ABSTRACT
The study analyzed the psychometric properties of Basic education Certificate examination (BECE) multiple choice items in mathematics in Abia state specifically to determine the content validity, item difficulty, discrimination indices, effectiveness of distracters, internal consistencies and coefficient of stability of BECE mathematic items. The population comprises all upper basic (Junior Secondary III) students of private, state, Federal Secondary Schools in Abia State. The study adopted the survey design. The instrument used were past BECE questions, the validity of the instruments is part of what this research work addressed using content validity through expert judgment and table of specification while reliability was addressed using Pearson product moment correlation coefficient for coefficient of stability and Kuder Richardson 21 for internal consistency. The research used past questions of 2014, 2015, 2016 BECE multiple choice items in mathematics which were administered to the students. The result shows satisfactory content validity for the different years with room for improvement; 81.6% of the items across the three years had satisfactory items difficulty while 18.3% items across the three years had poor item difficulty. The discrimination parameters shows 81% of the items across the three years have moderate discrimination indices implying that they are satisfactory while 19% of the items across the three years indicated low discrimination indices and should be discarded. 82% of the distracter items was seen to be effective, while 8% of distracter items across the three years was ineffective and should be discarded. Among the recommendations is the need for those involved in constructing BECE items be conscious of distracter/options they include in multiple choice items. Test development experts should create awareness and train teachers on their efficiency in constructing tests with good psychometric properties. BECE Mathematics in 2014, 2015 and 2016 are moderately valid and reliable, and should be used by teachers in preparation for future BECE as mock examination.
TABLE OF CONTENTS
TITLE PAGE i
DECLARATION ii
CERTIFICATION iii
DEDICATION iv
ACKNOWLEDGEMENTS v
TABLE OF CONTENTS vi
LIST OF TABLES viii
ABSTRACT ix
CHAPTER 1: INTRODUCTION
1.2
Background
to the Study 1
1.2 Statement
of the Problem 5
1.3
Purpose of the Study 6
1.4 Research
Questions. 7
1.5 Significance
of the Study 7
1.6 Scope
of the Study 9
CHAPTER
2: REVIEW OF RELATED LITERATURE
2.1 Conceptual Framework 10
2.1.1 Concept of Tests and Testing 10
2.1.2 Achievement Tests 13
2.1.2.1
Objective and Essay Achievement Test 14
2.1.2.2 Achievement test Development Procedures. 18
2.1.3 Concept of Psychometric Properties 23
2.1.4 Item Analysis 27
2.2 Theoretical Framework 30
2.2.1 Classical Test Theory 30
2.2.2 Item Response
Theory 32
2.2.3 Psychometrics: The technique of psychological measurement 34
2.3 Empirical
Studies 34
2.4 Summary
of Literature Review 39
CHAPTER 3: METHODOLOGY
3.1
Design of the Study 40
3.2
Area of Study 40
3.3
Population of the Study 41
3.4
Sample and Sampling Technique 42
3.5
Instrument for Data Collection 42
3.6
Validation of Instrument 43
3.7
Reliability of Instrument 43
3.8
Method of Data Collection 44
3.9
Method of Data Analysis 44
CHAPTER 4: RESULTS AND DISCUSSIONS
4.1 Results 46
4.2
Summary of Findings 66
4.3 Discussion
of Findings 67
CHAPTER 5: SUMMARY, CONCLUSION AND
RECOMMENDATIONS
5.1 Summary 71
5.2
Conclusion 74
5.3
Recommendations 74
5.4
Educational Implications of the
Study 75
5.5
Limitations of the Study 76
5.6 Suggestion
for Further Studies 76
REFERENCES 78
APPENDICES
2014 BECE Mathematics multiple
choice questions
2015 BECE Mathematics multiple
choice questions
Percentage of Testees who get the test
right
Table of specification
Guidelines for Evaluating Discrimination
Indices (DI)
LIST
OF TABLES
Table 4:1: Specification
on Mathematics Multiple Choice Test
items
in 2014 represent the content area in Basic Education
Certificate
Examination (BECE) Mathematics. 46
Table 4:2: Kendall
co-efficient of concordance of the items from five
experts
based on cognitive levels or objectives and content
areas
of the Basic Education Certificate Examination
(BECE)
Mathematics in 2014. 47
Table 4:3: Specification
on Mathematics items in 2015 represents the
content
area in Basic Education Certificate Examination
(BECE)
Mathematics in 2015. 48
Table 4:4: Kendall co-efficient of concordance of
the items from five
experts based on cognitive levels or
objectives and content
areas of the Basic Education Certificate
Examination
(BECE) Mathematics in 2015. 49
Table 4:5: Specification
on Mathematics items in 2016 represents the
content
area in Basic Education Certificate Examination
(BECE)
Mathematics. 50
Table 4:6: Kendall
co-efficient of concordance of the items from five
Judges
based on cognitive levels or objectives and content
areas
of the Basic Education Certificate Examination
(BECE)
Mathematics in 2016. 51
Table 4:7: The
item difficulty indices of the BECE Mathematics in 2014, 2015
and 2016 53
Table 4:8: The
discrimination indices of the BECE mathematics in 2014, 2015,
and 2016 56
Table 4:9: The effectiveness of distracters in 2014
BECE Mathematics
options of the test items. 59
Table 4:10: The effectiveness of distracters in 2015
BECE Mathematics
options of the test
items 61
Table
4.11: The effectiveness of
distracters in 2016 BECE Mathematics options of the test
items. 63
Table 4:12: The coefficient of stability of the 2014,
2015, and 2016
BECE
Mathematics tests items using the Pearson Product Moment
Correlation Coefficient. 64
Table 4:13: The Kudder Richardson 21 of the 2014, 2015, and
2016
BECE Mathematics tests items 65
CHAPTER 1
INTRODUCTION
1.1 BACKGROUND TO THE STUDY
Basic
Education spans through a 10 year period, comprising of 1year pre-primary, 6
years of primary education (3 years lower basic and 3 years of middle basic)
and 3 years of junior secondary education (upper basic) (FRN, 2013). This is in
line with the intention of achieving the sensitive targets of National Economic
Empowerment and Development Strategies (NEEDS) of the Nigerian Government
comprising value orientation, poverty eradication, job creation, wealth
generation and empowerment of the citizens through education (Okafor & Anaduaka,
2013). Among other goals, Basic Education according to the 6th
edition of the National Policy on Education of 2013, provides the child with
diverse basic knowledge and skills for entrepreneurship, wealth generation and
educational advancement as well as provide opportunities for the child in developing
manipulative skills and enabling same, effectively function in the society in
the limits of the child’s capabilities.
Furthermore, the
National Policy on Education (FRN, 2013) emphasizes it
to be free and compulsory. It also includes adult and non-formal education programmes
at primary and junior secondary education levels for the adults and
out-of-school youths. According to the
National Policy on Education, Basic Education Certificate Examination (BECE) is
sat for by the student at the completion of the 10 year formal schooling. The
Basic Education Certificate is issued by the State governments and the Federal
Capital Territory (FCT) administration and by NECO for federal schools. Efforts
are put in place towards achieving equitable access to educational opportunities
for all Nigerians in all parts of the country. On completion of junior secondary school, students shall be streamed into (i) senior secondary
school, (ii) higher school (iii) continuing education given in Vocational
Enterprise Institutions, The streaming shall be based on the result of tests’
to determine academic ability, aptitude and vocational interest; as much as
possible to achieve a transition of 50:50. The Basic Education Certificate
Examination (BECE) is based on continuous assessment and examination conducted
by state and federal examination boards. The BECE is conducted and administered
by 36 state Ministries of Education and the Federal Capital Territory (FCT) for
all the private and public state secondary schools within the various states and
FCT. The National Examination Council (NECO) also conducts BECE for federal
unity schools, armed forces secondary schools and other federal institutions
that operate secondary schools, inspite of the fact that the curriculum and the
expectation across the federation is the same. Could it be possible the quality
of NECO instruments may not be the same with the state ministries of education,
where expertise in developing and administration of examinations may be a
problem? Could there also be difference in the qualities of the different BECE
as administered by the individual state ministries of Education?
At the junior secondary
level, a maximum of 10 subjects are offered and Mathematics is among the
subjects offered. By the completion of junior secondary school, a Nigerian student
is expected to be proficient in number and numeration, basic (mathematics)
operations, measurement, algebraic processes, elementary geometry and
mensuration and everyday statistics. According to the National Educational
Research and Developmental Council (NERDC), (2007), the revised National
curriculum for mathematics curriculum for basic education programme in Nigeria
has the objectives which include (i) to acquire mathematical literacy that is a
necessary functionality in an information age. (ii) Cultivating the
understanding as well as the application of mathematical skills and concepts
necessary to drive the ever changing technological world. (iii) Developing the
essential element of problem solving, communication and reasoning within the
study of mathematics. (iv) Understanding the major ideas of mathematics with
the mindset that the world has changed and is still changing.
The observation over the
years in the outcome of public examinations both at the junior and senior secondary
level of education in the country has not received favourable commendation by
all stakeholders, becoming a source of concern to parents, educators,
government and the general public (Okafor & Anaduaka, 2013).Most school children in
Nigeria dread mathematics, with the perception of it as being difficult, complex
and abstract. Students do not also seem to see the use or applicability of the
subject in their everyday living and why being bothered with studying the
subject. (Okafor and Anaduaka, 2013).
The use of test or testing is a fundamental
part of teaching-learning process. It guides teaching and aids in the
development of curriculum as well as assessment of needs, learning
difficulties, level of mastery and differences among students. Tests can only
perform this function when it is valid or have appropriate psychometric
properties. Adebule (2009) infers that teaching and testing go together in
schools. The preparation and writing of questions in our schools are the sole
responsibilities of subject teachers. Nwana (2007) posits that majority of the
teachers do not give adequate attention and due consideration to quality of the
tests they set. Most of the test question items are not reliable while some
items are either too difficult or too simple. Nwana also affirmed that most
teacher-made tests have been found to be carelessly constructed without test
blueprint or table of specification. This has prompted inquiry as to how this
translates to a standardized test like BECE which is conducted at the level of
Ministry of Education in the different states and FCT.
Psychometric characteristics of examinations refer to
certain attributes inherent in tests. These characteristics include the
facility or difficulty indices, the discrimination index, the effectiveness of distracters,
validity and reliability indices. It’s perhaps worth mentioning that these
attributes of a test are most often ignored. These indicators of the extent of
quality of test items can be achieved through item analysis.
Oshkosh (2002) puts item analysis as a very important tool
to increase the effectiveness of a test. Scientifically it improves test
quality and test items as in an item bank and providing three important points
about the quality of test items. (i) Item difficulty – a measure of whether an
item is too easy or too hard, also called facility index. (ii) Item
discrimination – which is a measure of whether an item discriminates between
candidates who know the material well and candidates who do not. (iii) Effectiveness
of distracters – determination of whether distracters (incorrect but plausible
options) tend to be chosen by the less knowledgeable candidates and not by the
more knowledgeable candidates.
With the acknowledgment of the fact that some expectations
of teaching and learning are heaped on test outcomes, the seriousness of the
role tests and examinations play, informs the drive in probing into the quality
of tests given at different stages of academic growth. The basic education
level has caught the researcher’s fancy due to its importance as a formative
stage of academic development. How serious is this formative educational level
handled by stakeholders? It is probable that some weaknesses exist in the tests
developed and administered by the state ministries of education especially in
Abia State. It is also not certain that some of the state ministries of
education who develop and administer BECE examinations do not have measurement
experts who should be involved in item development and validation. It becomes
imperative in determining the extent to which Basic Education Certificate Examination
for mathematics test items satisfy the psychometric properties of validity,
reliability, item discrimination and item difficulty. Highlights of some of the
related works carried out in this area include (i) The psychometric properties
of mathematics in public examinations in Nigeria. Moyinoluwa,(2015). (ii) A
study of the comparative analysis of psychometric properties of two Nigerian
examining bodies for senior secondary schools mathematics. Kolawole,(2007).
(iii) The study on the development and standardization of achievement test in
senior secondary mathematics using item response theory. Enunwah and
Akwa,(2014). This brings to importance, the need to establish the place of BECE
mathematics in satisfying the psychometric properties.
1.2 STATEMENT OF
THE PROBLEM
The Basic Education Certificate Examination is of great
importance to the educational development of the child. This is because it is
at this stage that the child will start preparing himself/herself for future
career prospects. The outcome prepares the mind of the pupil towards branching
out to technical college and start towards skill acquisition or moving forward
to senior secondary for the sciences or arts. One would ask if BECE is actually
meeting up with the enormous responsibilities bestowed on it. If so then, being
able to satisfy the psychometric properties of a standardized test will be an
important factor in actualizing it.
Madu and Ihechu (2016) posit that tests and examinations at
all stages of education have been considered an important tool for decision
making in our competitive society, with people of all ages being evaluated with
respect to their achievement, skills and abilities. Zola and Ben-chain (2009)
have the opinion that the era in which we live is a test conscious age in which
the lives of many people are not only greatly influenced, but are also
determined by their test performance. This brings to the question of how valid
and reliable BECE is as a tool in decision making. And also can BECE be said to
be a quality tool or instrument to evaluate student achievement, skills and
abilities? This question calls to mind the nature of administration of this
examination, which is carried out by individual state government. How standardized
are the BECE examinations conducted by Abia state with respect to satisfying
the psychometric properties. Could there be areas of improvement on BECE as it
is currently administered?
At present, no study seems to have been carried out to
determine the psychometric properties of Basic Education Certificate
Examination in mathematics in Abia State. The problem of this study therefore
is: Can the psychometric properties of BECE mathematics in Abia State secondary
schools be verified? Since the answer is in the affirmative, then how
satisfactory are the psychometric properties of the test items?
1.3
PURPOSE
OF THE STUDY
The purpose of this study was to analyze the psychometric
properties of Basic Education Certificate Examination multiple choice items in
Mathematics in Abia State. Specifically the study sought to determine
1. The content validity of BECE
mathematics tests in Abia state.
2. The item difficulty of BECE
mathematics test items in Abia state.
3. The discrimination indices of BECE
mathematics test items in Abia state.
4. The effectiveness of distracters of BECE
mathematics the test items in Abia state
5. The internal consistencies of the
test instruments.
6. The coefficient of stability of BECE
mathematics in Abia state.
1.4
RESEARCH
QUESTIONS.
The following research questions guided this study.
1. To what extent do mathematics test items in BECE represent
content area in Basic mathematics?
2.
To what extent does BECE mathematics satisfy item
difficulty?
3.
To what extent does BECE mathematics satisfy discrimination
indices?
4.
What is the effectiveness of distracters of BECE mathematics
options of the test items?
5.
What are the coefficient of stability of BECE mathematics multiple
choice test items?
6.
What are the internal consistencies of the BECE mathematics
multiple choice test items?
1.5 SIGNIFICANCE
OF THE STUDY
The analysis of Psychometric properties of BECE multiple
choice items in mathematics in Abia State may impact on the general public, subject
teachers, guidance counselors, Examination boards, Ministries of Education,
Agencies associated with Education and Examinations, Students, Abia state and the Nation at large.
This work is important because it will contribute to the
efforts already being made in the improvement of tests and test outcomes. The
implication of this work is that aside from its contributions towards good and
quality instruments, humanity will hopefully be better for it. What with the
importance attached to mathematics in scientific and technological development
of any nation. Harnessing the results of the study will go a long way towards
bringing teaching and learning of mathematics closer to the students and make
them to start seeing its applicability and its importance towards better living
as well as encouraging the students to want to do more in the area of
mathematics. Abia state and Nigeria will be better for it in the area of
teaching and learning of mathematics. With mathematics as a fulcrum of other
subject areas, a good analysis on the administration of test items on the
subject matter will go a long way to ease off some of the ‘myths’ associated in
the teaching and learning of mathematics and mathematics test outcomes.
This work will certainly contribute in informing policy
making in the right direction. This study will identify gaps and shortfalls and
will hopefully be a wake-up call on stakeholders in correcting such and coming
out with better outcomes and experiences. There is no gainsaying that the
result of this study will showcase the overall quality of the BECE mathematics
of Abia State Ministry of Education and the public confidence on the standard
of the examinations to the different years. It will also enlighten the public
on the interpretations of student results in the examinations.
The students who will be sitting for this examination in
future will be the ultimate winners if the result of this study is put into use
by the authorities. This is because it will contribute in the enrichment of
subsequent BECE multiple choice items in mathematics in Abia state. Barriers
which would have hampered in the student performance would have been
eliminated, thereby enhancing the educational advancement of the students in
the state and Nigeria in general. The crucial need to employ the hands of
measurement and evaluation experts in preparing such examination and also
before the release of the examination results will be put into consideration.
A new perspective to this study will bring to bear the need
for more work to be done in the educational development of students at the
basic education level, since most studies are done at the senior secondary
school level. The analysis of the psychometric properties of BECE mathematics
multiple choice items will help highlight the need for subject teachers in
properly constructing their own test items for use during continuous assessment
and terminal examinations. There is also the need for the result of this study
be made known to Ministries of Education, examination boards, councellors and
other agencies that have a role to play in academic advancement of the student.
The outcome of this work will assist counselors in proper test utilization,
especially in the area of interpreting and communicating student needs
regarding the test.
This study is also linked to other knowledge since its
outcome will have to be replicated in other subject areas as well as adoption
of the proper procedure of testing where such is lacking. Other states of the
federation are not left out in the expected outcome of this study where its
outcome could be harnessed. So is with other areas of human endeavor outside
Education.
1.6 SCOPE
OF THE STUDY
This Study was focused on examining BECE multiple choice
items in mathematics as administered by Abia State Ministry of Education. The study
covered all the private, public and federal secondary schools in Abia state. It
also examined the psychometric properties, reliability and validity of BECE
mathematics test items used from 2014 to 2016.
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