**ABSTRACT**

The
topic of the study is effects of small class size on academic achievement of
pupils in mathematics in Ogbaru local government area of Anambra state. The
purpose of the study was to find out the effect of small class size on academic
achievement of pupils in mathematics in primary schools. The study adopted a quasi-experimental
research design, specifically the non-equivalent control group design. The
population of the study consisted of primary schools pupils in all the nineteen
(19) private primary schools in Ogbaru. The total population was 3490 pupils. A
purposive sampling technique was used to
select an intact class of small and large class of primary four (4) pupils. A
sample size of 65 was used. The study was guided by two(2) research questions
and two(2) research hypotheses were
tested at 0.05 level of significance using Analysis of covariance
(ANCOVA). The data were collected using fraction achievement test.
The Instrument was found to be reliable
by the reliability coefficient of 0.8 using Kuder-Richardson formula method
(K-R 20). Validation of the instrument was made by experts in mathematics
education and measurement and evaluation. Face validation of the instrument was
done as well as content validation through construction of a test blue print.
The result indicated that there is a significant difference in the achievement
of pupils taught mathematics in small class and those taught in large class The
study also showed that there is no significant difference between the
mathematics achievement of male and female pupils taught mathematics in small
class size. Hence, the study recommend that educators should develop great interest in finding ways of improving
pupils reasoning in mathematics and this could be achieved through reduction of class size which makes it easier
for the teacher to have more one on one interaction with the pupils.

**CHAPTER ONE**

**INTRODUCTION**

**Background of the Study**

Education
is the key factor to industrial and technological development of any country in
the world. Knowledge holds key to the attainment of the millennium development
goals, which include, food security, eradication of child mortality, and
reduction of the spread of HIV and AIDS, among others. Husen (2000) stated that
education is widely regarded as a basic human right, a key to enlightenment, and
a great tool for human and society development.
For any Nation to achieve her aims and objectives in education there
must be good, dedicated and committed teachers. The teachers must possess
characteristics that will enhance effective teaching and learning.

Therefore,
teachers play a major role in the educational sector and their role is a major
determinant of educational attainment of any students. However, for anyone to
qualify to be a teacher, the person must obtain degree or National Certificate
in Education during the course of study. The pre –service teacher will be
exposed to both pedagogy and content knowledge in the field of study;
psychology and philosophy courses in preparation for the teaching assignment.

To
be prepared to teach mathematics adequately, teachers must have a comprehensive
understanding of technology pedagogical content knowledge (TPCK)” (Niess,
2005). Shulman (1987) defined content knowledge as the knowledge about the
subject (such as knowledge of mathematics and mathematical representations),
while knowledge of students, knowledge of teaching, and knowledge of
educational contexts characterize pedagogical content knowledge. The sum and
intersection of technological knowledge, pedagogical knowledge, and content
knowledge serve as a framework for effective mathematics teaching and learning.
As mathematics teachers think about teaching with technology, they should
concurrently consider how to teach mathematical concepts in such a way that
students can experiment with ideas, make conjectures, test hypotheses, and form
generalizations.

For
more than two thousand years, Mathematics has been a part of the human search
for understanding the world. Mathematical discoveries have come both from the
attempt to describe the natural world and from the desire to arrive at a form
of inescapable truth from careful reasoning. These remain fruitful and
important motivations for mathematical thinking, but in the last century,
mathematics has been successfully applied to many other aspects of the human life.

Today,
mathematics as a mode of thought and expression is more valuable than ever
before. It is absolutely an essential subject in the world today. It is a
compulsory subject in both Primary and post primary schools in Nigeria. The
study of mathematics is taken serious amongst students and school authorities
of various institutions of learning. For instance, students generally cannot
gain admission into any course of study in higher institutions without a pass
or credit in mathematics.

Mathematics
is the study of topics such as quantity (numbers), structure, space, and change
(Encyclopedia Britannica, 2010). It is the science that studies and explains
numbers, quantities, shapes and the relationship between them (Merriam Webster
Dictionary 2015). It is alsothe systematic treatment of magnitude,
relationships between figures and forms, and the relations between quantities
expressed symbolically (Dictionary.com 2016). Mathematics is very useful in the
society, more so in the present science and technology age. A sound science
curriculum cannot be spoken of realistically without considering the important
role of mathematics (Nneji, 2011). Agwagah (2001) stated that mathematics is a
scientific tool in realizing the nation's scientific and technological aspirations.

Mathematics
is the mother of all sciences. No wonder Mathematics is a compulsory subject at
primary and secondary school levels, though, not all the students are expected
to become mathematicians but because Mathematics cuts across all the areas of
human life even at the domestic level. For a person to function very well
within the immediate environment, the knowledge of Mathematics is very
necessary.

Adesina
(2000) defined mathematics as the science that draws necessary conclusions and
also the manipulation of the meaningless symbols of a first order language
according to explicit, syntactical rules. Anibueze (2015) stated that,
mathematics plays important roles in three areas which are mathematics as a
core skill for life ,as a key to economic prosperity and mathematics education.

Mathematics
is the queen of science and a tool for scientific and technological
development, an indispensible tool for effective use of electronic resources
for national development. It is also a way to communicate ideas. More than
anything, it is a way of reasoning that is unique to human beings. Mathematics
is identified as a specialised language in which knowledge of the physical
world has been recorded; a language in which idea originating in the minds of
scientists can be encoded, transmitted to others and decoded with a much exact
method and much less error (Oyedeji, 1999). Olutosin (2007) described
mathematics as an instrument to ease or facilitate the learning of other
subjects and that, the importance of Mathematics permeates all aspects of human
endeavor. Mathematics ideas have helped make possible the revolution in
electronics, which has transformed the world the way we think and live today.

Mathematics
being an abstract subject which needs to be concretized, does not require much
population during the cause of teaching for effective learning to take place.

As
school population increases, class sizes also increase, the performances of
students become an issue. According to Dror (2010), class size has become a phenomenon
often mentioned in the educational literature as an influence on pupil’s
feelings and achievement, on administration, quality and school budgets. Dror
noted that class size is almost an administrative decision over which teachers
have little or no control. Most researchers start from the assumption that size
of the class would prove a significant determinant of the degree of success of
students. In fact, with the exception of a few, many studies have reported that
under ideal situation, class size in itself appears to be an important factor.
Class size refers to an educational tool that can be used to describe the
average number of students per class in a school (Adeyemi, 2008). It also
refers to the number of students a teacher faces during a given period of
instruction.

The
relationship between class size and academic performance has been a perplexing
one for educators. Studies have found that the physical environment, class overcrowding and teaching methods are all
variables that affect students
achievement (Molnar, Smith, Zahorik, Ehrle, Halbach, Kuehl 2000). Other factors
that could affect students achievement
are school population and class size (Gentry, 2000, and Swift, 2000). The issue
of poor academic performance of students in Nigeria has been of much concern to
all and sundry. The problems are so much that it has led to the decline in standard
of education. In order to better
understand the skill levels of students, it might be necessary to evaluate factors affecting their performance.
These factors can include; school
structure and organization, teachers quality, curriculum and teaching philosophies (Driscoill, Halcoussis and
Sony, 2003) and class size (Gentry,2000;
Swift, 2000).

According
to Michael (2010) and Lori (2016), each class has its own advantages and
disadvantages. Lori (2016), maintained that students in large classes are
independent, develop more ideas, have better social opportunities, develop
competitive spirit and discussion activity whereas for students in the smaller
classes, teachers have more of an opportunity to get to know students on a
personal level, helping them to tailor their teaching strategies to meet
individual learning needs.

It is noted that discussion time becomes fragmented
among students in large classes and instructors may rely on passive lecturing,
assign less written homework or fewer problem sets, and may not require written
papers. Instructors may find it difficult to know each student personally and
tailor pedagogy to individual student needs in a large class. According to
(Adeyemi 2013)overcrowded classrooms have increased the possibilities
for mass failure and make studentslose interest in school. This is because
large class sizes do not allow individual students to get attention from
teachers which invariably lead to low reading scores, frustration and poor
academic performance.

Small class size helps students to be able to forge
better relationships with classmates and teachers. Increasing class size
negatively affects students academic achievement that teachers change
pedagogical practices in smaller classrooms and their relationship with
students was much closer.

In smaller classes, teachers had a better
understanding of their students and could customize lessons to individual needs
much more than in larger classes. Teachers adopt more group work to take
advantage of the smaller classroom and also engage more students by varying
types of coursework. These changes create a greater sense of unity and
belonging in the classroom hence, it leads to increase in student achievement.
Englehart (2007) discovered that students were able to transition from one task
to another quicker in the small class and spent a greater amount of time
engaged in the material presented. In the small class, the atmosphere is much
more conversational and familial. This helps to facilitate their learning by
opening lines of communication between teachers and students. Thus, smaller
class size seems to be beneficial to student achievement. It (smaller class
sizes) leads to a decrease in classroom management issues which would be
particularly beneficial to lower achieving students. It fosters more
intrapersonal relationships with students. Teachers spend moretime for the
review of material if needed, and have fewer discipline problems in smaller

Classes.

Blatchford, Bassett, and Brown (2011) noted that
student engagement increased in smaller classrooms as well as their interaction
with teachers hence lower achievers were off-task much more.

Din (1999) found that students in smaller classes
tended to help the teacher with classroommanagement, had more positive
student-teacher interactions, and received more individualized help from
teachers. Fan (2012) found that smaller classes gave students more access
tocomputers and additional space, and teachers were able to spend less time on
classroommanagement, which in turn led to greater student achievement.
Konstantopoulos and Sun(2014) found that teacher effects (teaching skills and
practices) had a larger impact on student achievement in smaller classrooms
than regular size classrooms. Smaller class sizes also give teachers an
opportunity to increase parental involvement and improve teacher curriculum
planning and development. Researchers
found that smaller classes gave teachers moreopportunities to reach out to
parents and include them in the educational process. And teachers who used
smaller classes to differentiate and individualize their curriculums showed
significantgains in student achievement. Rodriguez and Elbaum (2014) analyzed
that teachers with smaller class sizes had more time to interact with parents
and to develop more personal bonds.

Isocrates
(392 B.C.) opened an academy of rhetoric in Athens to train Athenian generals
and statesmen, and insisted on enrolling not more than six or eight students in
the school at a time. Power (1966) explained that Isocrates admitted "only
a few students to the classes because of the extraordinary concern for
care." Quintilian (1875) a rhetorician writing in the Roman Empire around
100 CE, cited the practices in Isocrates' school as evidence that a caring
education required small class sizes. Quintilian argued in Institutes of
Oratory, as Power summarized the book's thesis, that "care had nothing whatever
to do with discipline: It meant simply that only a few students at a time could
be taught effectively. However, since there is no concensus on the effect of
class size on academic achievement. it becomes imperative to examine the effect
of class size on pupils achievement in Mathematics.

Moreover,
gender is another factor that could affect students’ achievement in
mathematics. The widespread belief that males outperform females in mathematics
is apparently a myth. A meta-analysis (Hyde, Fennema, and Lamon 1990) showed
that boys tend to do better in mathematics tests that involve problem solving,
at least by the time they reach high school. Girls, however, do better in
computation and there is no gender difference in understanding concepts.
According to Kimball (1989), girls tend to earn better grades in mathematics
than boys. Gender differences in
mathematics performance that favour males are usually attributed to gender
socialization (Boswell 1980; Brush 1980; Eccles and Jacobs 1986; Linn and
Peterson 1986; Parsons, Adler and Kaczala and Meece1982; Sherman 1979, 1980;
Sherman and Fennema 1997; Stallings 1979). Basically, the argument is that
girls are thought to have low aptitude for mathematics and that they will not
need skills in advanced mathematics as adults (Chipman and Thomas 1985). These
socialization practices cause girls to lose interest in mathematics and to lack
confidence in their mathematical ability. As a result, they avoid mathematics
courses in high school. This situation puts them at even a greater disadvantage
because the most accurate predictor of performance on tests in mathematics is
the number of mathematics courses taken (Jones 1984). Girls also may experience
math anxiety (fear of mathematics) because of the messages they receive, which
can interfere with learning and test performance (Meece, Wigfield and Eccles
1990; Tobias 1987).

Gherasim,
Butnaru and Mairean (2013) found gender effects in such variables as
achievement goals, classroom environments and achievement in mathematics among
young adolescents showing that girls obtained higher grades in mathematics than
boys. Girls reported higher classroom support, lower performance-avoidance
goals (Shim, Ryan and Anderson, 2008) and more mastery of the learning materials
(Perkun, Elliot and Maier, 2006). Another aspect, students' attitude, was
studied by Jones and Young (1995), who found that boys had more favorable
attitudes towards mathematics and science than girls. Emotions towards
mathematics were studied by Frenzel, Pekrun and Goetz (2007) who found that
girls experienced less enjoyment and pride than boys. Boys on the other hand ,
experienced less anxiety and less hopelessness towards mathematics than girls.
They also found that girls felt slightly more shame than boys.

**Statement of the Problem**

The
ever-growing world population and the craze for education mean that classes
will continue to grow. A common feature
in institutions of learning is the large number of students taught by a single
teacher. With such a high teacher-student ratio, the teacher has no option but
to adopt self-help measures, which are in no way ideal or adequate for
appropriate learning. A critical issue that becomes a focus in the recent
development is the issue of the ability of the regular classroom lessons to
meet the learning requirements of the pupils in mathematics subject. It is now
thought that complementing the classroom lessons with a small number of pupils
may help in guiding them towards better performance. Inspite of the importance
of Mathematics, there is a general low-level of pupils performance in
Mathematics in examination, therefore the class-size couldbe the cause of this
low performance.

**Purpose of the Study**

The
purpose of this study was to find out the effect of small class size on
academic achievement of pupils in mathematics in Primary schools. Specifically,
the study sought to find out

1.
The mean scores of the pupils taught mathematics in small class and those
taught in large class.

2.
The mean scores of male and female pupils taught mathematics in small class.

**Scope of the study**

This
study is restricted to primary four pupils in private owned primary schools in
Ogbaru Local Government Area in Anambra State in teaching and learning of
fractions in Numbers and numeration in
Mathematics.

**Significance of the study**

A
study such as this will be significant in many ways to the pupils, teachers,
educational administration, and government.

There
is going to be a great improvement on the part of the pupils who learn because
the teacher will know them, their skills, passion, strength and learning styles
and more likely offer individual attention and guidance to them.

They
are going to be exposed to more one on one interaction with the teacher,
thereby enhancing their strengths and improving their weaknesses. They will
have the opportunity to speak up and be heard among their peers which will help
them to build self confidence and public speaking skills.

Teachers
will be in the better position to justify the performance of each child which
will guide their subsequent steps and strategies towards enhancing better
teaching with regards to the pupil’s performance.

They
are going to be prevented from becoming overwhelmed and overworked, which leads
to higher teacher satisfaction rates. This is because small class size consists
of small number of pupils which the teacher will have limited time to spend
with.

This
study will be of great value to schools and educational administrators in their
educational planning and reformations by knowing the number of pupils that
should be taught in a particular class by a teacher.

Finally, the study will be very important as it
might create jobs for unemployed Mathematics teachers. The government might
realize the needs for more hands
with regards to recruitment of many Mathematics experts who would be deployed
in schools.

**Research questions**

The following Research questions
are formulated to guide the study

1.
What are the mean scores of the pupils taught Mathematics in small class and
those taught in large class?

2.
What are the mean scores of the male and female pupils taught mathematics in
small class.

**Research hypothesis**

The
following hypotheses are tested at 0.05 level of significance.

Ho

_{1: }There is no significant difference in the mean scores of pupils taught Mathematics in small class and those taught in large class.
Ho

_{2: }There is no significant difference in the mean scores of male and female pupils taught Mathematics in small class.**================================================================**

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