A study on mathematics

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The greatest treasure and asset of a nation are its educational institutions. They make or mar the destiny of that nation. Education is considered as one of the most important tools for national development, "it is an end in itself and a means for achieving other goals of development, such as economic growth, poverty reduction" (Glewwe and Ilias, 1996:395). The strength of a nation is built on human resources developed by its educational institutions which train the brains, provide skills and open a new world of opportunities and possibilities to the nation for economic growth, social justice and poverty alleviation (Lauder et al. 2006; Adentunde 2007).

According to Okuma-Nyström (2003) it is impossible to find a country anywhere in the world without any form of educational system. In all educational systems, students are introduced to a variety of subjects in all disciplines and programmes for both academic and professional purposes. However, mathematics holds a key position in the school curriculum and in virtually all countries it is a core component of the school curriculum. It is also seen as a pivotal subject, both in its own right, and also because of its important connections in diverse fields such as the natural sciences, engineering, medicine, and the social sciences (Keith, 2000).

It is upon this that, reflections on the importance of mathematics and the process of mathematics teaching and learning has been a long-standing issue in almost every part of the world for some time now (Törner and Sriraman 2006). Similarly, according to Blum (2002) the importance of mathematics in all realms of life and the recent debate on the falling standards of students' achievement in mathematics has triggered the growing attention for researchers, parents and education authorities in their quest for the way forward over the last two decades. For example, according to Blum (2002) most parents, and educators believe that, a good results in mathematics is not only a good measure for entering into institution of higher learning and getting a good programme, but also a requirement for most jobs. Blum (2002) further argued that, in view of this important role that mathematics plays in all realms of lives, college/high school students' have been spending hundreds of hours in mathematics classes both at school and at home to pass their mathematics examinations.

However, according to, Agudelo-Valderrama (1996) most students are not successful in achieving this and a number of students still find it difficult entering institution of higher learning due to poor grades in mathematics. Agudelo-Valderrama (1996) further added that, the way mathematics is conceived, taught and learnt has not only contributed to many students not realising their full potential but most students not realising the importance of the mathematics they learn at school since they are not able apply what they have learnt to their real life situations. Agudelo-Valderrama (1996) in arguing his case further added that it is not surprising we often hear many students asking questions like: where will I use this kind of mathematics? What are we learning this for?

In view of this, improving mathematics teaching and learning has been an issue of considerable concern in almost every part of the world, and the teaching and learning of mathematics has been undergoing through a number of restructuring coupled with the introduction of new school curriculum and new teaching methods. The evolution of these new school curriculum and its accompanied new teaching methods is rooted in finding ways of empowering students to learn to do mathematics (Thomasenia, 2000). In addition to this, Anku (2008) and Ampiah et al (1998) and others, have advocated for the need for a holistic view of changing the teaching-learning process of school subjects from a teacher centred with its accompanying rote learning to a transformative method which can help students to generate their own meaning and understanding of mathematical concepts. To achieve this, the government of Ghana and other stakeholders in the education sector have taken a number of initiatives in promoting effective teaching and learning of the subject.

For example, in transforming the teaching and learning of mathematics and education in general in Ghana, the Ministry of Education (MoE) in collaboration with the Teacher Education Division (TED) in 2003 reviewed the teacher education curriculum and upgraded all Initial Teacher Training Colleges (ITTC's) to Diploma awarding institutions with the aim of improving teachers' content knowledge and pedagogical skills in the various subject areas. In addition to this, the Ministry of Education (MoE) in collaboration with other international agencies such as the Japan International Cooperation Agency (JICA), United States Agency for International Development (USAID) and the Department for International Development (DFID) have shown enormous commitment by embarking on mathematics and science projects to improve the teaching and learning of mathematics.

In addition to this, as highlighted, standards in mathematics teaching and learning over the years has been an important goal in educational researches aimed at finding scientific evidence for improving the teaching and learning of the subject. According to Potari and Georgiadon-Kabouridis (2009) since independence, a considerable number of researches have been conducted in this area and the evidence of this is reflected in the theoretical shifts and changes in the teaching and learning strategies adapted in various mathematics classrooms. For example, empirical research evidence have provided educational authorities and policy makers with rich information on the context for the teaching and learning of mathematics which is used to identify the contextual variables such as teaching with multiple representations of mathematical concepts, that can be modified to bring about improvement in the learning and teaching (Anamuah-Mensah and Mereku, 2005).

1.3 The Genesis of This Study/ Conceptualising the Research

However, despite these considerable contributions of research highlighted above, and the need for further research into mathematics teaching and learning, it is believed that "academic texts that deny the personal voice and create an illusion of neutrality hurt the pursuit of truth" (Bochner 1997: 418). Thoughts about investigating into the status of mathematics teaching and learning in Ghanaian junior high schools had been necessitated by my personal experience as a student, mathematics educator and researcher. That is, the choice of this research topic for my doctoral dissertation was necessitated by my personal experience. For example, during my primary school education (6-12 years), I developed much interest in mathematics. This interest was inspired by my teacher who created learning environments which promoted active participation and understanding of mathematical skills and concepts.

However, my interest in the subject started waning out after my primary education because most of the classroom interactions were overwhelmingly teacher-centred and examination driven. Learning activities were through 'rote learning' where we had to memorize formulas without understanding them and their applicability, and the situation was not different at the university. I found the subject as the most difficult and abstract subject in the school curriculum and this did not only affect my performance, but also my interest in the subject. Similar to this, research by Eshun (2004) and Eshun-Famiyeh (2005) have also shown that, despite the importance of mathematics in all realms of life, a good proportion of Ghanaian students' find mathematics difficult and those who profess not to be good in mathematics take pleasure in doing so. According to Eshun (2004) and Eshun-Famiyeh (2005) mathematics as a subject taught in school, generates in many pupils and students a feeling of fear, anxiety, unease and insecurity. Responses such as: 'if you teach mathematics then you must be very brilliant', 'I never liked mathematics at school', and 'oh no, not mathematics! I am very poor at it', are very common expressions of the way other people especially students, also feel about and perceive mathematics (Orton and Frobisher 1996, Eshun-Famiyeh 2005).

In addition to this, my curiosity for research in the area of mathematics teaching and learning was stimulated at the latter part of my undergraduate education in the year 2002, when I was writing my thesis. I began my own research to examine the kind of mathematical concepts that junior high school graduates who find themselves in various vocations (eg. tailoring, dressmaking, carpentry and masonry) were using at their various work places. The purpose of this study was to examine the views of these graduates, on the relationship between the mathematical concepts they are applying at their respective work places and the mathematics they have learnt in school. The results from the study were interesting and puzzling in the sense that, the mathematical concepts that the apprentices presumed to be using at their respective work places were similar to what is documented in the national curriculum (eg. measurement, algebra and pattern formation).

However, though most of these graduates, mostly apprentices, knew they were applying some mathematical concepts at their respective workplaces, but they could not link these concepts to the mathematics they have learnt in school.

This confirms Anamuah-Mensah and Mereku (2005) assertion that, majority of the students do not have the opportunity to learn a substantial proportion of the content of the mathematics curriculum and that, most students lack the conceptual understanding of the mathematics they have learnt which is needed to make informed judgement and applications to other related context or problems. That is, in most times students are not able to conceptualize and apply the mathematical skills and concepts they have learnt in solving day to day problems. This is due to the because of the structured and procedural manner this information is presented where students follow a series of procedures and apply a formula to solve a particular problem without necessarily understanding why that problem is solved that way and its application to other related problems (Anamuah-Mensah and Mereku 2005). Hiebert and Carpenter (1992:76) in a similar vein contends that, if mathematical tasks are overly restrictive and structured, students' conceptual development of mathematical thinking is severely constrained, and the networks they build are bounded by these constraints and the likelihood of transferring this knowledge across different settings becomes problematic.

These puzzling results therefore inspired me to explore further to find out more about mathematics teaching and learning. During my years as a research assistant at the Institute of Education (IoE), University of Cape Coast, Ghana, I had the opportunity to interact and engage in discussions with mathematics educators and students to know their views on the state of mathematics teaching and learning in Ghana. Though these observations and listening did not provide definite answers to the results from my previous study, however, it did opened a new door and area of research for me, and I have come to realise that mathematics teaching and learning is influenced by several factors. Furthermore, the information gathered from these interactions have also shown that in our quest for improving mathematics teaching and learning, the voices of teachers and students are somehow neglected and most often, what goes on in the actual classroom is given little or no attention.

Reflecting on my personal experience and also examining a report of a national study, Criterion Reference Test (CRT) conducted in 1996 and 2000 which established that only 1.8% and 4.4% of primary six students' nationwide obtaining a mastery mark of 55% respectively, have shaped my interest in examining how mathematics is taught and learnt in Ghanaian schools (MoE 2002). Furthermore, the choice of this topic has been inspired by the results from the Trends in International Mathematics and Science Study (TIMMS) conducted for junior secondary two (grade 8) students' in 2003 which portrayed a generally poor performance of Ghanaian students, with a students' average of 276 in mathematics which was significantly lower than the international average of 467 (UEW/GES, 2003).

Following these trends in mathematics teaching and learning in Ghana and linking it to my personal experiences, I consider the timing appropriate to research into the issue empirically to complement to present efforts by providing input to ongoing debate on finding empirical evidence through research to improve the teaching and learning of mathematics in our schools.

1.4 The Research Problem

As indicated in section 1.2, mathematics teaching and learning has been a major concern in various countries and the past four decades have seen several waves of mathematics reforms, each entailing serious efforts to improve mathematics teaching and learning (Ball et all 2001: 434). Reforming school mathematics has therefore been a part of a broader set of contemporary ideas about improving education because of the pivotal role that mathematics plays in the school curriculum (Ball et al. 2001).

However, these changes have been very difficult and many students experience their mathematics differently and there is a continuous evidence for the search for improved ways of mathematics teaching the subject with accompanied interventions and restructuring of mathematics curriculum (Boaler 2009). For example, NCTM (2000) reported that in the United States, mathematics teaching has undergone and continues to undergo changes as a way of improving students' achievement, understanding and interest in mathematics (NCTM 2000). According to the NCTM (2000) report, one of the most common methods of teaching mathematics in the U.S, direct instruction or the traditional method of 'chalk and talk' has been criticized for its limitation of not helping students to develop understanding of mathematical concepts (NCTM 2000). In addition to this, Ball et al (2001: 434) have also argued that the school mathematics experience of most Americans is and has been uninspiring at best, and intellectually and emotionally crushing at worst and educational authorities, schools and teachers are becoming more involved in finding ways of improving it.

In the United Kingdom (UK), Orton and Frobisher (1996), reported that "whenever concerns are expressed about attainment of pupils in England and Wales and comparisons, whether legitimate or not, are made with pupils in other countries, mathematics is usually singled out as being a particularly worrying problem" (p. 1). Similarly, Baker (2008:1) have also argued that, there is a common understanding in the United Kingdom and North America that students of all ages experience a wide range of difficulties when attempting to study Mathematics. According to Chambers (2008) student's difficulties in learning mathematics and the low achievement in mathematics among most students in England over the years led to the introduction of the national curriculum in the United Kingdom in the 1980's which aimed at providing a level platform for all students.

In South Africa, Jita (2002) reported that, despite the numerous initiatives by the government to improve mathematics and science education, shifting classroom practices from the traditional way of teaching to a more transformative approach has been a major challenge and students' achievement in mathematics has still not reached the desired levels. Similarly, Ottervange (2002) reported that most classrooms in Sub-Saharan Africa are characterised by students playing passive role in the teaching-learning process which is characterised by students listening and copying notes while the teacher does all the talking.

In Ghana, research by Eshun (2004) and Eshun-Famiyeh (2005) have shown that the subject continues to be the most fearsome subject in the school curriculum. The general perception of mathematics been the most difficult subject in the school curriculum is reflected in students' performance at both the national and international levels in Ghana over the years. For example, the 1996 and 2000 National Criterion Reference Test (CRT) is clear manifestation of negative perception that students have in mathematics. Also the generally poor performance of Ghanaian students with a students' average of 276 in mathematics which was significantly lower than the international average of 467 in the third Trends in International Mathematics and Science Study (TIMSS) conducted in 2003 is another reflection of the status of mathematics teaching and learning in the country.

It is upon these issues that, how the subject is taught and learnt among other issues has therefore become the subject of national scrutiny in Ghana for some time now. Therefore, the problem of how to teach the subject to help students to develop interest and conceptual understanding of mathematics have therefore been the concern of mathematics educators, teachers, parents and indeed all those who manage education (Eshun-Famiyeh 2005). In response to this demand, researchers, educators and other stakeholders in the education sector have advanced educational arguments supporting the need for scientific evidence into the issue and the way forward.

For example, Eshun-Famiyeh (2005), reported that the socio-economic background of the individual student plays a crucial role in his/her mathematical competency. He added that students' with educated parents are more competent in mathematics than their colleagues from broken homes because parents are able to provide the right learning environment which makes them competent in solving mathematical problems. However, students from well-to-do homes and those from poor homes have some level of mathematical competencies but those from poor homes normally make more mistakes as compared with their other colleagues (Eshun-Famiyeh 2005).

In addition to this, Asiedu-Addo and Yidana (2004) also examined mathematics teachers content knowledge and argued that, how knowledgeable the teachers is in his/her subject area is very crucial as it determines how the teacher teaches. On the contrary, Agyeman (1993) reported that, despite the crucial role that a teacher's academic and professional qualification plays in improving the teaching and learning of the subject, a well qualified teacher who works under unfavourable conditions of service would be less productive and that is another factor which need to be given the needed attention.

In addition to this, Kraft (1994) and Ampiah et al (2000) in their research also identified the unavailability of text-books in most schools especially as another factor. This insufficiency of text-books does not only affect students learning at schools but also at home. According to Ampiah et al (2000) in Ghana, students are not allow to take text-books home and this makes it difficult for teachers to give students enough home work. In this current context, it can be argued that the problem is not only associated with one particular factor but a number of interrelated factors which calls for a holistic approach of investigating into the problem. However, research by Jansen (1995) have shown that one of the major critiques of educational research and for that matter research in mathematics teaching and learning has been the failure to locate conceptions and measures of school quality and effectiveness within everyday classroom processes of teaching, learning and assessment. For example Ampiah et al (2000) research was conducted outside the classroom using questionnaire and interview to gather information on the perception and attitudes of mathematic teachers and students toward mathematics. Also, Adetunde (2007) have also looked at improving the teaching and learning of mathematics in secondary schools in Ghana with particular reference to factors that impede the teaching and learning of mathematics. He also made reference to various approaches of teaching that can be used in the teaching of mathematics.

In addition to this, Hadman et al (2008) argued that, there is growing acceptance of the significance of the impact of the teaching and learning practices adopted in mathematics classrooms on students' learning and understanding of the subject. Similarly, McMahon (2001:1) also added that, classroom ethos has considerable potential for supporting or denying students access to the mathematical concepts that they have learn and apply in their daily activities. However, there is relatively little scientific evidence of studies that have examined mathematics classroom practices by collecting a variety of data from different sources to understand problem under consideration (Wilkins 2008). Also most of these studies were limited in scope as most of them were purely qualitative in nature which limits the generalizability of the findings to other similar settings.

For example, Kuwayama et al (2007) in their study involving three teachers aimed at examining the differences in cognition about teaching and learning among teachers, found differences in cognition about teaching and learning between more experienced and less experienced teachers. They argued that experienced teacher taught mathematical concept through activities apart from whether or not it could be fully attained while the inexperienced teacher regarded both knowledge and skills as the objectives of his lesson (Kuwayama et al 2007:107).

The focus of this present study is therefore is to, investigate into the teaching practices adopted by teachers and why teachers use these teaching practices as well as students' experiences of been taught mathematics. In this study, a mixed method inquiry approach will be used in investigating into the teaching and learning of the subject with emphasis on teachers teaching practices and students learning experiences by employing both quantitative and qualitative methods. The quantitative part of the study sought to characterise the perceived teaching practises of teachers and students perceived experiences of being taught mathematics, whilst the qualitative part seeks to explore teachers' actual classroom practices and why they teach the way they teach as well as students experiences of been taught mathematics.

1.5 Purpose of the Study

As highlighted, the general purpose of this study is to investigate into the teaching and learning of mathematics in Ghanaian Junior High Schools (JHS). In other words, this study seeks to explore and develop a deeper understanding of how mathematics is taught and learnt in Ghanaian Junior High Schools (JHS). Specifically, the study seeks to investigate into what teaching and learning strategies are adopted in mathematics classrooms and also, explore the characteristics of teachers teaching methods and why they use these methods. The study also seeks to examine students' experiences of been taught mathematics and the characteristics of students experience in mathematics classrooms from both a deductive and inductive perspective.

1.6 Research Questions

The primary research question is: How is mathematics taught and learnt in Ghanaian Junior High Schools (JHS)? The related research questions are:

a) What teaching methods are used by mathematics teachers?

b) Why do mathematics teachers use these teaching methods?

Is there any relationship between teachers' perception of their classroom practices and what they actually do in class?

What are students' perceptions of their teachers' teaching practices?

How do students experience mathematics in their respective classrooms?

The above questions are investigated through a three dimensional framework which will help in collecting data to answer these questions. The three dimensional framework incorporates:

A review of literature (all research questions)

A semi-structured questionnaire (questions one and three)

Classroom observation and individual interviews (all research questions).

1.7 Significance of the Study

International and national assessment of Ghanaian students has illuminated their poor academic achievement in mathematics. It is for this reason that, scientific evidence in the issue of mathematics teaching and learning has become a major concern for all stakeholders in the country. As highlighted, the need for scientific evidence on how the subject is taught and the way forward is long overdue. However, as highlighted, very few studies have explored this issue by employing multiple methods in collecting variety of data to have a clearer picture of the problem under investigation. This study is therefore expected to contribute to knowledge in the following ways: Firstly, the findings and the conclusions from this study will contribute to the understanding of how mathematics is taught and learnt in schools which is needed for possible curriculum restructuring as well as teacher training and development. In addition to this, the questions: what teaching methods do mathematics teachers use and why teachers use these methods, what are students experiences of been taught mathematics are very crucial in improving mathematics teaching and learning in schools. However, to date, no study has specifically investigated and answered these important questions in the Ghanaian context. It is a study with this focus that can provide useful information and data or a conceptual framework for educational authorities and policy makers on how to improve the quality of teaching and learning of mathematics.

Also the findings and conclusions from this study will provide a new conceptual framework which will contribute to the realisation of the objectives of the new mathematics curriculum which aims at enabling all young Ghanaians to acquire mathematical skills, insight, attitudes and values that they will need to be successful in their chosen careers and daily lives (MoESS 2007). Finally, the findings from this study will lay a foundation for further research and practical implications. For example, knowing how the subject is taught and learnt, methods could be proposed in exploring the relationship between teachers teaching practices and students learning experiences.

1.8 Limitations of the Study

The major drawback of this study is that the study is limited to only 12 schools in one district that provided the information to answer the research questions raised in the study.

1.9 Structure of the Thesis

The dissertation is divided into seven chapters. In the first chapter, the introduction, the author's personal reflections, background of the study, statement of the problem, purpose of the study, research questions and the conceptual framework of the study is presented.

The second chapter examines the educational system in Ghana with particular reference to the historical over view of the educational system in Ghana, the structure of Ghana's education system as well as challenges facing Ghana's education. With guidance from the research problem and the research questions, the third part presents the review of related literature with particular reference to teaching and learning strategies and research on mathematics classrooms and factors affecting mathematics teaching and learning. In addition to this the theoretical basis for the study is presented in this chapter.

The forth part presents the methodological considerations for the study is presented in this chapter. The research design, the general framework for the study, data collection procedures, research methods, sample and sampling techniques, validity and reliability issues as well as ethical considerations and the quality of the research process are discussed in this chapter.

The fifth part presents the data analysis of the quantitative data from the questionnaire examining the perceived teaching and learning practices of teachers and students. The sixth chapter presents the analysis of qualitative data from the classroom observation, interview and focus group discussions. The last part is devoted for the presentation of the summary and conclusions of the findings from both the quantitative and qualitative data analysis.

Chapter Summary

In this first chapter, the background of the study and personal motivation that led to the origin of this study as well as the aims of the study is presented. The problem of the statement, significance of the study as well as the research questions guiding the study is presented here. The limitations of the study are also acknowledged in this chapter. Lastly the structure of the whole thesis is also presented here. The next chapter presents an overview of Ghana's educational system.