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Procedia - Social and Behavioral Sciences 106 (2013) 2230 - 2240

Relationship between mathematical ability and achievement in mathematics among female secondary school students in Bayelsa

State Nigeria

Odual Nabhel Nizoloman *

Department Of Teacher Education Faculty Of Education Niger Delta University Wilberforce Island, _Bayelsa State, Nigeria._

Abstract

This study investigated the relationship between female senior secondary school students' mathematical ability and achievement level in mathematics in five (5) out of eight (8) local government areas in Bayelsa State Nigeria. This study adopted multi-stage sampling technique. Data were collected from a sample of 121 female students from rural and 141 female senior secondary school students from urban schools which were randomly selected using the simple random sampling method both at the Local Government, and at the school level. Two research questions and instruments were raised for the study. The instruments were Student Mathematical Ability Test (SMAT) with r = 0.68 and Mathematical Achievement Test (MAT) with r = 0.68 was established for the student Mathematics Achievement Test. Simple linear correlation was used to analysed the data collected at 0.05 alpha. Results showed that there was a positive significant relationship between mathematical ability and achievement in mathematics. Using multiple regression analysis showed that mathematical ability has a significant effect on achievement in mathematics with B = 0.386 and P < 0.05. Based on these findings, it was recommended that government should provide schools with facilities that will develop and sustain students' mathematical ability as it is a good predictor of students' achievement in mathematics.

©2013TheAuthors.PublishedbyElsevierLtd.

Selectionandpeer-reviewunderresponsibilityofTheAssociationofScience, EducationandTechnology-TASET,SakaryaUniversitesi, Turkey.

Keywords: Mathematical Ability; Mathematics Achievement; Female Students; Secondary School Students; Bayelsa State.

* Corresponding author. Tel.: +2347031134872; +2347052100159. E-mail address: oduniz@yahoo.com

1877-0428 © 2013 The Authors. Published by Elsevier Ltd.

Selection and peer-review under responsibility of The Association of Science, Education and Technology-TASET, Sakarya Universitesi, Turkey. doi:10.1016/j.sbspro.2013.12.254

Introduction

The vital role which mathematics plays in education is derived from the cultural, utilitarian and interdisciplinary values which the subject seeks to inculcate in the learner. Mathematics education is to a nation what protein is to a young human organism. It is a vital tool for the understanding and application of science and technology. The discipline plays the vital role of a precursor to the much needed technological and national development of Nigeria. Hassan (2002) opined that mathematics as a subject is now universally recognized and accepted as indispensable to self-reliance and sustainable development of any nation because of the perceived functional utility. Umuoyang (1998) warned that any nation seeking to develop a strong level of science and technology must pay attention to the teaching and learning of mathematics. He puts it as "any nation that seriously desires technology must not relegate the teaching and learning as well as research into mathematics to the background". In support of the above assertion, Eguawon (2002) is of the opinion that mathematics is a model for thinking, developing scientific situations, drawing conclusions as well as for solving problems. Mathematics trains the mind on attention and concentration which are bound to be useful for the student throughout life. He went further to stress that mathematics also promotes the habit of accuracy, logical, systematic and orderly arrangements. Because of the importance attached to the technological development, the Nigerian government has not only made mathematics a compulsory subject in the curriculum of the primary and secondary school levels of her educational system (Federal Republic of Nigeria, 2004) but also as a prerequisite to the study of science courses in her colleges, polytechnics and universities (JAMB Brochure 1992 - 2007).

Despite the relevance and usefulness of mathematics as a key in realizing any national development and aspiration, over the years, there has been a repeat of low level of achievement or poor performance and failure of students in mathematics at bothjunior and senior secondary school levels in both rural and urban schools. Poor achievement in mathematics in Nigerian secondary schools has assumed an alarming proportion and caused a lot of concern for many years. The concern for this poor performance is not only limited to mathematics educators but also parents and other stakeholders. However, the reason for the poor performance of mathematics from year to year has been ascribed to inadequacies in one or all of these areas namely, the nature of the subject, the learners factor and the teachers factors. Korau (2006) opines several variables ranging from the learners themselves, teachers, textbooks, curricular and school environment to have been responsible for students' poor achievement in mathematics. The above argument informed Hornby (1985) to define achievement as the act of achieving or something done successfully especially with efforts or skills. According to research, achievement is the end product oflearning experience, what students have gained as a result of what they have learnt.

Mathematics achievement deals primarily with the performance of students in their either teacher-made test or standardized achievement test administered by examining bodies. Looking at the academic achievement of students in mathematics across the country, the poor achievement becomes more striking. One wonders what then could be responsible for this poor performance despite its importance and recognition given by the society and various efforts made by the Federal Government and the Mathematical Association ofNigeria (MAN). Various factors have been adduced for the poor performance of students in mathematics. Such factors as the interest of students in mathematics which according to Aremu (1998) have been related to the volume of work completed; anxiety (Odunuga, 2005); motivation (Broussard and Garrison, 2004, Telia, 2007); reasoning and numerical ability (Adeleke, 2007); problem solving skill (Onabanjo, 2007); mathematics phobia (Bature, 2006) and instructional strategy (Onabanjo, 2007).

The wide spread low performance of students in secondary school mathematics can also be ascribed largely to how instructions on mathematics is presented to the students. According to Ale (2001) the paucity or scantiness of relevant mathematics textbooks stands a basic factor which affects the teaching and learning of mathematics in Nigerian secondary schools. In the Nigerian context, poor achievement in mathematics in secondary schools has

assumed alarming proportions and caused a lot ofconcern for many years. This poor performance is as a result of many factors which includes among others, self-concept, attitude, and mathematical ability. Gender factor is very strong in learning and thus determines the interest and achievement and consequent career choice. It is interesting to note that while Jahun, and Momoh (2001) established that gender is significant in school mathematics achievement, other studies such as that of Aiyedum (2000) found no significant difference between males and females in school mathematics achievement.

Whereas Meyer and Koehler, (1990) cited in Badmus (2009); is of the argument that males are better at mathematics than females because of genetic reasons, some because of societal influence and some said it is due to mathematical anxiety level. Also in agreement are Onabanjo (2000); Ojo (2004) who independently found out that boys perform significantly better than girls in senior secondary school mathematics. This difference is often overstated and its cause is often highly debated. For Benbow (1990) lower performance trends of females in mathematics have been observed to influence the lower participation of females in science and mathematics related profession. Still on gender difference in achievement in mathematics some other researchers puts male and female discrepancy in mathematics achievement in favours of males performing better than their female counterparts to be as a result ofthe female belieftowards mathematics.

Despite the importance of the girl-child education, there are still a number of cultural, social and economic barriers to girl-child education in Nigeria, that the cultural inhabitation is closely tied to religious affiliation and cultural practices. Nigerians are yet to accord the girl-child education the same level of importance as that of the boy-child.

1.1 Statement ofproblem

Observations and reports from examining bodies revealed that a high percentage of secondary school students failed mathematics examinations and the failure often generated much concern especially, to parents, teachers, students and other stakeholders in education business. In a situation where the student will be blamed for poor performance, emphasis is only placed on the students' cognitive or intellectual ability. Little or no attention is given to the fact that the student's mathematical ability can affect their achievement in mathematics. Based on the above assertion, this study intends to find out the relationship between mathematical ability and achievement in mathematics of female secondary school students.

1.2 Research questions

Based on the above problem, this study intends to provide answers to the following questions:

• What is the relationship between the mathematical ability and achievement in mathematics of female senior secondary school students?

• What is the relative effect of mathematical ability on achievement in mathematics of female senior secondary school students?

1.3 Significance of the study

This study is important to all stake-holders in education as it provides a better understanding on the relationship between students' variables in several ways. The results of the study will provide an empirical basis for development and improvement ofstudents achievements in mathematics among which are:

• The information obtained will unveil the effect of mathematical ability on the achievement in Mathematics offemale secondary school students.

• The results of this study will help provide a basis for curriculum planners to review and make necessary modifications or improvement in instructional methods and materials at the senior secondary school level.

2. Literature review

2.1 Gender and achievement

For full realization of this laudable objective of Mathematics education, subject mastery and demonstrated achievement should be evenly distributed across gender. Poverty, economic constraints, early marriage and teenage pregnancy, inadequate school infrastructure and cultural and religious misinterpretation are some of the main barriers preventing girls in Nigeria from going to school (UNICEF, 2007)

Alao, and Adeleke (2000) investigations showed that girls exhibit more fear for mathematics than boys in mathematics activities. Manger and Eikeland (2006) who worked on the effect of mathematics self-concept on girls' and boys' mathematical achievement, establish several results concerning gender and achievement. First, they found out that there was no significant effect of gender on overall mathematical achievement. Second, although the gender difference in achievement favoring boys increased with increasing task difficulty, no significant effects ofgender were found in sub-samples ofdifficult tasks.

2.2 Mathematical ability and achievement

Mathematical ability is the capacity to use or manipulate numbers effectively in clerical administrative, scientific and other areas of application of numbers. It is the ability to understand and work with numbers with ideas related to numbers. Tremblay, Garner, and Heipel (2000) studying the impact of the sample variables, supported the hypothesis that mathematical ability contribute to the prediction of achievement in statistics as suggested by Harlow, Burkholder, and Morrow (2002). Similarly, Oyekanmi (2008) in his work on mathematical ability and gender as correlates of students' achievement found out that there is no significant interaction effect of gender and mathematical ability on students' achievement in physical geography. This implies that gender and numerical ability do notjointly differentiate students' achievement in practical and physical geography achievement test.

3. Research Methods

3.1 Research type

This study is a non-experimental survey. This is so because the variables studied are already there in the students and the researcher will not in any way attempt to manipulate the variables.

3.2 Variables in this study

The independent variable is Mathematical ability. The dependent variable is Achievement in Mathematics

3.3 Target population

The focus and population of this study is made up of female students of Senior Secondary School year two in Bayelsa State both from rural and urban schools.

3.4 Sample

Thirty (30) out of the ninety eight (98) senior secondary schools in Bayelsa State were randomly selected. Ten (10) female students were randomly drawn from each of the thirty (30) selected schools to give a target population ofthree hundred (300) female students.

3.5 Sampling technique

This study adopted multi-stage sampling technique. Random sampling techniques were employed at the Local Government Area and at the school level.

3.6 Sampling at Lo cal Go vernment Level

As at the time of this study, Bayelsa state is made up of eight Local Government Areas. They are Brass, Ekeremo, Kolokuma/Opukuma, Nembe, Ogbia, Sagbama, Southern-Ijaw and Yenagoa Local Government Areas. Five out of the eight (8) Local Government Areas of Bayelsa State were randomly selected for this study given about 63% coverage ofthe entire Bayelsa State Senior Secondary Schools.

3.7 Sampling techniques at school level

A total of 30 senior secondary schools were randomly selected. This figure constitutes about 30% of the secondary schools in the sampled Local Government Areas. The sampled schools were made up of 60% urban schools and 40% rural schools.

4. Data collection

4.1 Instrumentait n

This study was designed to examine the relationship between students' mathematical ability and achievement in mathematics. The two instruments for this study were partly developed and partly adopted by the researcher. These are:

• Mathematical Achievement Test (MAT).

• Student Mathematical Ability Test (SMAT)

4.2 Mathematics Achievement Test (MAT)

To measure the students' mathematics achievement, an Mathematics Achievement Test (MAT) developed by the researcher using a table of specification generated 30 items from a pool of already standardized test items was used. This is a multiple-choice objective test made up of four options A, B, C and D. The instrument was validated by experts for face and content validity after consulting a conventional Public Senior Secondary School Mathematics teacher. Each item has one correct option (the key) and three distracters. The correct option will attract 1 mark.

4.3 Students' Mathematical Ability Test (SMAT)

Mathematical Ability Test consists of twenty (20) items was used in this study to assess students' mathematical ability. The students were allowed twenty minutes to respond to the items. A student's correct response to an item was scored 1, while a students' wrong response was scored 0. There was no penalty for guessing. The reliability coefficient of 0.72 for the instrument was established by the researcher using the Kuder-Richardson reliability coefficient formula (RK20). The test is curriculum referenced. The SMAT was adopted from Barret & Williams (1997).

4.4 Validity of the instruments

For the purpose of this study, both the face and content validity of the instruments were ensured. The content validity ofthe instrument was enhanced by suggestions from research experts in questionnaire construction at the Institute of Education, University of Ibadan. Based on the suggestions and comments of these experts and colleagues, the necessary corrections were made. The data collected showed that the students did not have problems responding to the items in the questionnaire.

4.5 Reliability of the instruments

The reliability ofthe students' responses to the instruments was established. The split half reliability coefficient ofthe thirty test items was determined by using Kuder Richardson Formula K21 which gave a reliability estimate of 0.68. This establishes the internal constituency ofthe student Mathematics Achievement Test.

4.6 Data collection procedure

Well structured, closed and scaled questions determined from pilot study were administered on respondents through SMAT and MAT. The administration and collection of all the necessary information was done during normal class periods personally by the researcher and with the help of research assistants. The necessary data for this study were obtained from students of the selected schools in the selected local government areas. The researcher and the assistants directly used the instrument to collect the required data. In each of the selected schools visited, permission to administer the instrument to their students was obtained from the principal of the concerned school. 300 copies of the instrument were distributed to the selected students in the 30 schools and were retrieved, among which 38 (11.4%) badly filled ones were discarded. A total of 262 (88.6%) instruments fully responded to were utilized and data collection lasted for 28 working days.

5. Data analysis and results presentation.

5.1 D ata Analysis

The scores for the items were encoded in SPSS software in order to analyze the data. The statistical procedures used to describe the variables include frequency counts and percentages. Variables linkages were performed on the data. All the research questions were tested at 0.05 significance level. The qualitative data collected were analyzed using descriptive statistics to explore respondent's views. T-tests, ANOVA, Correlation and Multiple Regression were used to determine associations between the independent variables and the dependent variable in answering the research questions.

5.2 Challenges

One of the limitation of the study was the missing values which affected the validity of the entire 300 questionnaire responded to by the students. One other challenge that was faced by the researcher during the study was associated with the insincerity of some students which was observed as some respondent either tick only one particular option or in an alphabetical order. They were however discarded. Selection and participation of students was a challenge in most schools. This problem was solved with the assistance of the Principal or a teacher in the school who helped the researcher addressed the students and sought the consent of those who wanted to participate in the exercises which were later selected at random. Finance was another big challenge. The study involved huge amount of money from cost of developing and producing the instruments to transportation logistic due to the terrain of Bayelsa State.

5.3 Results

The results are presented in line with the sequence of the research questions. An alpha level of .05 was used in statistical test.

Research Question One: What is the relationship between Mathematics Ability and Achievement in Mathematics ofFemale Senior Secondary School Students?

Table 1. Correlation for Mathematics Ability and Achievement in Mathematics of Female Senior Secondary School Students.

Achievement Mathematical Ability

Achievement 1.000

Mathematical 1.000

Ability

Note: **P<.01;*P<.05

Table 1 presents the correlation among variables. The table shows that the correlation between female senior secondary school students' mathematical ability and achievement in mathematics is 0.393. And it is statistically

significant at P > 0.01. This result implies that there is a positive relationship between mathematical ability mathematics and achievement in mathematics.

Research Question Two: What is relative effect of Mathematical Ability on Achievement in Mathematics of Female Senior Secondary School Students?

Table 2 Regression Coefficients Relative effect of Mathematical Ability on Achievement in Mathematics of Female Senior Secondary School Students.

Model Unstructured Coefficients Standard Coefficient T Sig

B Std. Error Beta B Std. Error

1 .425 .063 .386 6.740 .000

Results from table 2 shows that the predictor (mathematical ability) of female senior secondary school students on achievement in mathematics in Bayelsa State had a statistical significant effect on achievement with P = 0.386, t(260) = 6.74; P > 0.05. This is to say that mathematical ability is makes a significant contribution to achievement in mathematics.

5.4 Discussion

It is beneficial to note that the causes of students poor performance have not only been identified but that educators have been actively engaged in seeking clear understanding of the issues involved and in some cases proffer viable remedies. Yet the problem of poor performance in school works or in public examinations according to Salau (1995) seems to loom larger. He opined to the fact that the causes of student's under-achievement are perhaps less obscure than remedies. While in mathematics of which the results of this study tend to reveal, it may be true that high achievement in mathematics is a function of some inter-related factors, among which mathematical ability is; the impact of school factors and in particular overcrowding and dilapidating/unfurnished classrooms, can hardly be over-emphasized.

Research Question one: What is the relationship between Mathematics Ability and Achievement in Mathematics ofFemale Senior Secondary School Students?

The studies carried out by Naiz (1993); Simsek (1993) seemed to lend credence to the efficacy of mathematical ability groupings on learning outcomes. Despite the students demonstrating confidence in their abilities, the overall performance on the mathematics achievement test was quite poor, particularly considering the basic nature of the questions. The average score was about 50% and almost half the students achieved this or lower. This finding is in corroboration with WAEC, (2003) whose findings have also shown that poor performance of students in mathematics could be traced to their mathematical ability. The findings of this study also substantiate the results of the studies of Tremblay, Garner, and Heipel (2000) who studying the impact of the sample variables, supported the hypothesis that mathematical ability contributes to the prediction of achievement in statistics as suggested by Harlow, Burkholder, & Morrow, (2002). However, the students were seen to demonstrate a procedural knowledge ofthe ability to reason through the given mathematical situations, the ability to connect, employ and communicate an algorithmic process within the given problems with little ease. That is to say, the higher the mathematical ability of a student is, the higher his/her achievement in mathematics and the lower the mathematical ability of a student is, the lower his/her achievement in mathematics.

Research Question two: What is relative effect of Mathematical Ability on Achievement in Mathematics of Female Senior Secondary School Students?

The findings of this study from as shown in table 2 presents, the standardized and unstandardized regression coefficient and the corresponding T-values for each of the independent variables mathematical ability. The beta weight gives an indication ofthe relative contribution ofthe variable to the prediction ofstudents' achievement in mathematics when all other variables are controlled. The beta weight associated with mathematical ability is significant at .05 level. From the values of the standardized regression weights associated with the independent variable in table 2 above, it indicates clearly that students' mathematical ability is a potential contributor to students' achievement in mathematics. This is in agreement with the findings of the results of the studies of Tremblay, Garner, and Heipel (2000) who studying the impact ofthe sample variables, supported the hypothesis that mathematical ability contributes to the prediction of achievement in statistics as suggested by Harlow, Burkholder, & Morrow, (2002).

5.5 Summary of Findings

In secondary schools, the role and place of their mathematical ability affecting student's achievement in mathematics cannot be over-emphasised. It is in light of this that the present study has been carried out to investigate likely relationship between students' mathematical ability and achievement in mathematics. Two hundred and sixty two (262) female senior secondary school students out of which one hundred and twenty one (121) students from fifteen (15) schools in the rural areas and one hundred and fourty one (141) students from fifteen (15) schools in urban areas selected from five (5) out ofthe eight (8) local government areas in Bayelsa State were used for this study. The independent variable was mathematical ability, while the dependent variable was achievement in mathematics. The data collected were analysed using statistical tools known as linear correlation and multiple regression in the computer statistical package for social science (SPSS). The finding ofthis study based on the sample and data collected revealed:

• That there is a positive and significant relationship between students' mathematical ability and achievement in mathematics.

• That student's mathematical ability can predict achievement in mathematics.

5.6 Conclusion

This study highlights an important result that provides further information concerning the links between students' mathematical ability and achievement in mathematics. However, the results of this study also showed that mathematical ability is a strong predictor on students' achievement in mathematics.

5.7 Recommendation

The following recommendations are made.

• Students' confidence in their mathematical insights and abilities should be developed and maintained.

• Students should be made to have a feel ofthe enjoyment, curiosity, and perseverance when encountering new problems.

• Government should equip and provide social amenities in the rural schools so as to attract and sustain qualified staff.

• Teachers should make mathematics teaching interesting.

• Individual differences in students' ability, background and attitude should be taken into consideration by teachers and parents.

• Instructional materials should be designed and developed to aid mathematics teaching and learning.

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