ABSTRACT

Learning mathematics is a cognitive as well as affective endeavor with the affective factors playing major role in student achievement. The main purpose of this study was to examine the relationship between affective factors and students’ achievement in Mathematics in Ganze District, Kilifi County Kenya. Study was motivated by underrepresentation of females in advanced mathematics levels and related careers. The study was guided by the following three specific objectives: to establish the relationship between student attitude and mathematics achievement, to establish the relationship between student anxiety and mathematics achievement, and to assess the effect of confidence on mathematics achievement. This study employed descriptive survey research design. Target population comprised of both male and female students from secondary schools in Ganze District. The district had 4 zones with a total of 1620 male students and 1080 female students within the 20 schools among which 12 were mixed day secondary schools, 4 boarding schools and 4 single sex schools. Proportional stratified random sampling was done to ensure at least 50% of the schools were sampled from every zone. The study had a stratified sampled size of 250 students; mainly form 4 and 3 students of which 150 were male and 100 female. The affective factors (attitude, anxiety, confidence) formed the independent variables, learning factors in mathematics class room as intervening variables and mathematics achievement as the dependent variable. The valid and reliable research instruments included mathematics attitude questionnaire, mathematics anxiety rating scale, mathematics confidence questionnaire and mathematics test. Data were analyzed using SPSS program of IBM 2015 American version and presented in text and tabular forms. The mode of analysis mainly involved Correlational Analysis of Pearson Product moment correlation coefficient (r_xy) indicating the statistical significant correlation value for either accepting or rejecting the null hypothesis, “there is no statistical significant relationship between affective factors and students’ achievement in mathematics”. The findings revealed females outweigh males at higher positive attitude; males outweigh females in lower anxiety; but no disparity in confidence. The researcher concluded attitude and confidence are directly proportional to mathematics achievement but anxiety is indirectly proportional. The relationship between affective factors and students’ achievement in mathematics is beyond gender differences and academic abilities; for females outweigh males in mixed day, males outweigh females in mixed boarding but no disparity in single sex boarding secondary schools. The following recommendations are made from the study: a) Mathematics teachers have to inculcate positive attitude classroom environment for better achievement since attitude is direct to achievement. b) Anxiety is indirect to achievement therefore mathematics teachers have to create friendly learning environment that avoid students being anxious toward mathematics. c) Mathematics teachers need to guide students through solving mathematics problems in order they develop self-confidence since confidence is direct to achievement. Lastly, the researcher suggested further research to be done on the impact of special teaching methods for students with negative attitudes, high anxiety and low confidence towards mathematics; effect of group discussion for female students with positive attitudes, low anxiety and high confidence towards mathematics under guidance; and effect of teachers` affective factors towards teaching and achievement in mathematics among students.

CHAPTER ONE:

INTRODUCTION

1.0   Introduction.

This chapter presents the background to the study; Statement of the problem; Purpose and objectives of the study; Research hypothesis; Significance of the study; Delimitation and limitations; Assumptions; Theoretical and Conceptual framework; and Operational definition of terms.

1.1   Background to the Study.

Learning Mathematics is a cognitive endeavor. Yet, in mathematics, as in other cognitive fields, affect can play an important role in students’ decisions about how much mathematics they will need in the future and how they approach the mathematical content they do study. In this study, affective referred to emotional behaviors or actions driven by students` feelings about mathematics, aspects of classroom, or about themselves as learners of mathematics. The definition was not intended to limit the affective domain to general feelings such as liking/disliking of mathematics, nor was it meant to exclude perceptions of the difficulty, usefulness, and appropriateness of mathematics as a school subject (Asheraft, 2001).

In fact, a major reason for studying affective factors in mathematics education is to find ways to help students learn more mathematics (Andrej’s, 2015). Another reason to study affective variables is that a positive attitude toward mathematics is an important educational outcome, regardless of achievement level. However, this study did not advocate on positive attitude per se but how attitude, anxiety and confidence affects the students’ achievement in mathematics (Papanastatsiou, 2000). These affective variables are important in influencing the learning environment in a classroom. Students’ willingness to work on a variety of mathematics tasks and

their persistence in dealing with these tasks might make a difference in the degree to which a class is task-oriented and easy to motivate. Decisions about how many and which mathematics courses to take in middle school, high school, and college can be influenced by student affective characteristics developed over a period of many years (Ma & Kishor, 1997). Therefore course background plus these same affective factors can affect mathematics career related choice (Hyde,2006; Saha, 1994).

Studies have stated causes of the gender differences in mathematics attitude were found to be multifaceted. Researchers have identified parental and societal attitudes (Papanastatsiou, 2000; Wong, 1992), and students` classroom experiences (Fisher and Rickards, 1998; Forgasz and Leder, 1996) as being influential in making female students internalize the feeling that they are inferior to boys in mathematics. Also the studies have considered that the behaviors of the teachers in the classroom environments is a factor associated with the attitudes of the students. Fisher and Rickards (1998) found that students` attitudes towards mathematics tended to be more positive in classrooms where students perceived greater leadership and helping or friendly behaviors in their teachers, and more negative in classrooms where students perceived their teachers as admonishing and enforcing strict behaviors.

In Jamaica, poor attitude to mathematics as a subject evident and view the subject as being little or no use outside schools as according to the Ministry of Education, Youth & Culture (2003). In South Africa, Mji and Makgato (2006) pointed out that those who take mathematics do not perform well because they are not motivated. Yega (2002): teachers, students and parents have negative attitude towards teaching and learning of mathematics. Chiriswa (2003) agreed with the above view and recommended that mathematics teachers and students be given incentives to raise their moral for better grades in mathematics.

Nigeria has not yet able to identify a single direction of difference in achievement in mathematics between female and male students (Kadiri, 2004). Although most studies have found boys performing better (Fennema & Sherman, 1978); a few others saw girls out- performing boys while others established no significant difference. Supported by Alao & Adeleke (2000) that girl’s recorded low performance than boys in mathematical activities in Nigeria Secondary School. This was supported by Manger (1996) in Norway who had same view, but observed that the difference was small. For New Zealand, Blith, Forbes, Clerk and Robinson (1994) reported a consistent difference in performance in favor of boys while Armstrong (1981) noted that sex difference existed at high level and not at the junior level in mathematics achievement, thus a problem to be studied.

For traditional African systems, informal education tended to be more of gender disparities rather than of affective considerations. The co-opting of girls into boys schools (Knight, 1999) was adopted over time due to civil pressure and advocacy for the recognition of equal rights of the girl child in education. This was evidenced by the general results of study for year 1999 to 2001 of a sample of 1489 candidates in 4 secondary schools in Nakuru District, Kenya indicated that streaming based on gender improved overall student achievement in mathematics and especially that of girls.

With Costello (1991) view that boys are impulsive, holistic in approach, field independent, have convergent attributes and are confident. While girls are reflective, serials, field dependent, divergent in thinking and cautious in the process of dealing with matters (Mondoh, 2001). These different cognitive attributes affect boys and girls differently, especially with regard to confidence levels, attitudes, anxiety, ability to take risks, interaction and intellectual dexterity. However, not all but only some of these attributes favor boys more compared to girls with

respect to learning and understanding mathematics (Fawe, 1998; Changeiywo, 2000). This explains why, given a similar age cohort of students, boys are more likely to be good in science and mathematics compared to girls. However, separation of classes based on gender may not be a viable option to effective management of curriculum implementation at the school level as regard to mathematics teaching and examination. This area is still a rich ground for in-depth studies and investigation as a policy option.

Furthermore, the public secondary schools in Ganze District, Kilifi County Kenya, have been performing poorly in mathematics for the last three years as shown in Table 1.1 below.

Key: Mixed Day (MD), Mixed Boarding (MB), Boarding Boys (BB), Boarding Girls (BG), Boys (B), Girls (G).

Table 1.1: KCSE Ganze District Mathematics Performance 2012 to 2014

S/ N O	SCHO- OL	T Y P	EN- TR- Y	2014 GRADE DISTRIBUSTION & MEAN SCORE	MEANS
A	A –	B +	B	B –	C +	C	C –	D +	D	D-	E	MS	2013	2012
1	Godoma	M B	71B	2	0	2	1	3	4	4	8	5	23	17	2	3.81	4.06 D+	3.25 D
47G	1	0	1	2	1	4	2	6	4	16	6	4	4.21
2	Sokoke	B B	87	2	1	0	3	3	2	3	5	10	17	23	18	3.43	3.34 D	3.26 D
3	Ganze	B B	60	0	1	2	1	1	1	1	1	3	11	19	18	1.96	2.67 D	1.78 D-
4	Jila	M D	16B	0	0	0	0	1	0	1	1	1	6	0	6	3.00	2.77 D	2.81 D
11G	0	0	0	0	0	1	1	0	1	4	1	3	2.00
5	Ganze	B G	60	0	0	0	0	1	0	3	3	3	20	22	8	2.75	2.72 D	2.81 D
6	Jaribuni	M B	64B	0	2	0	1	1	1	2	1	2	4	19	30	2.36	2.32 D-	2.40 D-
42G	0	0	1	0	1	0	1	2	7	6	6	18	2.62
7	Vitenge- ni	M B	78B	2	0	0	1	0	1	2	3	3	8	20	38	2.32	1.87 D-	2.75 D
52G	0	1	0	1	1	1	0	2	3	6	15	22	2.44
8	Dungicha	M D	10B	0	0	0	0	0	0	1	0	0	1	2	6	1.9	NEW
6G	0	0	0	1	0	0	0	0	0	1	1	3	2.83
9	Bale	M B	15B	0	0	0	0	0	1	0	0	0	3	5	6	2.13	2.21 D-	2.06 D-
10G	0	0	0	0	0	0	0	0	1	2	4	3	2.1
10	Kachoro- roni	M D	20B	0	0	1	0	0	0	0	1	0	1	6	11	1.55	1.43 E	1.65 D-
13G	0	0	0	0	0	1	0	0	0	1	4	7	1.92
11	Mwange- a	B G	38	0	0	0	0	2	0	0	0	0	3	17	16	1.97	2.0 D-	1.87 D-
12	Mitanga- ni	M D	26B	0	0	0	1		0	0	0	1	3	5	16	1.81	2.25 E	2.64 D
17G	0	0	0	0	1	0	0	0	0	2	4	10	1.88
13	Bandari	M D	13B	0	0	0	0	0	0	0	2	1	1	1	8	2.08	2.86 D	NEW
8G	0	0	0	0	0	0	0	0	0	1	2	5	1.5
14	Magogo- ni	M D	19B	0	0	0	0	0	0	0	2	0	1	5	11	1.79	1.84 D-	2.16 D-
12G	0	0	0	0	0	0	0	0	1	1	2	8	1.58
15	Shangw- eni	M D	11B	0	0	0	0	0	1	0	0	0	1	3	6	2.0	1.87 D-	1.82 D-
7G	0	0	0	0	0	0	0	0	0	1	2	4	2.14
16	Sosoni	M D	9B	0	0	0	0	0	0	0	0	0	2	2	5	1.67	NEW
4G	0	0	0	0	0	0	0	0	1	1	0	2	2.25
17	Vyamba- ni	M D	13B	0	0	0	0	1	0	0	0	1	1	1	9	2.0	1.22 E	0.783 E
10G	0	0	0	0	0	0	0	0	1	1	2	6	1.7
18	Palakumi	M D	11B	0	0	0	0	0	0	0	0	0	1	1	9	1.27	1.6 D-	1.94 D-
7G	0	0	0	0	0	0	0	0	0	0	1	6	1.14
19	Petanguo	M D	11B	0	0	0	0	0	0	0	1	1	1	1	7	1.91	2.41 D-	3.25 D
8G	0	0	0	0	0	0	0	0	0	1	2	5	1.5
20	Mayowe	M D	23B	0	0	0	0	0	0	0	0	0	2	3	18	1.30	NEW
15G	0	0	0	0	0	0	0	0	0	2	1	12	1.33
TOTALS	934	7	5	7	1 2	1 6	1 8	2 1	3 8	47	15 5	23 0	36 6	2.22 E	2.32 E	2.33 E

Source: DEO, Ganze 2014

The trend above indicates poor mathematics achievements among students. Most mixed day girls performed higher than boys at minimal range due to their low enrollment. For mixed boarding girls outweigh boys at wide range as are taught in separated classes based on their gender. Boys indicated higher achievement in mathematics than girls in single sex boarding schools. Researches within Ganze District identified problem of the students` poor achievement in mathematics was attributed to gender differences, academic abilities, school management committees and teacher motivation. DEO (2012) and other educational stakeholders addressed the problem by improving decision making, recognition, working conditions and supervision such as transferring and re-distributing 54 teachers within Ganze District based on their genders and abilities but yet low mathematics trends.

Unfortunately little research in this area has been carried out in Ganze district one of poorest districts located in semi-arid part of Kenya. Researches done in Ganze have only so far focused on constraints in the implementation of free primary education, biological differences, school management committees and teacher motivation to explain the poor mathematics achievement in Ganze but neglecting affective factors and mathematics achievement. This study area has not yet been carried out in the larger Kilifi County in which Ganze district lies. On the bases of such, this study sought to establish the relationship between affective factors and students` achievement in mathematics in Ganze District, Kilifi County.

1.2   Statement of the Problem.

A meta-analysis of gender comparisons of mathematics attitudes and affect, published on 28^th July 2006 by the Department of Psychology, Curriculum and Instruction in University of Wisconsin-Madison, WI53706, USA, revealed that the diminishing of male domain stereotyped attitudes of -0.90 effect size proves mathematics is no longer a male domain subject. This indicates we cannot relate on gender differences and academic abilities in explaining the substantial underrepresentation of females in advanced mathematics classrooms and mathematics related careers. Furthermore, studies posit that separation of classes based on gender may not be a viable option to effective management of curriculum implementation at school level as regard to mathematics teaching and examination.

Researches about affective influence on student achievement failed to explain the underrepresentation of females in advanced mathematics classroom and related careers but focused on, “classroom environments to infer that teachers` classroom behavior is a factor associated with students` attitudes. The studies found that students` attitudes towards mathematics tended to be more positive in classrooms where students perceived greater leadership and helping or friendly behaviors in their teachers, and more negative in classrooms where students perceived their teachers as admonishing and enforcing strict behaviors”.

This study was carried out in Ganze one of the poorest and semi-arid regions of Kenya neglected in terms of research and developments. The region holds strong negative view on the advancement of females which is not the case in this study of affective factors and mathematics achievement. Even Ganze District educational stakeholders have continuously addressed the problem of performing poorly in mathematics based on their genders and abilities. This study has not been done in Ganze District that why the need to study on the relationship between affective

factors (attitude, anxiety and confidence) and students` achievement in mathematics in Ganze District, Kilifi County.

1.2.1    Purpose of Study.

The purpose of this study was to establish the relationship between affective factors and achievement in mathematics among secondary school students in Ganze District, Kilifi County Kenya. It aimed at establishing the relationship of attitude, anxiety and confidence with mathematics achievement beyond gender differences and academic abilities. This is because the study was motivated by the underrepresentation of females in advanced mathematics levels such as in higher education and related careers.

1.2.2    Objectives.

Specifically the purpose of this study was:

1. To establish the relationship between student attitude and mathematics achievement.

1. To establish the relationship between student anxiety and mathematics achievement.

1. To assess the effect of confidence on mathematics achievement.

1.2.3    Research Hypothesis.

The null hypothesis of this study was, “There is no statistical significant relationship between affective factors and students` achievement in mathematics”.

1.2.4    Research Questions.

The following questions were used in this research:

1. How is attitude as an affective factor influence mathematics achievement?

1. To what extend is anxiety relevant in mathematics achievement as an affective factor?

1. What are the determinants of confidence as an affective factor in mathematics achievement?

1.3   Significance of the Study (Rationale).

The findings of this study are important to all stakeholders in education such as Ministry of Education (MOE), Teacher Service Commission (TSC), policy makers, school management, teachers and students. It is hoped that this study would inform correctly the students’ achievement on mathematics basing on affective factors rather than biological differences which is outdated. The study findings are of great help to the education system, supervisors, quality assurance officers, serving principals, teachers, students, community and teaching fraternity in general. This would form a base of addressing the trending low mathematics achievement successful basing on affective factors. For the improvement of teaching-learning practice and development of knowledge is hoped to be contributed much by the affective factors on the attributes of ability, task difficulty, effort and luck towards high mathematics achievement.

1.4   Delimitation and Limitations.

1.4.1    Delimitation.

This study addressed the relationship between affective factors and achievement in mathematics among secondary school students in Ganze District, Kilifi County Kenya. This study targeted mainly the mixed day secondary schools in the above mentioned locality. It also included some boarding and single sex schools for comparison of findings to enrich the discussion. The study involved Correlation Analysis to quantify the data collected. The computational formula of Pearson Product moment correlation coefficient (r_xy) indicated the statistical significant correlation value for either accepting or rejecting the null hypothesis. It did not use interview schedules nor observation forms; because already in-depth study on gender differences has been done basing on knowledgeable expertise but excluding affective factors in the secondary schools through questionnaires on students. The implication of narrowing the scope was to specifically address the actual gap of not being able to explain and manage the problem posed by

underrepresentation of females in advanced mathematics careers, other subjects and levels of education without considering gender differences and academic abilities.

1.4.2    Limitations.

The limitations of this study include high transport costs due to remoteness, inadequate funding of the research and limited time due to other school activities. Through sponsorship and adequate time a larger sample size was covered.

1.5   Assumptions.

The study assumed that:

1. The respondents provided accurate and honest responses to the questionnaires.

1. The students in Form Three had learned the same amount of content of mathematics as prescribed by KIE syllabus for mathematics.
2. Among all other factors that influence learning of mathematics among secondary school students; attitude, anxiety and confidence played major role in students` achievement in mathematics.

These issues were assumed to be constant in all sampled schools thus taken for granted in the conduct of this study.

1.6   Theoretical and Conceptual Framework.

1.6.1    Theoretical Framework.

This study considered the Attribution theory developed by Weiner (1974). Within social psychology, attribution theory is a large, quickly growing area of research that deals with what a person perceives as the cause of certain events. In the educational research literature these attributions are concerned with causes of success and failure in school-related tasks. The theoretical underpinnings for attributions of academic success and failure are found both in the

general attribution theory literature and the achievement motivation literature. Mathematics education research concerning attributions deals with students’ and teachers’ perceptions of the causes of student success or failure on mathematics tasks. This was developed mainly to help understand gender-related differences in mathematics achievement and course selection.

Attribution Theory attempts to explain the world and to determine the cause of an event or behavior (e.g. why people do what they do) originated by Bernard Weiner (1935- ) with Key terms: Attribution, locus of control, stability, and controllability. Attribution Theory (Weiner) indicated that Weiner developed a theoretical framework that has become very influential in social psychology today. Attribution theory assumes that people try to determine why people do what they do, that is, interpret causes to an event or behavior. A three-stage process underlies an attribution:

1. behavior must be observed/perceived

1. behavior must be determined to be intentional

1. behavior attributed to internal or external causes

Weiner’s attribution theory is mainly about achievement. According to him, the most important factors affecting attributions are ability, effort, task difficulty, and luck. Attributions are classified along three causal dimensions:

1. Locus of control (two poles: internal vs. external)

1. Stability (do causes change over time or not?)

1. Controllability (causes one can control such as skills vs. causes one cannot control such as luck, others’ actions, etc.)

When one succeeds, one attributes successes internally (“my own skill”). When a rival succeeds, one tends to credit external (e.g. luck). When one fails or makes mistakes, we will more likely use external attribution, attributing causes to situational factors rather than blaming ourselves. When others fail or make mistakes, internal attribution is often used, saying it is due to their internal personality factors.

Mathematics education attribution research as developed by Weiner (1974) uses a formulation of attribution of academic success and failure. Weiner proposes a two-dimensional model with four major causes of success and failure (ability, effort, task difficulty, and luck) organized in a 2×2 matrix table 1.2 below:

Table 1.2 Attributions of Success and Failure (from Weiner 1974).

Stability                                                           Locus of control Internal                                            External

Stable                                           ability                                                  task difficulty Unstable                                        effort                                                         luck

The two dimensions are locus of control and stability. Locus of control relates to whether the cause of success or failure is perceived to result from some factor within or outside of the individual; stability is concerned with whether the cause can change for an individual from one time to another. Since ability is the same from one time to another and is due to a factor within a person, it is categorized as stable and internal. Effort is internal and unstable because the individual has control over effort and may vary the effort expended in different situations. Task difficulty is stable, because a given task does not change in difficulty from one situation to another. Task difficulty is also external, since a person has no control over it. Luck changes from

time to time and is independent of the individual; therefore, it is classified as unstable and external.

Therefore the theory is much relevant to this study because affective factors (attitude, anxiety and confidence) roots on person’s perception about his/her success and failure. When a person perceives the cause of success and failure as stable (ability or task difficulty), the change in expectations will be greater than when unstable factors (effort or luck) are seen as the cause. For example, when success is attributed to ability or ease of the task, the increase in expectancy for future success in that situation will be larger than if the success had been attributed to good luck. Similarly, when failure is seen as caused by low ability, the drop in expectancy for future performance is greater than when failure is attributed to lack of effort or bad luck. On the average, females and males seem to differ in their patterns of attribution of success and failure. In academic achievement situations, girls are more likely to see success as caused by effort and less likely to see success as caused by ability than are boys. In failure situations, girls are more likely than boys to attribute their failure to lack of ability than lack of effort. However, these gender differences in attributions are not large and will be more pronounced when the task is gender-stereotyped.

1.6.2    Conceptual Framework.

The graphic presentation of this study as shown in the figure below have independent variable: affective factors – mathematics attitude, mathematics anxiety and mathematics confidence; with dependent variable: mathematics achievement.

Figure 1.1 Conceptual Framework, Source: Adapted from Fennema & Sherman (1977).

From the conceptual framework, Figure 1.1, the students` achievement in the mathematics test depends on the independent and intervening variables. This is because the independent variables are the influencing factors which include the affective factors (attitude, anxiety and confidence) that were being explored in this study while relating their impact on the students` achievement of the mathematics test subjected to them. Therefore since it involved the mathematics classroom context, then intervening variables such as teaching techniques, individual differences, competition and indiscipline were put in consideration during the study.

Therefore since attribution is a three stage process: (1) behavior is observed, (2) behavior is determined to be deliberate, and (3) behavior is attributed to internal or external causes; then it can be relatively inferred that attitude, anxiety and confidence are behavioral too. As

achievement can be attributed to (1) effort, (2) ability, (3) level of task difficulty, or (4) luck; as well as intervened by other learning factors such as entry behavior, resources, teaching techniques and subject assessment.

ABSTRACT

Learning mathematics is a cognitive as well as affective endeavor with the affective factors playing major role in student achievement. The main purpose of this study was to examine the relationship between affective factors and students’ achievement in Mathematics in Ganze District, Kilifi County Kenya. Study was motivated by underrepresentation of females in advanced mathematics levels and related careers. The study was guided by the following three specific objectives: to establish the relationship between student attitude and mathematics achievement, to establish the relationship between student anxiety and mathematics achievement, and to assess the effect of confidence on mathematics achievement. This study employed descriptive survey research design. Target population comprised of both male and female students from secondary schools in Ganze District. The district had 4 zones with a total of 1620 male students and 1080 female students within the 20 schools among which 12 were mixed day secondary schools, 4 boarding schools and 4 single sex schools. Proportional stratified random sampling was done to ensure at least 50% of the schools were sampled from every zone. The study had a stratified sampled size of 250 students; mainly form 4 and 3 students of which 150 were male and 100 female. The affective factors (attitude, anxiety, confidence) formed the independent variables, learning factors in mathematics class room as intervening variables and mathematics achievement as the dependent variable. The valid and reliable research instruments included mathematics attitude questionnaire, mathematics anxiety rating scale, mathematics confidence questionnaire and mathematics test. Data were analyzed using SPSS program of IBM 2015 American version and presented in text and tabular forms. The mode of analysis mainly involved Correlational Analysis of Pearson Product moment correlation coefficient (r_xy) indicating the statistical significant correlation value for either accepting or rejecting the null hypothesis, “there is no statistical significant relationship between affective factors and students’ achievement in mathematics”. The findings revealed females outweigh males at higher positive attitude; males outweigh females in lower anxiety; but no disparity in confidence. The researcher concluded attitude and confidence are directly proportional to mathematics achievement but anxiety is indirectly proportional. The relationship between affective factors and students’ achievement in mathematics is beyond gender differences and academic abilities; for females outweigh males in mixed day, males outweigh females in mixed boarding but no disparity in single sex boarding secondary schools. The following recommendations are made from the study: a) Mathematics teachers have to inculcate positive attitude classroom environment for better achievement since attitude is direct to achievement. b) Anxiety is indirect to achievement therefore mathematics teachers have to create friendly learning environment that avoid students being anxious toward mathematics. c) Mathematics teachers need to guide students through solving mathematics problems in order they develop self-confidence since confidence is direct to achievement. Lastly, the researcher suggested further research to be done on the impact of special teaching methods for students with negative attitudes, high anxiety and low confidence towards mathematics; effect of group discussion for female students with positive attitudes, low anxiety and high confidence towards mathematics under guidance; and effect of teachers` affective factors towards teaching and achievement in mathematics among students.

CHAPTER ONE:

INTRODUCTION

1.0   Introduction.

This chapter presents the background to the study; Statement of the problem; Purpose and objectives of the study; Research hypothesis; Significance of the study; Delimitation and limitations; Assumptions; Theoretical and Conceptual framework; and Operational definition of terms.

1.1   Background to the Study.

Learning Mathematics is a cognitive endeavor. Yet, in mathematics, as in other cognitive fields, affect can play an important role in students’ decisions about how much mathematics they will need in the future and how they approach the mathematical content they do study. In this study, affective referred to emotional behaviors or actions driven by students` feelings about mathematics, aspects of classroom, or about themselves as learners of mathematics. The definition was not intended to limit the affective domain to general feelings such as liking/disliking of mathematics, nor was it meant to exclude perceptions of the difficulty, usefulness, and appropriateness of mathematics as a school subject (Asheraft, 2001).

In fact, a major reason for studying affective factors in mathematics education is to find ways to help students learn more mathematics (Andrej’s, 2015). Another reason to study affective variables is that a positive attitude toward mathematics is an important educational outcome, regardless of achievement level. However, this study did not advocate on positive attitude per se but how attitude, anxiety and confidence affects the students’ achievement in mathematics (Papanastatsiou, 2000). These affective variables are important in influencing the learning environment in a classroom. Students’ willingness to work on a variety of mathematics tasks and

their persistence in dealing with these tasks might make a difference in the degree to which a class is task-oriented and easy to motivate. Decisions about how many and which mathematics courses to take in middle school, high school, and college can be influenced by student affective characteristics developed over a period of many years (Ma & Kishor, 1997). Therefore course background plus these same affective factors can affect mathematics career related choice (Hyde,2006; Saha, 1994).

Studies have stated causes of the gender differences in mathematics attitude were found to be multifaceted. Researchers have identified parental and societal attitudes (Papanastatsiou, 2000; Wong, 1992), and students` classroom experiences (Fisher and Rickards, 1998; Forgasz and Leder, 1996) as being influential in making female students internalize the feeling that they are inferior to boys in mathematics. Also the studies have considered that the behaviors of the teachers in the classroom environments is a factor associated with the attitudes of the students. Fisher and Rickards (1998) found that students` attitudes towards mathematics tended to be more positive in classrooms where students perceived greater leadership and helping or friendly behaviors in their teachers, and more negative in classrooms where students perceived their teachers as admonishing and enforcing strict behaviors.

In Jamaica, poor attitude to mathematics as a subject evident and view the subject as being little or no use outside schools as according to the Ministry of Education, Youth & Culture (2003). In South Africa, Mji and Makgato (2006) pointed out that those who take mathematics do not perform well because they are not motivated. Yega (2002): teachers, students and parents have negative attitude towards teaching and learning of mathematics. Chiriswa (2003) agreed with the above view and recommended that mathematics teachers and students be given incentives to raise their moral for better grades in mathematics.

Nigeria has not yet able to identify a single direction of difference in achievement in mathematics between female and male students (Kadiri, 2004). Although most studies have found boys performing better (Fennema & Sherman, 1978); a few others saw girls out- performing boys while others established no significant difference. Supported by Alao & Adeleke (2000) that girl’s recorded low performance than boys in mathematical activities in Nigeria Secondary School. This was supported by Manger (1996) in Norway who had same view, but observed that the difference was small. For New Zealand, Blith, Forbes, Clerk and Robinson (1994) reported a consistent difference in performance in favor of boys while Armstrong (1981) noted that sex difference existed at high level and not at the junior level in mathematics achievement, thus a problem to be studied.

For traditional African systems, informal education tended to be more of gender disparities rather than of affective considerations. The co-opting of girls into boys schools (Knight, 1999) was adopted over time due to civil pressure and advocacy for the recognition of equal rights of the girl child in education. This was evidenced by the general results of study for year 1999 to 2001 of a sample of 1489 candidates in 4 secondary schools in Nakuru District, Kenya indicated that streaming based on gender improved overall student achievement in mathematics and especially that of girls.

With Costello (1991) view that boys are impulsive, holistic in approach, field independent, have convergent attributes and are confident. While girls are reflective, serials, field dependent, divergent in thinking and cautious in the process of dealing with matters (Mondoh, 2001). These different cognitive attributes affect boys and girls differently, especially with regard to confidence levels, attitudes, anxiety, ability to take risks, interaction and intellectual dexterity. However, not all but only some of these attributes favor boys more compared to girls with

respect to learning and understanding mathematics (Fawe, 1998; Changeiywo, 2000). This explains why, given a similar age cohort of students, boys are more likely to be good in science and mathematics compared to girls. However, separation of classes based on gender may not be a viable option to effective management of curriculum implementation at the school level as regard to mathematics teaching and examination. This area is still a rich ground for in-depth studies and investigation as a policy option.

Furthermore, the public secondary schools in Ganze District, Kilifi County Kenya, have been performing poorly in mathematics for the last three years as shown in Table 1.1 below.

Key: Mixed Day (MD), Mixed Boarding (MB), Boarding Boys (BB), Boarding Girls (BG), Boys (B), Girls (G).

Table 1.1: KCSE Ganze District Mathematics Performance 2012 to 2014

S/ N O	SCHO- OL	T Y P	EN- TR- Y	2014 GRADE DISTRIBUSTION & MEAN SCORE	MEANS
A	A –	B +	B	B –	C +	C	C –	D +	D	D-	E	MS	2013	2012
1	Godoma	M B	71B	2	0	2	1	3	4	4	8	5	23	17	2	3.81	4.06 D+	3.25 D
47G	1	0	1	2	1	4	2	6	4	16	6	4	4.21
2	Sokoke	B B	87	2	1	0	3	3	2	3	5	10	17	23	18	3.43	3.34 D	3.26 D
3	Ganze	B B	60	0	1	2	1	1	1	1	1	3	11	19	18	1.96	2.67 D	1.78 D-
4	Jila	M D	16B	0	0	0	0	1	0	1	1	1	6	0	6	3.00	2.77 D	2.81 D
11G	0	0	0	0	0	1	1	0	1	4	1	3	2.00
5	Ganze	B G	60	0	0	0	0	1	0	3	3	3	20	22	8	2.75	2.72 D	2.81 D
6	Jaribuni	M B	64B	0	2	0	1	1	1	2	1	2	4	19	30	2.36	2.32 D-	2.40 D-
42G	0	0	1	0	1	0	1	2	7	6	6	18	2.62
7	Vitenge- ni	M B	78B	2	0	0	1	0	1	2	3	3	8	20	38	2.32	1.87 D-	2.75 D
52G	0	1	0	1	1	1	0	2	3	6	15	22	2.44
8	Dungicha	M D	10B	0	0	0	0	0	0	1	0	0	1	2	6	1.9	NEW
6G	0	0	0	1	0	0	0	0	0	1	1	3	2.83
9	Bale	M B	15B	0	0	0	0	0	1	0	0	0	3	5	6	2.13	2.21 D-	2.06 D-
10G	0	0	0	0	0	0	0	0	1	2	4	3	2.1
10	Kachoro- roni	M D	20B	0	0	1	0	0	0	0	1	0	1	6	11	1.55	1.43 E	1.65 D-
13G	0	0	0	0	0	1	0	0	0	1	4	7	1.92
11	Mwange- a	B G	38	0	0	0	0	2	0	0	0	0	3	17	16	1.97	2.0 D-	1.87 D-
12	Mitanga- ni	M D	26B	0	0	0	1		0	0	0	1	3	5	16	1.81	2.25 E	2.64 D
17G	0	0	0	0	1	0	0	0	0	2	4	10	1.88
13	Bandari	M D	13B	0	0	0	0	0	0	0	2	1	1	1	8	2.08	2.86 D	NEW
8G	0	0	0	0	0	0	0	0	0	1	2	5	1.5
14	Magogo- ni	M D	19B	0	0	0	0	0	0	0	2	0	1	5	11	1.79	1.84 D-	2.16 D-
12G	0	0	0	0	0	0	0	0	1	1	2	8	1.58
15	Shangw- eni	M D	11B	0	0	0	0	0	1	0	0	0	1	3	6	2.0	1.87 D-	1.82 D-
7G	0	0	0	0	0	0	0	0	0	1	2	4	2.14
16	Sosoni	M D	9B	0	0	0	0	0	0	0	0	0	2	2	5	1.67	NEW
4G	0	0	0	0	0	0	0	0	1	1	0	2	2.25
17	Vyamba- ni	M D	13B	0	0	0	0	1	0	0	0	1	1	1	9	2.0	1.22 E	0.783 E
10G	0	0	0	0	0	0	0	0	1	1	2	6	1.7
18	Palakumi	M D	11B	0	0	0	0	0	0	0	0	0	1	1	9	1.27	1.6 D-	1.94 D-
7G	0	0	0	0	0	0	0	0	0	0	1	6	1.14
19	Petanguo	M D	11B	0	0	0	0	0	0	0	1	1	1	1	7	1.91	2.41 D-	3.25 D
8G	0	0	0	0	0	0	0	0	0	1	2	5	1.5
20	Mayowe	M D	23B	0	0	0	0	0	0	0	0	0	2	3	18	1.30	NEW
15G	0	0	0	0	0	0	0	0	0	2	1	12	1.33
TOTALS	934	7	5	7	1 2	1 6	1 8	2 1	3 8	47	15 5	23 0	36 6	2.22 E	2.32 E	2.33 E

Source: DEO, Ganze 2014

The trend above indicates poor mathematics achievements among students. Most mixed day girls performed higher than boys at minimal range due to their low enrollment. For mixed boarding girls outweigh boys at wide range as are taught in separated classes based on their gender. Boys indicated higher achievement in mathematics than girls in single sex boarding schools. Researches within Ganze District identified problem of the students` poor achievement in mathematics was attributed to gender differences, academic abilities, school management committees and teacher motivation. DEO (2012) and other educational stakeholders addressed the problem by improving decision making, recognition, working conditions and supervision such as transferring and re-distributing 54 teachers within Ganze District based on their genders and abilities but yet low mathematics trends.

Unfortunately little research in this area has been carried out in Ganze district one of poorest districts located in semi-arid part of Kenya. Researches done in Ganze have only so far focused on constraints in the implementation of free primary education, biological differences, school management committees and teacher motivation to explain the poor mathematics achievement in Ganze but neglecting affective factors and mathematics achievement. This study area has not yet been carried out in the larger Kilifi County in which Ganze district lies. On the bases of such, this study sought to establish the relationship between affective factors and students` achievement in mathematics in Ganze District, Kilifi County.

1.2   Statement of the Problem.

A meta-analysis of gender comparisons of mathematics attitudes and affect, published on 28^th July 2006 by the Department of Psychology, Curriculum and Instruction in University of Wisconsin-Madison, WI53706, USA, revealed that the diminishing of male domain stereotyped attitudes of -0.90 effect size proves mathematics is no longer a male domain subject. This indicates we cannot relate on gender differences and academic abilities in explaining the substantial underrepresentation of females in advanced mathematics classrooms and mathematics related careers. Furthermore, studies posit that separation of classes based on gender may not be a viable option to effective management of curriculum implementation at school level as regard to mathematics teaching and examination.

Researches about affective influence on student achievement failed to explain the underrepresentation of females in advanced mathematics classroom and related careers but focused on, “classroom environments to infer that teachers` classroom behavior is a factor associated with students` attitudes. The studies found that students` attitudes towards mathematics tended to be more positive in classrooms where students perceived greater leadership and helping or friendly behaviors in their teachers, and more negative in classrooms where students perceived their teachers as admonishing and enforcing strict behaviors”.

This study was carried out in Ganze one of the poorest and semi-arid regions of Kenya neglected in terms of research and developments. The region holds strong negative view on the advancement of females which is not the case in this study of affective factors and mathematics achievement. Even Ganze District educational stakeholders have continuously addressed the problem of performing poorly in mathematics based on their genders and abilities. This study has not been done in Ganze District that why the need to study on the relationship between affective

factors (attitude, anxiety and confidence) and students` achievement in mathematics in Ganze District, Kilifi County.

1.2.1    Purpose of Study.

The purpose of this study was to establish the relationship between affective factors and achievement in mathematics among secondary school students in Ganze District, Kilifi County Kenya. It aimed at establishing the relationship of attitude, anxiety and confidence with mathematics achievement beyond gender differences and academic abilities. This is because the study was motivated by the underrepresentation of females in advanced mathematics levels such as in higher education and related careers.

1.2.2    Objectives.

Specifically the purpose of this study was:

1. To establish the relationship between student attitude and mathematics achievement.

1. To establish the relationship between student anxiety and mathematics achievement.

1. To assess the effect of confidence on mathematics achievement.

1.2.3    Research Hypothesis.

The null hypothesis of this study was, “There is no statistical significant relationship between affective factors and students` achievement in mathematics”.

1.2.4    Research Questions.

The following questions were used in this research:

1. How is attitude as an affective factor influence mathematics achievement?

1. To what extend is anxiety relevant in mathematics achievement as an affective factor?

1. What are the determinants of confidence as an affective factor in mathematics achievement?

1.3   Significance of the Study (Rationale).

The findings of this study are important to all stakeholders in education such as Ministry of Education (MOE), Teacher Service Commission (TSC), policy makers, school management, teachers and students. It is hoped that this study would inform correctly the students’ achievement on mathematics basing on affective factors rather than biological differences which is outdated. The study findings are of great help to the education system, supervisors, quality assurance officers, serving principals, teachers, students, community and teaching fraternity in general. This would form a base of addressing the trending low mathematics achievement successful basing on affective factors. For the improvement of teaching-learning practice and development of knowledge is hoped to be contributed much by the affective factors on the attributes of ability, task difficulty, effort and luck towards high mathematics achievement.

1.4   Delimitation and Limitations.

1.4.1    Delimitation.

This study addressed the relationship between affective factors and achievement in mathematics among secondary school students in Ganze District, Kilifi County Kenya. This study targeted mainly the mixed day secondary schools in the above mentioned locality. It also included some boarding and single sex schools for comparison of findings to enrich the discussion. The study involved Correlation Analysis to quantify the data collected. The computational formula of Pearson Product moment correlation coefficient (r_xy) indicated the statistical significant correlation value for either accepting or rejecting the null hypothesis. It did not use interview schedules nor observation forms; because already in-depth study on gender differences has been done basing on knowledgeable expertise but excluding affective factors in the secondary schools through questionnaires on students. The implication of narrowing the scope was to specifically address the actual gap of not being able to explain and manage the problem posed by

underrepresentation of females in advanced mathematics careers, other subjects and levels of education without considering gender differences and academic abilities.

1.4.2    Limitations.

The limitations of this study include high transport costs due to remoteness, inadequate funding of the research and limited time due to other school activities. Through sponsorship and adequate time a larger sample size was covered.

1.5   Assumptions.

The study assumed that:

1. The respondents provided accurate and honest responses to the questionnaires.

1. The students in Form Three had learned the same amount of content of mathematics as prescribed by KIE syllabus for mathematics.
2. Among all other factors that influence learning of mathematics among secondary school students; attitude, anxiety and confidence played major role in students` achievement in mathematics.

These issues were assumed to be constant in all sampled schools thus taken for granted in the conduct of this study.

1.6   Theoretical and Conceptual Framework.

1.6.1    Theoretical Framework.

This study considered the Attribution theory developed by Weiner (1974). Within social psychology, attribution theory is a large, quickly growing area of research that deals with what a person perceives as the cause of certain events. In the educational research literature these attributions are concerned with causes of success and failure in school-related tasks. The theoretical underpinnings for attributions of academic success and failure are found both in the

general attribution theory literature and the achievement motivation literature. Mathematics education research concerning attributions deals with students’ and teachers’ perceptions of the causes of student success or failure on mathematics tasks. This was developed mainly to help understand gender-related differences in mathematics achievement and course selection.

Attribution Theory attempts to explain the world and to determine the cause of an event or behavior (e.g. why people do what they do) originated by Bernard Weiner (1935- ) with Key terms: Attribution, locus of control, stability, and controllability. Attribution Theory (Weiner) indicated that Weiner developed a theoretical framework that has become very influential in social psychology today. Attribution theory assumes that people try to determine why people do what they do, that is, interpret causes to an event or behavior. A three-stage process underlies an attribution:

1. behavior must be observed/perceived

1. behavior must be determined to be intentional

1. behavior attributed to internal or external causes

Weiner’s attribution theory is mainly about achievement. According to him, the most important factors affecting attributions are ability, effort, task difficulty, and luck. Attributions are classified along three causal dimensions:

1. Locus of control (two poles: internal vs. external)

1. Stability (do causes change over time or not?)

1. Controllability (causes one can control such as skills vs. causes one cannot control such as luck, others’ actions, etc.)

When one succeeds, one attributes successes internally (“my own skill”). When a rival succeeds, one tends to credit external (e.g. luck). When one fails or makes mistakes, we will more likely use external attribution, attributing causes to situational factors rather than blaming ourselves. When others fail or make mistakes, internal attribution is often used, saying it is due to their internal personality factors.

Mathematics education attribution research as developed by Weiner (1974) uses a formulation of attribution of academic success and failure. Weiner proposes a two-dimensional model with four major causes of success and failure (ability, effort, task difficulty, and luck) organized in a 2×2 matrix table 1.2 below:

Table 1.2 Attributions of Success and Failure (from Weiner 1974).

Stability                                                           Locus of control Internal                                            External

Stable                                           ability                                                  task difficulty Unstable                                        effort                                                         luck

The two dimensions are locus of control and stability. Locus of control relates to whether the cause of success or failure is perceived to result from some factor within or outside of the individual; stability is concerned with whether the cause can change for an individual from one time to another. Since ability is the same from one time to another and is due to a factor within a person, it is categorized as stable and internal. Effort is internal and unstable because the individual has control over effort and may vary the effort expended in different situations. Task difficulty is stable, because a given task does not change in difficulty from one situation to another. Task difficulty is also external, since a person has no control over it. Luck changes from

time to time and is independent of the individual; therefore, it is classified as unstable and external.

Therefore the theory is much relevant to this study because affective factors (attitude, anxiety and confidence) roots on person’s perception about his/her success and failure. When a person perceives the cause of success and failure as stable (ability or task difficulty), the change in expectations will be greater than when unstable factors (effort or luck) are seen as the cause. For example, when success is attributed to ability or ease of the task, the increase in expectancy for future success in that situation will be larger than if the success had been attributed to good luck. Similarly, when failure is seen as caused by low ability, the drop in expectancy for future performance is greater than when failure is attributed to lack of effort or bad luck. On the average, females and males seem to differ in their patterns of attribution of success and failure. In academic achievement situations, girls are more likely to see success as caused by effort and less likely to see success as caused by ability than are boys. In failure situations, girls are more likely than boys to attribute their failure to lack of ability than lack of effort. However, these gender differences in attributions are not large and will be more pronounced when the task is gender-stereotyped.

1.6.2    Conceptual Framework.

The graphic presentation of this study as shown in the figure below have independent variable: affective factors – mathematics attitude, mathematics anxiety and mathematics confidence; with dependent variable: mathematics achievement.

Figure 1.1 Conceptual Framework, Source: Adapted from Fennema & Sherman (1977).

From the conceptual framework, Figure 1.1, the students` achievement in the mathematics test depends on the independent and intervening variables. This is because the independent variables are the influencing factors which include the affective factors (attitude, anxiety and confidence) that were being explored in this study while relating their impact on the students` achievement of the mathematics test subjected to them. Therefore since it involved the mathematics classroom context, then intervening variables such as teaching techniques, individual differences, competition and indiscipline were put in consideration during the study.

Therefore since attribution is a three stage process: (1) behavior is observed, (2) behavior is determined to be deliberate, and (3) behavior is attributed to internal or external causes; then it can be relatively inferred that attitude, anxiety and confidence are behavioral too. As

achievement can be attributed to (1) effort, (2) ability, (3) level of task difficulty, or (4) luck; as well as intervened by other learning factors such as entry behavior, resources, teaching techniques and subject assessment.

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