ABSTRACT
This study was undertaken to determine the influence of cognitive style and gender on students’ achievement in selected areas of mathematics. The study was motivated by the poor achievement of students in senior secondary school mathematics. The study therefore looked at achievement of male and female students, categorized under field independent and field dependent students in geometry, algebra and statistics. Six research questions and six research hypotheses guided the study. The study adopted the ex-post factor research design. The population of the study consisted of 3,932 SS2 mathematics students of 2011/ 2012 academic year in the five co-education schools of Ogoja Education Zone of Cross river state. The sample of the study is 620 mathematics students selected through multi-stage sampling techniques. The instruments for data collection were Group Embedded figure Test (GEFT) and Mathematics Achievement Test (MAT). Data collected were analyzed using spss (special packages for social sciences) to determine mean, standard deviation and t-Test results. The results of the findings reveal that field independent students achieved better than the field dependent students in geometry, algebra and statistics. There is significant difference in the mean achievement scores of field independent and dependent students in these areas of mathematics. Male students achieved higher than female students in geometry and algebra while in statistics there was no significant difference in achievement of male and female students. There was significant difference in the mean achievements of male and female students in geometry while Gender was a significant factor on students’ achievement in geometry. The results have implications for learners, teachers, and professional bodies. Based on the results some recommendations were made, which include use of instructional materials and techniques that can make males and females develop critical thinking abilities to improve teaching and learning of mathematics. This will help to eliminate gender imbalance in class-room instructions and achievement because the objective of teaching is to make pupil learn or achieve higher irrespective of sex.
CHAPTER ONE
INTRODUCTION
Background Of the study
Mathematics is one of the key subjects at both the primary and secondary school education system in Nigeria. According to the Federal Government of Nigeria (FGN, 2004), mathematics is a compulsory subject taught at the primary and secondary levels of education in Nigeria. Its function and relevance to education and the society makes it to be regarded as the bedrock of science and technological development. In view of this, Okafor (2005) argued that no nation can develop scientifically and technologically without proper foundation in mathematics.
Hardy (2003) posits that mathematics is an aid to representing and attempting to resolve situation in all disciplines. Thompson, (2004) opines that mathematics is a subject that teaches critical thinking and problem solving in a much applied form. Thompson maintained that science and mathematics are two fields of studies that work together, towards the natural and physical relationship with other sciences. This may be why Stroud (2000) stated that mathematics should be seen beyond a subject to be taught and understood by students rather than as a service to other sciences. Therefore, one cannot avoid considering the utilitarian aspects of mathematics in preparing people for useful living. According to Federal Republic of Nigeria (FRN, 2004), the general objective of secondary education is to generate interest in mathematics for everyday living, counting notation, addition, subtraction, multiplication, division, weighing, measuring, selling and buying are some of the simple and fundamental processes of mathematics which have practical value in life. Thus, these cultural goals of mathematics will “foster Nigeria unity with an emphasized interest on the commonties that unite us in our diversity” as well as “develop and protect Nigeria culture…” (2004, P.11).
Mathematics is extensively employed in experimental biology, to resolve statistical problems. According to Akinbuwa (2001), mathematics techniques and methods are closely interlined with biological work in cell growth, enzymatic reactions, physiological tracers, biological fluid dynamics and diffusion all of which follow a course in elementary differential equations, linear algebra or graph theory. Adetula (2002) noted that in medicine, problems that can be tackle using mathematics include; the conduction of electronic signals by nerves, flow of blood, calculations of radiation treatment of patients’ with diffusion of radio active tracers and other chemicals in the body. Mathematics is a language in which scientific ideas are expressed; it is the means by which other sciences including Physics, Chemistry, Biology, and disciplines like Engineering, Geology are understood. Mathematics enables the various sciences to draw the implications of their observational and experimental findings. Mathematics has become so valuable that there is nothing in all human endeavors that does not apply mathematics knowledge. Therefore, scientific knowledge is impossible without a sound knowledge of mathematics. Equally; those who are grounded in mathematics are able to contribute meaningfully to scientific and technological development.
In spite of the importance and usefulness attached to mathematics, Kurumeh (2006) reported that students achieved poorly in public examinations in mathematics. For instance, in Nigeria, in the years 2008, 2009,2010 and 2011 the percentage pass with credit and above in mathematics were 23.0%, 31.0%, 24.94% and 38.98% respectively (Kurumeh & Imoko 2008; Moseri 2010; Iyi 2011). Also, the chief examiner’s report (2008-2011) from West African Examination Council (WAEC) shows that students’ achievement in senior school certificate examination SSCE May/June in Mathematics has not been encouraging. Harbor-Peters (2001), reported that achievement of students in mathematics is as a result of poor and ineffective
instructional skills and methodologies by mathematics teachers. Azurku (2006) and Tukur (2007) noted that mathematics classes in the state secondary schools are over crowded, most times one find a single teacher in a class with about one hundred (100) students which lead to use of ineffective teaching method. John (2003) argues that students’ attitudes towards learning mathematics in Nigeria secondary schools are not encouraging, particularly at junior secondary school which is the background level. Apart from these factors, there are other factors which also contribute to poor achievement in mathematics such as parental attitude towards mathematics, inadequate number or quality teachers to handle the subject particularly at the secondary level and incompetence of teachers to teach some selected areas in mathematics. The major factor is that of teachers not being able to teach some aspects of mathematics concept such as algebra, geometry, trigonometry and Statistics. This incompetences of teachers expose the students to solve mathematics problems any how and thus have a notion that some areas are very difficult to handle. The students thus develop a dislike for some aspects of mathematics
Eraikhuemen (2003) noted that students dislike certain topic because they feel the topics are difficult and could not be understood easily. Some teachers lack techniques and materials in teaching some topics to the extent that if they have a choice they will not teach such topics, also the teachers believe that these topics are difficult and not easy to teach. For these reasons many children in secondary schools experience difficulties in learning some aspects of mathematics in the curriculum. Teachers also experience difficulties in achieving effective teaching in the school system (Habor-Peters, 2002). Mathematics is made up of many branches like probability, statistics, algebra, geometry trigonometry, number numeration and so on. This study specifically covers geometry, statistics and algebra.
Geometry is an aspect of mathematics which deals with the study of geometric objects (shapes, diagrams and curves) which is done through direct observation, description and analysis of spatial distribution of points. It is a special branch of mathematics and it follows that if teachers of mathematics do not have adequate knowledge of geometry, the teaching and learning of mathematics will likely be deficient.
Algebra is an aspect of mathematics which deals with the representation of alphabets to represent numbers. Statistics is another branch of mathematics which is involve with collection, analyzing and interpretation of data. These three selected areas in mathematics may have different influence on students’ cognitive style. That is to say that, a student may be performing better in geometry without performing well in algebra and statistics. This call for the need to explore the influence of cognitive style on students’ achievement in these selected areas.
The situation of poor achievement in mathematics or other science subjects have warranted this study to explore students’ cognitive learning style which may be of benefit in improving achievement in selected areas in mathematics. It has been observed that students have different ways of perceiving and reasoning mathematics concepts based on their mental readiness. In other words, students have different cognitive style which may affect their learning. The word cognitive derived from cognition To understand cognitive style a definition of cognition must first be understood .Cognition is a collection of mental processes that includes awareness, perception, reasoning, and judgment. Cognitive style is an individual way of learning, perceiving, thinking and reasoning . Cognitive psychologist such as Ausubel, Bruner, Gagne and educators (teachers) have been interested in understanding the individual differences in cognition and their impact on learning and instruction (Altun and Cakar, 2006).
Cognitive style is a psychological construct which is concerned with how an individual learns, thinks, remembers, solves problems and relates to others. Pitch (2002), defined cognitive style as the relatively stable strategies, preferences and attitudes that determine an individual’s typical modes of perceiving, remembering and problem solving. This implies that each student has a preferred cognitive style, which is affected by such factors. The Cognitive style which has received the greatest attention in research is field dependent (FD) and field independent (FI). Zhang (2004) defined field dependent and field independent as a reflection of the extent to which an individual uses external or internal cues for conduct. FI / FD are typically referred to as a variable cognitive style. An individual is either a field independent (FI) or field dependent (FD) (Witkin 1977). A Field Independent (FI) Cognitive style learner is described as analytic, competent
,individualistic, task oriented, intrinsically motivated ,self structuring, detail oriented and skills (Felder, 2000). A Field-dependent cognitive style learner is describe as global (holistic) group oriented, sensitive to social interactions and criticisms, externally motivated, passive learners who prefer external information and group project( Hall, 2000).
Cognitive processing style affect how one store knowledge and retrieved it, when it is needed (Tinajero and Paramo, 1997).The students cognitive styles may hinder or facilitate the acquisition of knowledge in science ( Okwo and Otuba, 2007).There is the need to determined how students cognitive style may influence achievement in mathematics. This is because the knowledge of students’ cognitive style is very useful in teaching (Bahar and Hansell, 2000)
.Students’ ability is associated with their cognitive styles which help to measure teacher effectiveness and learning outcome (Kalu, 2004). Students ability as well as cognitive style may be influenced by gender.
Gender refers to the roles of men and women that are socially or culturally based .Sex on the other hand, refers to the biological differences of men and women .Therefore, most people agree that learning differences are gender based and are related to the individuals socialization and culturalization rather than based on biological differences (Feldstein and Jiggins, 1994).Gender relates to the difference in sex (that is, either male or female) and how this quality affects their dispositions and perception toward academic activities (Okoh, 2007). Also Okeke (2006) explained that gender is socially or culturally constructed characteristic, qualities behaviours and roles which different societies ascribe to females and males. Unlike sex which is biological, gender expectations, roles and characteristics of member of a society are made evident in the approved process of socialization dictated by the society.
Studies have shown that gender as a variable relates to performance (Ezeugo and Agwagah, 2000). For instance, Olaguaju, (2001) observed that boys choose science courses in high schools than girls, especially mathematics, Chemistry, and Physics. This is due to the long held view that women are weaker vessels who cannot stand the stress involved in the subject. To this end, ugwu (1998) argued that at present females are struggling to fight the oppression, suppression and domination by their male counterparts in mathematics. Etukudo (2002) found that female students performed significantly higher than their male counterparts in mathematics. In view of these study will also examine the influence of gender on achievement of students’ in the selected areas of mathematics. More also since mathematics plays a vital role in technological progress as well as being one of the basic and core subjects taught in Nigeria secondary schools, everybody ought to have the same opportunity to learn and achieve in mathematics. There is need to explore the influence of cognitive style, and gender differences on student’s achievement in selected areas of mathematics.
Statement of Problem
Mathematics is a compulsory subject offered by both sciences and art students in senior secondary certificate examination .In spite of the important place of mathematics in the educational system in Nigeria, students in secondary schools continually achieve poorly at senior secondary certificate examination and other external examinations .There are several outcries over students poor achievement at mathematics in various levels of education .This could be attributed to inadequate teachers, use of ineffective instructional materials ,poor teaching methods and incompetence of teachers in teaching some mathematics topics like geometry, algebra, trigonometry and statistics. Gender have been a controversial issue in mathematics and other science subjects, despite the effort made at global level in promoting gender equality in education and the society at large .All these reports point to the fact that there are gender gap in the field of mathematics and sciences. Factors such as the students’ cognitive style and gender have been implicated in the students’ poor achievement in mathematics. Students have different cognitive styles which may affect their learning. Students with certain cognitive styles are either facilitated or hampered by the particular teaching methods to which they are exposed to. Teaching students to reason, think critically and solve problems in mathematics and sciences generally have been a concern to all educators. The problem of this study posed as a question therefore is: Do cognitive style and gender influence students’ achievement in selected areas of mathematics?
Purpose of the Study
The purpose of this study is to determine the influence of cognitive style and gender on students’ achievement in selected areas of mathematics. Specifically the study is set out to:
1. Ascertain the Influence of cognitive styles on students’ achievement in geometry
2. Find out the influence of cognitive styles on students’ achievement in algebra
3. Established the influence of cognitive styles on students’ achievement in statistics
4. Determine the influence of gender on students’ academic achievement in geometry
5. Ascertain the influence of gender on students’ academic achievement in algebra
6. Find out the influence of gender on students academic achievement in statistics.
Significance of the Study
The findings from this study may be of benefit to the learners, mathematics teachers, curriculum planners, guidance counselors, and cognitive theorist. It may allow students to develop their process skills that may lead to expertise in problem solving. This study has promise for improvement of students’ achievement in mathematics; since it is directed at finding out the appropriate way students learn which will help to improve students’ low achievement this may facilitate learning and inculcate positive attitude in students. That is, its hope that with the researcher recommendation if judiciously applied to classroom situation the students will improve which will go a long way to solve perennial poor achievement in mathematics A clear understanding of students’ cognitive style and gender might be important in order to determine their strength and weakness in various areas of mathematics.
Mathematics teachers are not left out in the race for the indispensability of this study. The findings of the study might be relevant to Mathematics teachers as it may reveal students’ cognitive styles in Mathematics class-rooms, and to make teachers to understand the levels at which their students are functioning and ascertain their students cognitive levels in order to adjust their teaching accordingly. By emphasizing methods of reasoning, provide critical direction so that the learner can discover the concepts through investigation .The knowledge gained on cognitive style of students and its influence in Mathematics learning might affect mathematics teacher’s
approach to teaching. As a result of this, the Mathematics teacher may shift from teacher centered method to students based which may improve the achievement in Mathematics. The result of this study may further help teacher’s patterns which may enhance sequence of activities in which the teacher would provide an environment in which equilibrium occurs in learners minds
It is hoped that the result of this study may enable the curriculum planners to design a curriculum that allows students to develop their skills that may lead to expertise in problem solving, create an environment that will nurture the capabilities of students and develop learners potential to the fullest and to encourage curriculum planners to focus curriculum studies on depth and understandings rather than on breath of coverage of syllabuses and scheme of work .Course content should be restructured to match students levels of cognitive reasoning abilities . In addition it may be of great importance to the psychologist because it may enable the psychology to know areas which the learner needs to improve on and to find a remedy for it .curriculum planners and psychologist should work together to find ways of extending Piaget’s clinical approach with individuals and groups to development of science and Mathematics curricula.
To guidance counselors, the findings of this study may help to categorized students into cognitive styles, for career choice according to their brain make- up irrespective of their gender. This might be of importance to guidance counselors, who from time to time have to guide and counsel the students both in academics and other areas of life.
Theoretically, the findings may add to the body of knowledge in line with the theories of some psychologists like Ausubel, Brunner and Gagne who are of the view that meaningful learning occurs when there is interaction between the students prior knowledge and the new materials to be learned .These theories explain how students learn through interactions with materials in the environment so that the students can use the experience gained in learning process in another
situation. That is to say with the knowledge of cognitive style an individual may be able to process the information in well organized environment so as to relate it to others.
Scope of the study
The study is limited to Senior Secondary two (SS2) Mathematics students in Ogoja
Education zone of Cross River State. The senior secondary two was chosen for this study because:
a. The students are not preparing for any external examination unlike the senior secondary three (SS3) students.
b. The class might have covered the senior secondary one mathematics work and both field dependent and field independent groups are likely to be found among the students in SS2 and would therefore allow for generalization.
c. the topics used for the study were taken from year two mathematics of the national curriculum for senior secondary school. The content scope to be examined includes: geometry, algebraic and statistics process. Variables of gender and cognitive style and their influence on students’ achievement will be examined.
Research Questions
In this work the following questions will guide the study.
1. What is the achievement mean score of field-dependent and field independent mathematics students in geometry?
2. What is the achievement mean score of field-dependent and field independent mathematics students in algebra?
3. What is the achievement mean score of field-dependent and field independent mathematics students in statistics?
4. What is the achievement mean score of male and female students in geometry?
5. What is the achievement mean score of male and female students in algebra?
6. What is the achievement mean score of male and female students in statistics?
Hypotheses:
The following null hypotheses (Ho) will be tested at 0.05 levels of significance.
H01: There is no significant difference in the mean achievement score of field dependent and field independent students in geometry.
H02: There is no significant difference in the mean achievement score of field dependent and field independent students in algebra.
H03: There is no significant difference in the mean achievement score of field dependent and field independent students in statistics
H04: There is no significant difference in the mean achievement scores of male and female students’ in. geometry.
H05: There is no significant difference in the mean achievement scores of male and female students’ in. algebra.
H06: There is no significant difference in the mean achievement scores of male and female students’ in. statistics.
This material content is developed to serve as a GUIDE for students to conduct academic research
INFLUENCE OF COGNITIVE STYLE AND GENDER ON STUDENTS’ ‘ACHIEVEMENT IN SELECTED AREAS OF MATHEMATICS
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