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Numerous studies have been undertaken to establish the impact of anxiety as an affective factor on academic achievement not only in mathematics, but in practically all the domains of learning. Anxiety, which is mostly taken to be synonymous with

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stress, is also reported as a symptom of stress. The concept of general anxiety is explained before specific attention is directed at Mathematics anxiety, the factors which cause Mathematics anxiety and research on anxiety and achievement in Mathematics.

2.2.2.4.1 Description of the concept anxiety

Anxiety can be defined as an unrealistic fear resulting in physiological arousal and is accompanied by the behavioural signs of avoidance or escape (Hey, Bailey & Stouffer, 2001:81). The difference between fear and anxiety is that fear is triggered by a realistic objective source of danger while anxiety is a generalised subjective and unrealistic sense of fear about something out there that seems menacing. This implies that general anxiety is an apprehensive feeling of tension or worry which can manifest itself as a symptom of stress. This was backed by Feldman (2009:521) who defined anxiety as a feeling of tension or apprehension in reaction to stressful situations. Some of the symptoms of anxiety according to Hey et al (2001:82) include trembling, feeling shaky, muscular tension, aches, soreness, restlessness, fatigue, shortness of breath, palpitations, fast heartbeat, sweating, dryness of the mouth, dizziness, light-headedness, nausea, flushes, frequenting the toilet, fragmented concentration, irritability, and trouble falling or staying asleep. Experiencing several of the above symptoms simultaneously is likely to interfere with one’s achievement in Mathematics. However, Feldman (2009:521) argued that anxiety, just like stress, is not totally bad because without anxiety many learners will not be adequately motivated to study in preparation for examinations.

2.2.2.4.2 Anxiety in Mathematics

Mathematics anxiety can be defined as an inconceivable tension, apprehension or dread of Mathematics that can interfere with a person’s ability to manipulate numbers and solve mathematical problems within a variety of everyday life and academic situations (Smith, 2004:4; Sherman & Wither, 2003:138; Sheffield & Hunt, 2007:19). Unpleasant feelings of fear or tension that sabotage a learner’s Mathematics problem-solving ability or other activities related to Mathematics can be described as Mathematics anxiety (Wei, 2010:6). Mathematics anxiety has been defined by Zakaria and Nordin (2008:28) as the feeling of tension, helplessness, mental disorganisation and fear which grips someone when he or she is tasked to solve mathematical problems through manipulating numbers and shapes. Sufficient

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research evidence indicates that learners with high levels of Mathematics anxiety achieve at a lower level in Mathematics (Scarpello, 2007:34).

2.2.2.4.3 Factors causing anxiety in Mathematics

Anxiety may be caused by a variety of stressful life events, numerous hereditary factors, personal background, personality and physical illness (Hey et al, 2001:82). Mathematics anxiety can be caused by parental influences, past classroom experiences and remembering poor past achievement in Mathematics (Scarpello, 2007:34). Hey et al (2001:82) claimed that anxiety is contagious since children and adolescents living with anxious caregivers are more likely to have the same anxiety disorders. Mathematics anxiety can be attributed to a host of variables which entail truancy, poor self-image, inadequate coping skills and teaching methods which emphasise rote learning at the expense of meaningful learning (Zakaria & Nordin, 2008:28). According to Stuart (2000: 330-335), Mathematics anxiety can stem from lack of confidence when manipulating mathematical problems. Smith (2004:7) maintained that Mathematics anxiety is caused by poor test scores, reluctance or inability to complete challenging assignments, negative parental predispositions and the Mathematics teacher’s personality and attitudes. According to the above beliefs, the conclusion can be made that Mathematics anxiety can be caused by many factors which can be categorised into learner-related factors, school-related factors and home-related factors. The influence of some of these factors on Mathematics achievement is scrutinised in the current study.

2.2.2.4.4 Research on anxiety and achievement in Mathematics

Zakaria and Nordin (2008:27-30) undertook a research in Malaysia to establish the effects of Mathematics anxiety on motivation and achievement with a sample of 88 learners comprising 73 females and 15 males. The study established a strong negative correlation of −0.72 between Mathematics anxiety and achievement. The results of this study provided evidence that Mathematics anxiety has an important effect on academic achievement and it cannot be ignored (Zakaria & Nordin, 2008:30).

A longitudinal study to explore the relationship between anxiety and Mathematics achievement was undertaken by Sherman and Wither (2003:149). Starting from the

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well-documented finding that a negative correlation exists between Mathematics achievement and anxiety, the study tested three additional hypotheses. The three hypotheses revolved around establishing whether Mathematics anxiety is a cause or an effect of Mathematics achievement as well as the possibility of a third underlying variable which influences the relationship between Mathematics anxiety and Mathematics achievement. A sample of 66 respondents was used. The study confirmed that there is a negative correlation between Mathematics anxiety and Mathematics achievement. However, challenges were encountered in trying to establish the direction of causality. The study statistically failed to establish whether Mathematics anxiety really causes poor Mathematics achievement. Insufficient evidence was also found to confirm that lack of achievement causes Mathematics anxiety or that the presence of a third factor influences the relationship between Mathematics achievement and Mathematics anxiety. As a result of the unclear findings, Sherman and Wither (2003:149) recommended that more specific studies involving these variables be undertaken. The researchers advised that the experiment be replicated or a more direct line of inquiry such as measuring the changes in the Mathematics achievement of people undergoing an anxiety reduction programme be conducted so as to generate more insights regarding the relationship between Mathematics achievement and Mathematics anxiety.

Wei (2010:07) studied the impact of treatment messages on learners’ Mathematics anxiety and Mathematics learning in a computer-based environment. Anxiety treatment messages are statements based on psychological theories which are delivered to people for the sake of helping them to cope with anxiety. For instance, the statements can be based on cognitive-behavioural principles of Beck’s cognitive therapy and disputation techniques derived from the rational emotive behaviour therapy advanced by Ellis. A pre-test, post-test experimental research design was used. A sample of 128 grade nine respondents participated in the study. Technologically animated human-like characters called pedagogical agents who acted as tutors interacted with the research participants in a computer-based environment. The respondents were randomly assigned to the experimental and control groups. While the pedagogical agents who interacted with the experimental group presented anxiety treatment messages, the pedagogical agent of the control group did not present any anxiety treatment messages (Wei, 2010: iii). The study

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revealed that there were significant interaction effects between treatment messages and the learners’ prior levels of Mathematics anxiety on current Mathematics anxiety. It was discovered that treatment messages reduced the anxiety levels of highly anxious learners in the treatment group. It was also established that the anxiety of the low-anxious learners in the control group increased probably because they had interacted with non-human pedagogical agents who did not equip them with any mechanisms to cope with anxiety. On the other hand, the anxiety of the low-anxious group in the experimental group remained constant tentatively because they benefited from the treatment messages presented by the pedagogical agents, despite being subjected to an artificial environment.

Working on the premise that Mathematics anxiety affects learners’ achievement in Mathematics, Smith (2004:15-17) undertook a study to establish the role played by teachers in determining their learners’ Mathematics anxiety. Using two different classes, each with a different teacher, Smith (2004:15-17) used the Minnesota Mathematics Attitude Inventory (MAI) to measure learners' attitudes to Mathematics. Seventh graders participated in the study. The attitudes of the two Mathematics teachers of the participating classes were also measured. The study established that the attitudes of the two teachers towards Mathematics were different. The teacher with a negative attitude towards Mathematics was found to have a higher level of Mathematics anxiety than the teacher with a favourable attitude towards Mathematics (Smith, 2004:28). After comparing the results of the seventh graders and their respective teachers, it was established that the attitudes of teachers towards Mathematics have an influence on their learners’ attitudes towards Mathematics. According to Smith (2004:3), the difference between the two teachers’ attitudes implies that teachers play a role regarding the extent to which learners can be affected by Mathematics anxiety. Such a conclusion was based on the argument that teachers who understand Mathematics anxiety better are better positioned to prevent it and assist learners to overcome it (Smith, 2004:3).

It has been established that Mathematics achievement can be influenced by anxiety in general and Mathematics anxiety in particular (Zakaria & Nordin, 2008:30; Wei, 2010:7; Scarpello, 2007:34). It is possible for some irrational beliefs to be related to anxiety which emanates from studying Mathematics. For example, the irrational

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belief that if something is or may be dangerous or fearsome, one should be terribly upset and endlessly obsess about it can foster anxiety among learners. The irrational belief that human emotional misery is mostly externally caused and that people have little or virtually no ability to regulate their emotional sorrows and disturbances also seems to be related to anxiety as a learner affective variable. Subsequent chapters in the current verify the existence of relationships between irrational beliefs and anxiety in a Mathematics learning context.