CHAPTER TWO FACTORS WHICH INFLUENCE MATHEMATICS ACHIEVEMENT AT SECONDARY SCHOOL LEVEL
This chapter explores the various factors which can influence the Mathematics achievement of secondary school learners. Psychological theories and studies related to the different factors are discussed. Since the current study focuses on the influence of irrational beliefs on Mathematics achievement, the relationship between some of the factors which influence Mathematics achievement and irrational beliefs is deliberated on. The variables which influence secondary school learners’ academic performance in Mathematics can be broadly categorised into internal factors and external factors relative to the learners as shown in Figure 2.1. Under internal factors, the current study focuses on cognitive and affective factors as well as the learners’ study habits and learning styles. It can be argued that it is through exploring internal factors that one can gain a better understanding of how Mathematics achievement is influenced by the variables which are inherently embedded in the learners (McLean, 2003:40). The cognitive factors of the learners entail intelligence, aptitude, information processing, language and previous academic performance (Gerrig & Zimbardo, 2005:314; Mwamwenda, 2004:252-253). The various theoretical perspectives on intelligence including Gardner’s theory of multiple intelligences are discussed as well as the relationship between aptitude and intelligence (Sternberg, 2009:414). Moreover, the views of Piaget and Vygotsky on the development of thought and its possible influence on Mathematics achievement are elaborated (Bruce, 2006:98; Gravett & Geyser, 2004:71). With regard to information processing, the Atkinson-Shiffrin model, as outlined by Feldman (2009:217) and Kosslyn and Rosenberg (2006: 279) is examined together with the various memory enhancing techniques which learners can employ to boost their Mathematics achievement. Regarding language, the influence of language on cognition is discussed in conjunction with Vygotsky’s sociocultural theory and the Sapir-Whorf hypothesis (Bhatt, 2007:37; Matsumoto & Juang, 2008:241; Nisbett & Norenzayan, 2002:6). One major justification for focusing on previous academic performance is that it normally acts as a credible benchmark upon which one determines the probable standard of performance in future tasks (Snowman, McCown & Biehler, 2009:274).
The affective variables discussed in this chapter include motivation, self-concept, stress and anxiety. Intrinsic motivation, extrinsic motivation, the self-determination theory and McClelland’s need theory are examined under motivation as affective variables which can influence Mathematics achievement (Rao & Rao, 2003:25; Gagne & Deci, 2005:335; Visser, 2009:11; Yates, 2002:4). The mutual relationship between affect, beliefs, behaviour and cognition necessitated the exploration of the stated internal factors (Forgas, 2001:17; Al-Salameh, 2011:137). Identity formation as theorised by Erikson, Allport’s views on self-concept, Rogers’ theory of self-concept development and Harter’s self-perception profile for adolescents act as the theoretical bases for the self-concept (Birjandi, Mahmoudi & Abdolahi, 2012:8719; Tuckman & Monetti, 2011:383; Manning, 2007:11). Selye’s and Lazarus’s theories of stress together with the Yerkes-Dodson law are used to elaborate the concept of stress (Stickle, 2010:40; Lahey, 2009:367). Anxiety in general and Mathematics anxiety in particular, as pointed out by Feldman (2009:521) and Zakaria and Nordin (2008:28) respectively, are discussed in relation to their possible impact on Mathematics achievement. Study habits and learning styles such as the VARK model (Saadi, 2012:35) and Kolb’s experiential learning are also discussed relative to their possible influence on achievement in Mathematics at secondary school level. It was deemed necessary to scrutinise study habits and learning styles because individual differences among learners relative to the manner in which they respond to intellectual stimuli can to some extent account for the variance in their academic performance.
The external factors, the variables which the learner cannot directly control, are broadly divided into home factors and school factors. Bronfenbrenner’s ecological systems theory, as portrayed by Donald, Lazarus and Lolwana (2010:40) is discussed as a broad theoretical overview of the external factors which can impinge upon secondary school learners’ academic performance in Mathematics. The exploration of external factors is justified by Tuckman and Monetti (2011:171) who argue that internal factors such as a learner’s aptitude and intelligence cannot be realised unless home and school factors are adequately stimulating and supportive.
Under the home-related variables, parenting styles mainly as outlined by Baumrind and parental involvement and socioeconomic background are examined (Santrock, 2004:74; Woolfolk, 2007:165). The home, being the setting in which children are nurtured even before they enrol for formal schooling, arguably remains a critical determinant of children’s ultimate academic success (Rivkin, Hanushek & Kain, 2005:417). It is in the home that children gain their early childhood experiences which can lead to the development of irrational beliefs (Birjandi et al, 2012:8719; Al-Salameh, 2011:137). Parents, just like teachers, are important adults who can influence learners’ academic performance in ways which correlate positively with the level of their involvement (Ozmete & Bayo-Lu, 2009:314).
The school-related factors include classroom management and teacher-related factors. Lewin’s leadership styles together with Blake and Mouton’s managerial grid form the theoretical underpinnings of classroom management as a variable which can influence Mathematics achievement (Dhameja & Dhameja, 2009:82). By virtue of being the setting in which teaching and learning occurs, the school context and its allied variables were deemed to be important in the current study (Rivkin et al, 2005:417). Attention is also directed at teacher-related variables such as the expectations of teachers, the quality of teaching instructions and the personality of teachers (Awolola, 2011:91; Snowman et al, 2009:105). Ausubel’s and Gagne’s theories shed more light on the quality of teaching instructions (Ifamuyiwa, 2011:129; Mwamwenda, 2004:200). Under the personality of teachers, Bandura’s social learning theory and Eysenck’s three factor personality model are highlighted (Feldman, 2009:458; Bee & Boyd, 2004:20). Teacher-related factors are discussed because the teacher is a qualified professional who manipulates the variables in the school setting to facilitate learning (Berns, 2010:235; Mohd, Mahmood & Ismail, 2011:49). The chapter ends with a conclusion in which the variables ultimately to be considered during the empirical investigation are specified
In this study, internal factors refer to the variables which can be directly attributed to each individual learner. The factors are categorised into cognitive factors, affective factors, study habits and learning styles.
In a bid to establish the influence of cognitive factors on achievement in Mathematics at secondary school levels, cognitive factors such as intelligence, aptitude, the development of thought, information processing models, language issues in Mathematics education and the learners’ previous academic performance are considered as shown in Figure 2.2.
Intelligence and aptitude
The terms intelligence and aptitude have been used both separately and interchangeably by different authorities to portray human ability. Intelligence and aptitude have a lot in common. According to Kinra (2008:25), intelligence is concerned with general mental ability while aptitude connotes specific aspects of intelligence such as mechanical, artistic, professional, perceptual and motor abilities. Mwamwenda (2004:252-253) posits that aptitude and intelligence are influenced by both hereditary and environmental factors. The terms intelligence and aptitude, which are related but not necessarily synonymous, are separately outlined.
Description of the concept of aptitude
According to Sethi (2011:1), aptitude is a set of characteristics or a condition regarded as symptomatic of a person’s ability to acquire skills such as the ability to speak a language or play a musical instrument as a result of training. This means aptitude is an individual’s specific ability or capacity to profit from future experience (Mwamwenda, 2004:480). Sujata (2005:09) observed that aptitude is a person’s acquired or innate ability to learn or develop knowledge or a skill in some specific area. An aptitude focuses on an individual’s potentialities to acquire knowledge or skills in a specific domain at some point in the future (Kinra, 2008:24). More comprehensively, an aptitude is an acquired, innate or developed competence for a specific subset of mental skills which offers vital information on an individual’s potential, particularly with regard to education and employment. This implies that aptitude and achievement, not only in Mathematics but in other disciplines, should correlate positively
Description of the concept of intelligence
Intelligence has proved to be an intricate concept which is difficult to define to everyone’s satisfaction (Feldman, 2009:285). According to Kosslyn and Rosenberg (2006:380), psychologists have offered many definitions of intelligence which are not in total agreement. While some psychologists view intelligence as a single quantifiable score, others contend that intelligence has many components which must be separately explored (Gerrig & Zimbardo, 2005:314). As a result of these ambiguities, intelligence has in some cases been defined as a single entity and in other cases as a collection of elemental attributes. According to Sternberg (2009:395), intelligence can be broadly viewed as the capacity to learn from experience and the ability to adapt to the demands of the environment. Intelligence can also be viewed as a general mental capability that, among other things, involves the ability to plan, solve problems, reason, think abstractly, comprehend intricate ideas, learn quickly and learn from experience (Gerrig & Zimbardo, 2005:314). This is supported by Kosslyn and Rosenberg (2006:381) who define intelligence as the individual’s ability to solve problems adequately and to learn and understand intricate material. The above definitions concur that an intelligent person has minimum difficulties in learning new content, solving problems and adapting to novel environmental phenomena if all other variables are held constant. If this is related to achievement in Mathematics, it can be claimed that there should be a strong positive correlation between intelligence and achievement in Mathematics.
Intelligence has also been expressed as a single numerical index called the intelligence quotient (IQ). The intelligence quotient is an index obtained by dividing the mental age by the chronological age so as to enable the comparison of intellectual capabilities of children of different ages (Tuckman & Monetti, 2011:169; Lahey, 2009:294). However, Kosslyn and Rosenberg (2006:381) observed that the IQ has evolved to the extent of incorporating norms which measure general intelligence. People believe that aptitude and the IQ are closely related but represent opposing views of human mental ability, that is, an IQ denotes intelligence as a single quantifiable trait whereas aptitude disintegrates that intelligence into several different characteristics that are relatively independent of each other. It is also important to note that although aptitude and intelligence are conceptually different, a significantly strong positive correlation between IQ scores and aptitude scores exists. One aspect of intelligence is the ‘general factor’ which Spearman developed and denoted by ‘g’. According to Kosslyn and Rosenberg (2006:386), ‘g’, the general factor is a single intellectual capacity that underlies the positive correlations among a variety of tests of intelligence. It has to be admitted that the use of a single IQ to measure intelligence has proved to be inadequate (Sternberg, 2009:388)
CHAPTER ONE STATEMENT OF THE PROBLEM AND PROGRAMME OF RESEARCH
1.1 AWARENESS OF THE PROBLEM
1.2 FORMAL STATEMENT OF THE PROBLEM
1.3 AIMS OF THE INVESTIGATION
1.4 PROGRAMME OF THE RESEARCH
CHAPTER TWO FACTORS WHICH INFLUENCE MATHEMATICS ACHIEVEMENT AT SECONDARY SCHOOL LEVEL
2.2.1 Cognitive Factors
2.3 EXTERNAL FACTORS
CHAPTER THREE IRRATIONAL BELIEFS AND MATHEMATICS ACHIEVEMENT .
3.2 EXPLORATION OF THE NATURE OF BELIEFS
3.3 THEORIES ON THE DEVELOPMENT OF IRRATIONAL BELIEFS
3.4 IRRATIONAL BELIEFS IN A SCHOOL CONTEXT
CHAPTER FOUR METHOD OF EMPIRICAL INVESTIGATION
4.3 RESEARCH DESIGN
CHAPTER FIVE .RESULTS OF THE EMPIRICAL INVESTIGATION
5.2 ITEM ANALYSIS AND RELIABILITY
5.3 SUMMARY OF RELIABILITY OF THE QUESTIONNAIRE SUBSECTIONS
5.4 TESTING OF HYPOTHESES
5.5 SUMMARY OF FINDINGS
CHAPTER SIX CONCLUSIONS AND RECOMMENDATIONS
6.4 LIMITATIONS OF THE STUDY
6.5 POSSIBILITIES FOR FURTHER RESEARCH
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