**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

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

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

**CHAPTER TWO: REVIEW OF RELATED LITERATURE**

### Conceptual Framework

### Theoretical Framework –

### Empirical Studies –

### Summary of Literature Review

**CHAPTER THREE: RESEARCH METHODS**

### Research Design

### Area of the Study

### Population of the Study

### Sample Techniques and Size

### Instrument for data Collection

### Validity of Instrument

### Reliability of Instrument

### Experimental Procedure

### Control of Extraneous variable

### Method of Data Collection

### Method of Data Analysis

**CHAPTER FOUR: RESULTS **

### Presentation of Data

**CHAPTER FIVE:DISCUSSION, SUMMARY AND RECOMMENDATION **

### Discussion of Findings

### Conclusion

### Implications of the study – – – – – – – –

### Recommendations – – – – – – – –

### Limitations of the study – – – – –

### Suggestion for further Studies – – – – – – –

### Summary of Findings – – – – – – – –

## References

## Appendix A

## Appendix B

## Appendix C

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