Mathematics Teachers’ Perceptions on Problem-Solving in Ghana
CHAPTER 1
Introduction
Overview
This chapter covers the background of the study, a statement of the problem, the purpose of the study, significance of the study, research questions, delimitations, and limitations of the study.
Background of the Study
In Ghana, mathematics is a compulsory subject at all levels of pre-university education. Since it has impact, various governments have committed themselves to ensuring to provide high-quality mathematics education. These governments have made varying attempts, in the past, to improve achievement in mathematics in schools. For example, in 2003, the Ministry of Education (MOE), in a group effort with the Teacher Education Division (TED), reviewed the teacher education curriculum. As a result, they upgraded all Early Teacher Training Colleges (ETTC’s) to diploma-awarding institutions, with the aim of improving teachers’ knowledge in content and pedagogical skills in the different subject areas. The MOE, in a group effort with other international agencies, such as the Japan International Cooperation Agency (JICA), the United States Agency for International Development (USAID), and the Department for International Development (DFID), have shown dedication. They have helped by embarking on mathematics projects to improve the teaching and learning of mathematics at the basic, senior high, teacher training, and tertiary levels (Ampiah et al. 2000). Educational Reforms (Anamuah-Mensah National Education Review Committee Report 2002), of which implementation started in September 2007, is one of the recent improvements of education in Ghana. The curriculum in mathematics at the Senior High School (SHS) stresses on skill gain, creativity, and the arts of inquiry, and problem-solving. Curriculum documents suggest that teachers should start every lesson with a useful problem to help students gain the habit of analytical thinking and the ability to apply knowledge in solving applied problems (MOE, 2000). However, there is the need to make use of calculators and computers for problem-solving and application of real-life situations (MOESS, 2007). This direction to teaching and learning needs more than recommendations contained in the syllabuses.
In recent times, educationists recommend that teaching and learning of mathematics in the classroom should be more problem-solving oriented and student-centered. Problem-solving is one of the important aspects of the school mathematics curriculum in Ghana (MOE, 2007). I started experiencing problem-solving in 2007, when the Ghana Education Service (GES) posted me to the SHS as a mathematics teacher. I used problem-solving in my teaching after my first-degree training as Bachelor of Education in Mathematics (B. Ed), in the University of Education, Winneba (UEW), in Ghana. Then, the government initiative to motivate Science and mathematics teachers to prepare students to solve real and practical problems, through teaching and learning, was gradually gaining root. Further, during my internship, I applied the problem-solving (PS) technique in teaching, which yielded a positive result. This helped my students to understand the ideas that I taught them.
PS refers to finding solutions to problems when the student does not have the method readily available. In this case, the teacher presents problems for students to solve. Students afterwards wrestle to find and apply the needed principle to solve the problems. The teacher next checks students’ performance in applying the idea and, in doing so, clarifies, justifies, and specifies the principle (Mereku, 2004). PS is also a form of teaching in which students, through discussions, prescribe suitable solutions to problems. Problems that they had no idea of its solution, but consciously perform research to reach a target designed. The PS mathematics curriculum includes using and applying mathematics in the natural environment, in problems that may confront man daily, and within mathematics itself. It covers a wide range of routine mathematical problems to problems in unfamiliar contexts. It also makes room for open-ended investigations that make use of the relevant mathematics and thinking (Singapore, MOE, 2000).
PS could have a positive effect on students’ ability to understand and solve problems. This is because PS would enable students to study mathematics through the practical experiences that their teachers provide. Thus, the teaching students face in school goes a long way to shape their understanding of mathematics, their ability to use it to solve problems, and their confidence in it. This means that to improve mathematics education for all students needs effective mathematics teaching in all classrooms. Careful studies of the Chief Examiners’ Report of the West African Examination Council (WAEC) revealed that students in Ghana have serious problems in solving non-routine problems. The WAEC Chief Examiners Report [2003; 2004; 2005; and 2006] consistently reported candidates’ lack of skill in answering almost all the questions asked in general mathematics. WAEC Chief Examiners Report [2003, 2005] identified candidates’ weakness in the geometry of circles and mensuration problems. According to their reports, most candidates avoided questions on the 3-dimensional problem and story problems. The few who attempted them, the majority did not show a clear understanding of the PS skill. Clearly, the WAEC [2004] reported candidates’ weakness in dealing with algebraic expressions and word problems, among others. By this, clearly, they lack the skills and confidence to solve such problems. By this, the Ghana Government, though the 2007 educational reform, have called on mathematics teachers to teach mathematics through PS. This would enable our students to improve their ability to answer non-routine problems. Whether teachers would accept the challenge depends on their views of teaching through PS.
PS would afford well-balanced citizens with enough knowledge, skills, values, aptitudes, and attitudes. Students would become useful and productive citizens for total development, democratic advancement of the nation, and related matters (Education Act, 2008). Our current fast-growing societies need to solve new problems one after another. We need generations that can face and provide proper solutions to problems that may arrive from all sectors of the economy. To achieve this, teachers should introduce students to PS early, while they are still in school, so they could apply the same when, in the future, they graduate and start serving the nation. Asabere-Ameyaw & Dei (2012) suggested the need to make use of a practical approach in handling the topics in the mathematics syllabus. They held the most effective and a teaching strategy is PS. This is the reason the government of Ghana supports the practical method of teaching mathematics. Clear evidence is the provision for Science Resource Centers across the country. The education sector continues to support programs that increase the interest and participation of students. It occurs in the study of Science, such as the Science, Technical, and Mathematics Education (STME) clinics (MOF, 2012). This measure was to address the fallen standards of mathematics, Science, and Technology education. Government financially supports an annual mathematics; Science and Technology Education Scholarship Scheme to motivate students to aim for mathematics. This means that with slight effort from teachers, students should excel in mathematics.
Teaching through PS offers opportunities for students to engage in mathematical debate and excel in mathematics. Educating people who can solve problems, communicate findings, and perform group activities is what the SHS mathematics education Programme by (MOE, 2007) intends. Issues related to achievement of students in both lower and higher learning institutions in Ghana have always been of concern about the society. Despite government efforts, mathematics has not undergone much change in teaching and learning. These reflect consistently in low achievement levels in mathematics among students. Results from the Trends in International Mathematics and Science Study (TIMSS) in 2003 and 2007 at the Junior High School level (grade eight equivalents) are instances of poor mathematics achievement in the country. In the study, Ghana’s eighth-graders scored 43rd position among 44 and 46th among 47 countries that joined the study in 2003 and 2007, respectively (Mullis et al. 2004, 2008). For many years, the failure rate in mathematics has been dramatically higher in SHS’s. The low scores of students over the years in the WASSCE testify to these reports (Ottevanger et al. 2007). The report reflects on students’ passive attitude, lack of stimulus, and weakness in problem analysis (TIMSS, 2003; 2007). The lack of communication skills has prompted that teachers should give the PS approach the needed attention. PS actions in mathematics and Science should provide context for teaching students for the real world. Mathematics and Science teachers should collaborate and devise a needed skill to aid students to overcome difficulties faced in PS (Anamuah-Mensah, Mereku & Ghartey-Ampiah, 2007).
Teachers should not consider PS as a topic but an integral part of the various topics in the mathematics-teaching syllabus. PS benefits best when it forms part of the curriculum instead of being an isolated subject. One of the necessities of PS is to assimilate specific ideas and classroom contexts for improving students’ critical thinking skills and PS ability. This idea serves as a powerful tool to allow learners to have a sense of control of their language and learning (Mereku & Cofie, 2008). For the last few years, there have been attempts to make PS the focus of school mathematics rather than being an isolated part of the mathematics curriculum. Similarly, in the new Ghanaian mathematics curriculum, PS forms an integral part of mathematics learning and one of the common basic skills that students need to display for all subject matters (MOE, 2007). This would make the PS experience of students seen in a broader perspective, which would go a long way to mold students better and shape their critical thinking ability.
Importantly, teachers’ perceptions and beliefs have a great effect on the nature of their classroom practices. Therefore, these have an impact on their students’ beliefs, attitudes, interest, curiosity, and performances. For a step-up in mathematics teaching, it is vital that teachers believe and have a positive attitude towards PS. The GES, Non-Governmental Organizations (NGO), and SHS have organized series of in-service training to back teachers, but to no benefit. Frequent training given to teachers on PS cannot be effective if teachers do not have the right perceptions towards teaching through PS. Many of these training sessions linger on PS skills and rarely touch on misconceptions. To address teacher-mistaken beliefs about PS, there is the need to research into SHS teachers’ views and practices of teaching mathematics through PS. This would help shape the implementers of the curriculum to make the curriculum real and practical. It would help improve students’ performance in the West Africa Examination (WASSCE). It is, therefore, important that we examine the SHS mathematics teachers’ perceptions and practices of teaching mathematics through PS.
Problem Statement
Various studies have suggested that students perform well in mathematics if the subject relates to their environment and real-life experience (for example Amisah, 2000; Ball, Ferrini-Mundy, Milgram, Schmid, & Schaar, 2005; Meyer, Dekke & Querelle, 2001). However, in Ghana, research has proved that students find it difficult to solve practicable and non-routine mathematical problems (Mereku & Cofie, 2008). Students only see mathematics as a set of rules and formulae to memorize (Awanta, 2000). Students’ inability to solve non-routine problems could be a reflection of teachers’ perceptions and practices of teaching through PS. Teachers’ views towards teaching mathematics through PS influence their teaching of mathematics through PS in a way that students would benefit from mathematics instruction.
Thus, many teachers at SHS in Ghana have unfavorable perceptions towards teaching mathematics through PS. These views affect their practices in teaching mathematics through PS. This could contribute to students’ low performance in mathematics.
Purpose of the Study
The purpose of the study is to explore the mathematics teachers’ perceptions of teaching mathematics through PS in the SHS of Ghana. It would consider how these perceptions affect their practices of teaching mathematics through PS. It is also to back teachers to help reduce the difficulties that students face in solving non-routine mathematical problems and help improve their students’ performance.
Objectives of the Study
The overall objective is to explore mathematics teachers’ opinions and practices of teaching and learning mathematics through PS that might be more productive for teaching in the SHS of Ghana. It would further examine mathematics teachers’ perceptions on students’ ability and inability to respond to teaching and learning through PS. Specifically, the objectives of the study are to explore SHS mathematics teachers’:
- General perceptions of teaching through PS
- Causes likely to affect PS
- Role in teaching through PS
- Influence on students’ performance in mathematics
- Ability to teach through PS
Research Questions
The study raises questions about SHS teachers’ perceptions and practices of teaching through PS. In addition, how these perceptions affect instruction. Specific questions to be addressed by this study are as follows:
- What are the general perceptions of teachers on teaching mathematics through PS?
- What practices affect teaching mathematics through PS?
- What differences exist between teaching mathematics through PS and without PS?
- To what extent do teachers’ perceptions of teaching through PS influence their practices of teaching mathematics?
Significance of the Study
This study would create awareness to serve as an instrument for mathematics teaching and learning, as well as a basis for further research in mathematics education. This study is important to education, teaching, and learning of mathematics. Recent records show that more students in the SHS perform badly in mathematics. The study tests teachers’ opinions and practices of the PS technique to see how useful this technique would be in the teaching and learning of mathematics in the SHS. The result of the study could help policymakers and educational planners become aware of the teachers’ opinions of PS in the teaching and learning of mathematics.
Delimitation
This research would focus on SHS mathematics teachers in the Greater Accra region of Ghana. The study shall involve about 100 SHS in the Accra Metropolis in the Greater Accra Region of Ghana. About forty item questionnaires given out to teachers within the city provided signals of how intensely teachers see and respond to the teaching and learning of mathematics through PS in the metropolis and reflect Ghana as a whole. Selecting the schools considered the purpose of the study, intended targets, and available funds.
Limitation of the Study
This study focuses on teachers who are teaching in urban schools located in the Greater Accra Region of Ghana, the capital city. Limits were unavoidable due to the nature of the study. The participants may try to please the researcher by providing particular data in questionnaire or interview responses. The study is limited because it did not cover the entire Accra Metropolis but targeted 100 SHS within the metropolis. The results may not involve all teachers in the metropolis; hence, it would affect the coverage and generalizing results somehow. The nature of the design (mixed design) for this study; organization, arrangement, grouping of data analysis, and discussions is likely to be tedious. Therefore, the study did streamline the analysis of the study. Organized interviews and observations aided proper presentations for proposing an accurate analysis.