in that subject .He also found out that twenty five per cent in England and twenty six percentage in Norway of the pass rate was accounted for by the students’ attitudes towards mathematics .To further substantiate the earlier observation ,results of a study on causal attribution of performance by students in Lesotho showed that generally a majority of the students had undesirable attribution patterns in mathematics performance and this contributed to poor and deteriorating performance in the subject (Nenty ,1998) . (Aremu and Sokan ,2003 ) have also identified four factors that contribute to low performance .The first one was identified as the cause resident in the learner such as cognitive skills ,physical and health factors ,psycho emotional factors and lack of interest in the school programme . For example, a learner can perform badly in mathematics because some concepts were introduced while the student was absent due to poor health. Again , a student can also perform poorly due to lack of awareness on the value of mathematics in his/ her life .The other factor identified is resident in the family ,such as lack of finance and lack of role model to influence the learners behaviour positively .To give credence to the above observations ,students have been known to do well because their brothers and sisters were also mathematics major at school .In this instance attributions are influenced positively by family members .The assumption here is ,if the student comes from a sound mathematical background and is not dull then the teacher should examine the school for the source of the student’s negative perception of one’s low performance .
For a teacher to know and understand the Attribution Theory and be able to use it to change negative perceptions of students, he or she must possess a professional qualification in the teaching of mathematics and be in possession of knowledge in educational Psychology which is in the foundation of one to be an effective teacher. The next section discusses the teacher qualification in an attempt to find out if teachers and students influence performance in mathematics at Ordinary level.
2:3 Qualifications of the teacher and the teaching of mathematics
Teacher qualification contributes immensely to the pupils performance in mathematics .Research has consistently shown that teachers’ content and pedagogical knowledge provide a basis for classroom practices .Ferguson and Ladd (1996) observes that ,research studies have found that teachers more effectively teach and improve student achievement if they themselves have strong academic skills .Varelas (1991 )asserts that ,a growing number of research shows that student achievement is more heavily influenced by teacher quality and not by student race, class ,prior academic record or school a student attends .Research indicates that the achievement gap widens each year between students with most effective teachers and those with least effective teachers .This suggests that the most significant gains in student achievement will likely be realised when students receive instruction from good teachers over consecutive years . Abraham and Keith (2006) used a questionnaire as a basis for constructing an index of school effectiveness and their findings revealed that teachers were the key drivers of internal school change. Oshodi (1991) investigated resource utilisation and students’ academic performance and used Spearman rank correlation coefficient to determine the most influential factor on students’ academic performance and found that the quality of teachers was the most important determinant of students’ academic performance in schools .There is need for appropriate formal training in the field in which they teach and several years of teaching experience. Sweeney (1998 )observes that ,students perform better in mathematics at Ordinary level when taught by teachers with more years of teaching experience considering the common saying that experience is the best teacher .Chivore (1997) concurs by saying that teaching is about how to put across what one knows to the learner. If a teacher lacks content knowledge he or she cannot teach effectively resulting in poor performance by students. Many studies support the notion that, teachers who teach subjects that they have previously studied in depth are particularly effective .However advanced degrees in general thus degrees that that are not in the subject matter being taught have not been found to be associated with higher student achievement. Galaba (2001) reiterates that, the teacher is the heart of classroom instruction and his or her effectiveness depends on his or her competence that is academic and pedagogic. In addition, the teacher needs efficiency which can be seen through his or her ability to tackle different mathematics concepts with confidence ,handle his or her work load without succumbing to the pressure and commitment to duty .
Mosha (2004) has observed that mathematics is a skill that is difficult to acquire and because the teaching profession does not play well there is shortage of qualified teachers resulting in poor performance by learners .In most schools in Zimbabwe, there is always a vacancy for teaching in mathematics departments even if the school is overstaffed in other departments due to shortage of students in that area. Another situation that is common among Zimbabwean schools is the employment of advanced level school leavers to teach Ordinary level mathematics students as a way of alleviating the problem of the shortage of qualified mathematics teachers. Those mathematics teachers who are available are overloaded with work resulting in low morale as most of them are given examination classes and leave non examination classes for untrained teachers. This observation is supported by the findings by the Ministry of education through the Curriculum Development Unit (CDU) (1993) who discovered that, the majority of mathematics teachers were young and lacked experience .They also discovered that most teachers had Ordinary level as their highest academic qualification and a certificate in education as the highest professional qualification.
A research carried out by the Department of education in California cited by Sweeney (1998) established many ways of explaining why many mathematics teachers perform poorly in the classroom besides lack of motivation .One of the findings was that ,the teachers never learned the subject properly all the way from kindergarten through college .This then precludes the possibility of good teaching because one cannot teach what one does not know .Another explanation offered for the teachers ‘poor performance is that their stilted ,constructed and rigid approach to the subject turns students off at the onset . This means that such teachers lack the knowledge of making their lessons interesting to enhance understanding on the student. Bandura in Oleyede (1996) through his theory of Social Learning supports that the teacher should demonstrate his or her own enthusiasm in mathematics learning so as to mode a desirable behaviour to students .If the teacher looks bored according to this theory so will the students .
It is believed that a motivated teacher always complete the work set for him even when such work is difficult or uninteresting .Freud (1990 ) and other psychologists like Taylor (1994 ) generally agreed that man is motivated by the desire to satisfy a number of needs .This is true because there is no doubt that teachers whose financial needs are not satisfied will be psychologically and socially demoralised in their working attitudes and this is of great effect to performance of such teachers. Most teachers come into school only to put their names in the attendance register and moves out in pursuit of other jobs which will earn them a large amount of money to make ends meet since teachers ‘salaries are very small .This attitude of teachers make the students go home after the whole day with nothing learnt either one or two subjects for the day .This lowers the students’ academic performance .
Maslow (1954 ) came up with the theory of the hierarchy of needs .Maslow’s theory states that ,if a number of the features of a person’s needs are satisfied at any given time ,satisfaction of the most proponent ones will be more pressing than that of the other .This implies that teachers’ behaviour at work like ,coming to work late ,lazy to teach ,poor teaching methods are caused by lack of motivation by the employer and hence there is poor academic performance in schools .Victor (1964 ) in his contributions advanced the Expectancy Valence Theory .He stated that ,if an individual worker believes that working hard will lead to salary increase ,he will intensify his or her effort and work hard .The theory recognises that people act only when they have a reasonable expectation that their actions will lead to a desired goal. The theorist goes on to say, motivation is the function of the expectancy of attaining a certain outcome in performing certain act multiplied by the value of the outcome for the performance. In support on the need for motivation McGregor’s (1960) asserts that, on average human beings have an inherent dislike of work and will avoid it if possible .Hence this will cause poor academic performance in students as teachers will relax whilst at work .
This problem of poor performance in mathematics is not only in Zimbabwe alone, in South Africa it has been reported that out-dated teaching practices and lack of basic content knowledge have resulted in poor teaching standards .South Africa participated in the Third World International mathematics study conducted in 1995 and came out last with a mean score of three hundred and fifty one .This mean score was significantly lower than the international bench mark of five hundred and thirteen. The study was carried out again in 1999 and revealed that Ordinary level learners once again performed poorly .Their mean score was found to be lower than that of Morocco ,Tunisia and other developing countries like Chile ,Indonesia, Malaysia and Philippines . Kour (2004) discovered that in Singapore the problem of teaching mathematics needed qualified teachers for students to perform better and recommended that the Ministry of education could do better to equip mathematics teachers with necessary skills through in-service courses. This came as a result of under qualified teachers who were producing poor results at Ordinary level.
Odhiambo (2006) also pointed out that there is a shortage of mathematics teachers in Kenya .He further revealed that the student ‘teacher ratio in many secondary schools in Kenya is also contributing to the high failure rate. Huebler , (2008) agrees with the above notion and said that, the pupil teacher ratio is an indicator of education quality and in crowded classrooms with a high number of pupils per teacher the quality of education suffers. In Zimbabwe ,a number of mathematics graduates join the teaching service while hunting for something better to do and as soon as an opportunity arises they leave without giving notice to enable another teacher to be found hence affecting the students ‘performance negative as these pupils will be left without a teacher for a long time .Since mathematics teachers can be employed elsewhere ,the problem is going to continue to plaque the education sector unless the employer manages to match the level of remuneration with that offered elsewhere and with the current state of our economy the government will not manage to do so .
In the research under study pupils are still producing poor results as evidenced by the ZIMSEC results cited before. Zimbabwe teachers are considered competent thus they possess both knowledge and skills .A proof of this is that teachers are being recruited in South Africa, Botswana and Namibia and also abroad like in UK in large numbers. Whilst Zimbabwean teachers are labelled as competent elsewhere, one is left wondering why students at home are still producing poor results at Ordinary level in mathematics. The problem could be that teachers with high qualifications are the ones who are in demand and are leaving the country leaving those with lower qualifications to teach the Ordinary level mathematics.
2:4 Teaching methods and students’ performance
The fashion of teaching mathematics has historically changed from one approach to the other and in practice ,individual teachers have picked their own place on the methodology spectrum dependent upon their mathematics background ,training and their experiences with students .The instruction process is very crucial in terms of equipping the student with mathematical knowledge and skills . Henderson and Landesman (1995) advocate that mathematics should not be taught in a top ‘bottom approach, that is from the teacher to the student all the time, but should be dominated by bottom up information processing assumptions. It is assumed that all teachers have undergone teacher training and refresher courses and have been introduced to Piaget’s theory on teaching which is based on pre operational, concrete operations and formal operations which caters for every learner. Such background knowledge on the teacher will enable him or her to structure problems according to the student’s level of learning and this would solve the problem of poor performance on students. This is stated by Bruner’s Theory of Instruction which states that any body of knowledge can be presented in the form simple enough so that any learner can understand it in recognised form (Oloyede, 1996).Clark and Steir (1988) blames teachers for poor performance by candidates in Ordinary level mathematics due to teaching methods which they employ ,which show lack of commitment in preparing and imparting knowledge to pupils .They argue that variation of teaching methods by teachers tend to improve performance .They also argue that the methods of teaching which enhance performance are those methods that are child centred rather than teacher centred ones .These learner centred methods are guided discovery ,group process ,projects and programmed learning. Bruner (1993) encourages learning mathematics through the method of guided discovery .He argues that knowledge acquired without sufficient structure to it is the knowledge likely to be forgotten .He went on to say that one must acquire rational understanding that centres on how something works and why it works .
However, the situation on the ground is different as some teachers have academic qualifications only without professional qualifications that equip them with the necessary theories of education and appropriate teaching methods .Such teachers are likely to lack knowledge needed for them to cater for individual differences which would result in very few students understanding the mathematical concepts. Quilter and Harper (2003) observed that many students have negative attitudes towards mathematics because of how it is taught and that there is also perception that mathematics teachers present Ordinary level Mathematics as being difficult and only accessible to the selected few. They carried out a study on students who had graduated from University but who were not interested in mathematics and were unable to solve simple mathematics problems .In their investigation they used attitude questionnaires and interview schedule and came up with several variables.
Good and Brophy (1990) said pupils remember 10% of what they see ,40% of what they do .Cognitivists like Bruner (1996 ) and Piaget (1969 ) support Quilter and Harper’s (1988) findings because they believe in learning by doing where students discover their knowledge through guided discovery. Bruner (1966) believes that learners who use their energy to discover knowledge gain intrinsic motivation and Piaget (1969) maintains that a more satisfactory means of advancing learning should be the one which brings the child face to face with inadequacy of existing schemata and new accommodation .Hence performance can be enhanced if the afore mentioned principles are instilled in pupils .
In Bruner’s theory of instruction, the technique of simplifying content involves what he terms three modes of presentation which are enactive, iconic and symbolic. Enactive presentation involves action which is psychomotor activity thus a student can demonstrate an understanding of an action if it is inactively presented. Understanding a concept is by doing .The iconic presentation involves the use of images or model to present an idea object or principle .Hence, the teacher should make teaching materials such as charts, graphs and others to enhance the student’s understanding of mathematical concepts .The symbolic presentation can be used to explain some concepts that use language to demonstrate an idea or event .Bruner’s theory of instruction implies that the teacher should analyse mathematics content to be taught so that the modes of representation are appropriate to the different levels of the material as well as to the development of the learner .Hence knowledge of which mode to use depends on the teacher’s qualification .
Tharp (1989) believes that using cooperative methods can improve performance in mathematics .This is in agreement with Henderson and Landesman (1995) who also advocate for cooperative teaching in learning situations. They believe that this method can improve students’ performance in mathematics .However the two differ slightly with Tharp (1989) in their findings on effects of thematically integrated mathematics instruction on students of Mexican origin .They discovered that cooperative learning and heterogeneous grouping do not by themselves guarantee success .However this was disputed by Mevarech (1999) in his study of meta cognitive training ,embedded in cooperative learning methods .He discovered that cooperative methods work well in small groups of students of mixed ability when they work together to solve mathematics problems and complete tasks .
Good (1989) cited by Mulyran (1992) in his study of cooperative small group instruction in mathematics, identified important cognitive and effective consequences of work in this setting for students. Thus students who worked in cooperative small groups were more active learners and more motivated and enthusiastic about mathematics than students who did not have the opportunity to work in cooperative groups. Kwari and Mtetwa (2003) in their study on active learning in Zimbabwe in mathematics performance said, one of the reasons for low performance was the methodology used during instruction. They discovered that students were performing poorly in mathematics because of the way the subject was taught. In support of this notion, Nziramasanga (1999) observed that most students failed mathematics because of the methods employed by the teachers which were not motivating.
Engels (1993) cites three goals of instruction that every mathematics teacher should aspire to achieve so as to avoid poor performance by students .These goals are content coverage ,understanding and problem solving ,positive attitudes and equitable outcomes .According to Kwari and Mtetwa (2003 ) content coverage is not a problem in Zimbabwe as most teachers aim at it and succeed in completing the syllabus .It is the other two goals that do not seem to be getting adequate attention and that is equipping students with problem solving skills and cultivating in them positive attitudes towards the subject .A number of factors such as space ,time ,materials and poor teaching strategies could be contributing to this inadequacy . Anthony (1996) carried out an investigation in active learning in a constructive frame work in mathematics teaching and discovered that there are two dimensions .The first dimension denotes learning activities in which students are given considerable autonomy in and control of their direct learning .This is identified as investigation work ,problem solving ,small group work ,collaborative learning and experimental learning .The second dimensions concentrates on developing the quality of pupils’ mental experience through active intellectual involvement in the learning experience characterised by increased insight and understanding .Sosniak ,Ethington and Varelas (1991) pointed out that ,a teacher should not waste time waiting for each and every learner to discover a concept because the curriculum would not be completed .They believe that giving autonomy to the students would waste time and could lead to discovery of concepts not related to the syllabus .This view is also shared by Siann and Ugwebu (1989) who gave a warning that ,mathematics teachers should not give autonomy as this can lead to absence of structure ,both in the classroom and in the student’s understanding resulting in confusion .This means that a teacher should dictate what is to be learnt most probably through the guide of the syllabus ,otherwise poor performance would persist and there would be confusion in the classroom as each pupil learns what he or she wants through discovery work .
Therefore it is of importance for teachers to have background knowledge of psychological theories that guide classroom operations by the teacher .The next section will look at the value of mathematics in the learners’ lives in an attempt to find out the causes of low performance in mathematics at Ordinary level.
2:5 Value of mathematics to students
Sayers (1991) asserts that, pupils failed to see the usefulness of mathematics as applied to daily living .It was taught as an abstract subject, a subject that is not related to life, with no social context of problems exploited. Failure to accept and recognise the usefulness of mathematics at school and in society caused low achievement of pupils in the subject .Most pupils thought that at school mathematics was mainly needed in science subjects like Physics which could not have been in their field of interest. A study carried out in Jamaica on poor attitudes to mathematics as a subject proved that many students had negative attitudes towards the subject and some viewed it as being of little or no use to them outside school, Ministry of education Youth and Culture Jamaica (2003).Hence pupils memorise formulas for examination purposes and forget about the subject as soon as they leave school.
In South Africa Mji and Makgato (2006) pointed out that, few students take mathematics and those who do so do not perform well because they are not motivated which ultimately lead to mass failures .Many factors can cause lack of motivation in the student and it could be how the subject is taught or it’s because of pupils’ ability .If students know the true value of the subject they would make an effort to understand it. Yeya (2002) had similar views that many teachers, students and parents have a negative attitude towards the teaching and learning of mathematics .Chiriswa (2003) agreed with the issue and recommended that mathematics teachers and students be given incentives to raise their morale for better grades in mathematics. He recommended students to be given awards for excelling in mathematics or offered scholarships even at school level or encourage mathematics projects where students display their accomplishments.
Values influence how students feel about mathematics .If students learn mathematics because it is one of the core subjects at Ordinary level ,they are likely to aim for a minimum pass ,but if they learn that they would need the subject in their lives they are likely to develop an interest in the subject .This knowledge would influence the students ,attitude towards the subject . Attitude is the behaviour that is measured by various evaluating processes .In Zimbabwe, Ordinary level students view mathematics as a subject for the gifted students, mainly because when students start Ordinary level syllabus they are screened into sciences, arts and commercial subjects. After high school a pass at Ordinary level mathematics is also a prerequisite for entry into college irrespective of what one wants to study .Therefore mathematics subject is viewed as a filter that filters students out of careers or university.
At teachers’ colleges bridging courses have been introduced hence one needs to pass mathematics at Ordinary level to actually start teaching programmes .If students are aware of how available mathematics is then one has to seriously examine the amount of time allocated to the learning of the subject in the school system in an attempt to find out the causes of low performance in mathematics at Ordinary level.
2:6 Time allocated to the teaching of mathematics
Keiser and Lambdin (1994) postulates that, numerous studies have documented how little time is allocated for mathematics at all levels .Zimbabwe has not been spared in the aspect of little time especially with the common double sessions in our high density schools .Mji and Makgato (2006) asserts that non completion of the syllabus is a major determinant to the students’ performance in mathematics.Yeya (2005 ) observed that students in boarding schools cover the syllabus in time and are exposed to more remedial exercises because they are ever in school compared to day schools which are characterised by absenteeism of both teachers and students of which this will lead to non-completion of the syllabus in a given year .In Zimbabwe coverage of a syllabus is not a problem as most teachers aim at it and succeed in completing it .Zimbabwe schools seem to have a limited time allocation for mathematics at Ordinary level that is six hours per week .Again it is a perennial problem in terms of lesson delivery as most pupils engage in extra lessons to compete the syllabus ,hence research for time must be carried out so that undeveloped countries will follow what developed countries are doing for further enhancing students ‘performance in mathematics .
The problem of time is found to be caused mainly by double sessions that are conducted per school which limits use of resources for teachers and students as they have to share .There are a number of cases when mathematics lessons loose much time due to activities such as assemblies, staff meetings and sports.