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Representations of mathematical concepts are very important in the teaching and learning of mathematics. Visual representations are used to present mathematical concepts to solve, explore or explain the concepts. The purpose of this study... more
Representations of mathematical concepts are very important in the teaching and learning of mathematics. Visual representations are used to present mathematical concepts to solve, explore or explain the concepts. The purpose of this study was to examine undergraduate mathematics education students’ visual representations of multivariable functions using matching items tasks. The study was qualitative research conducted with 10 second-year undergraduate mathematics education students at a University in Zimbabwe. The students matched the functions of several variables which are represented in symbolic and graphic forms. The result showed that most of the students were able to match the functions with their graphical representations. However, most of the students had difficulties in communicating mathematical information and these difficulties emanate from language problems and conceptual understanding.
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Making connections between the representations of trigonometric functions and an interpretation of graphs of the functions are major challenges to many students. This study explores the effectiveness of the GeoGebra on grade 12 students’... more
Making connections between the representations of trigonometric functions and an interpretation of graphs of the functions are major challenges to many students. This study explores the effectiveness of the GeoGebra on grade 12 students’ success in making connections between the representations of trigonometric functions and the interpretation of graphs. A non-equivalent control-group pre-test post-test quasi-experimental design was used. The sample of the study consisted of sixty-one grade 12 students from two schools. The results showed that there was a statistically significant difference between the mean achievements of the experimental group and the control group on making connections between representations of trigonometric functions, and on analyses and interpretations of representations of trigonometric functions, in favour of the experimental group. This study extends the findings of previous studies on the effectiveness of dynamic mathematics software on students’ learning...
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Textbooks play a central role in the teaching and learning of mathematics. In some schools, textbooks serve as the only resource material available to teachers and students. Yet, little is known about the learning opportunities in... more
Textbooks play a central role in the teaching and learning of mathematics. In some schools, textbooks serve as the only resource material available to teachers and students. Yet, little is known about the learning opportunities in mathematics textbooks in most countries. This study investigated the opportunities to learn Euclidean Geometry in two textbooks of tenth-grade mathematics in South Africa. It examined the content coverage, content organization, and the type of tasks used in teaching the topic in the textbooks. This study followed a case study research design and a qualitative approach. The Curriculum and Assessment Policy Statement's (CAPS) grade 10 Euclidean geometry curriculum and Gracin's mathematical activity types served as frameworks for the analyses. The data were analyzed following the deductive content analysis approach. The result shows that the contents of Euclidean geometry were well covered in both textbooks following the curriculum and the contents we...
Education stakeholders and researchers in South Africa have emphasised the need to enhance teachers’ creativity through problem-solving tasks. Teachers’ creativity entails using new ideas of creative devices to solve problems, implement... more
Education stakeholders and researchers in South Africa have emphasised the need to enhance teachers’ creativity through problem-solving tasks. Teachers’ creativity entails using new ideas of creative devices to solve problems, implement solutions, and make learning more effective. In the research reported on here, Guilford’s theory was used to explore primary school pre-service teachers’ solutions to pattern problem-solving tasks based on 3 components of creativity. The data for this research were produced from primary school pre-service teachers’ written responses to the pattern problem-solving tasks, and an extract from participants’ semi-structured interviews. The research involved a qualitative design using convenient purposive sampling to sample 62 pre-service teachers enrolled for a primary mathematics module at a selected higher education institution. Participants’ responses to the written tasks were analysed using content analysis, while the semi-structured interviews were a...
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The Student Evaluation of Teaching (SET), although controversial, is a common practice at the higher education level for faculty appraisals and promotions, but seldom at secondary school level. Concerns have been raised as to whether... more
The Student Evaluation of Teaching (SET), although controversial, is a common practice at the higher education level for faculty appraisals and promotions, but seldom at secondary school level. Concerns have been raised as to whether students are informed and experienced enough to evaluate teachers’ teaching practices in a reliable way and arrive at valid outcomes. The purpose of this research was to explore the reliability of students’ evaluations of mathematics teaching at secondary school level. This research involved eight teachers, and 194 Grade 11 students from eight secondary schools in Bojanala District, North West province in South Africa. A SET questionnaire was developed, validated and used for data collection. The data were analysed by calculating the average deviation index of the students’ evaluations of each teacher per item and the Intraclass Correlation Coefficient (ICC) with SPSS. This was done using one-way random effects, absolute agreement and a multiple raters/measurements model. Both the ADI and ICC values showed a high degree of reliability of the SET. Hence, SET at secondary school level may provide a reliable indication of teachers’ educational practices that might be used for the formative assessment of teachers’ instruction. It can also assist in designing teacher training programmes for pre-service teachers and professional development programmes for in-service teachers.
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ii DECLARATION iv ACKNOWLEDGEMENTS v TABLE OF CONTENTS vi LIST OF ABBREVIATIONS viii CHAPTER 1 1 ORIENTATION OF THE STUDY 1 1.
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The purpose of this study is to investigate the effectiveness of the university curriculum in preparing pre-service technology teachers. The study examines the course guide of the technology education course at one of the universities of... more
The purpose of this study is to investigate the effectiveness of the university curriculum in preparing pre-service technology teachers. The study examines the course guide of the technology education course at one of the universities of technology in South Africa in relation to grades 7–9 (senior phase) of the technology policy document. The study found that the university technology curriculum places emphasis on both content breadth (CB) and content strands (CS). However, some of the CSs in the university technology curriculum have no relevance to the CB and were not designed to enhance its depth. Therefore, this means that the CSs of the university technology curriculum were not designed to focus on the notion of ‘fitnessfor-purpose’ which is market driven. However, it is imperative that students be given an opportunity to explore both CB and content depth (CD) as well as how other CSs can be used to develop a deeper understanding of CB. Résumé Le but de cette étude est d’examine...
Making connections between the representations of trigonometric functions and an interpretation of graphs of the functions are major challenges to many students. This study explores the effectiveness of the GeoGebra on grade 12... more
Making connections between the representations of trigonometric functions and an interpretation of graphs of the functions are major challenges to many students. This study explores the effectiveness of the GeoGebra on grade 12 students' success in making connections between the representations of trigonometric functions and the interpretation of graphs. A nonequivalent control-group pre-test post-test quasi-experimental design was used. The sample of the study consisted of sixtyone grade 12 students from two schools. The results showed that there was a statistically significant difference between the mean achievements of the experimental group and the control group on making connections between representations of trigonometric functions, and on analyses and interpretations of representations of trigonometric functions, in favour of the experimental group. This study extends the findings of previous studies on the effectiveness of dynamic mathematics software on students' le...
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In this article we present a framework for analysing mathematical task performance. The framework employs systems engineering production methods and cognitive science research findings to explain mathematical problem solving process. In... more
In this article we present a framework for analysing mathematical task performance. The framework employs systems engineering production methods and cognitive science research findings to explain mathematical problem solving process. In systems engineering, designing a solution to a problem involves designing an input-process-output system that converts the input to the desired output. In mathematical terms the input is the problem, the process is all that the problem solver invokes to arrive at the solution. The framework identifies two types of errors namely, structural and execution errors. These errors may occur as the problem solver carries out the process. The value of the framework is in identifying a person’s mathematical ability.
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The acquisition of procedural and conceptual knowledge is imperative for the development of problem solving skills in mathematics. However, while there are mixed research findings on the relationship between the two domains of knowledge... more
The acquisition of procedural and conceptual knowledge is imperative for the development of problem solving skills in mathematics. However, while there are mixed research findings on the relationship between the two domains of knowledge in some branches of mathematics, the relationship between learners’ procedural and conceptual knowledge of algebra has not been well explored. This research paper examined the relationship between Grade 11 learners’ procedural and conceptual knowledge of algebra. Data for the study was collected using an algebra test administered to 181 grade 11 learners in Gauteng province, South Africa. Descriptive statistics and Pearson’s correlation coefficient were used to analyse the data in SPSS. The study revealed that the learners have low levels of both procedural and conceptual knowledge of algebra. However, they displayed better procedural knowledge than the conceptual knowledge of algebra. In addition, a statistically significant moderate positive linear...
There is some disparity in the quality of education among the various races and provinces in South Africa. Since the dawn of democracy in 1994, the government has tried to bridge the gap using quintile categorisation of public schools and... more
There is some disparity in the quality of education among the various races and provinces in South Africa. Since the dawn of democracy in 1994, the government has tried to bridge the gap using quintile categorisation of public schools and its concomitant funding. The categorisation is based on the socioeconomic status of the community in which the schools are located. This study investigated the achievement of learners in the first four quintiles from one school district on the topic of probability. The study employed a quantitative research approach and used Bloom’s taxonomy as the conceptual framework. A total of 490 Grade 12 learners from seven schools participated in the study. Results showed that learners in Quintile 4 had significantly higher achievement scores than learners in the lower quintiles at all levels of Bloom’s taxonomy except synthesis. Counter intuitively, Quintile 1 students had higher achievement than those in Quintiles 2 and 3 at all cognitive levels of Bloom’s...
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The purpose of this study was to explore the effectiveness of GeoGebra assisted instruction on students’ achievement in drawing graphs of linear functions and interpretation of the representations of linear functions. These aspects of... more
The purpose of this study was to explore the effectiveness of GeoGebra assisted instruction on students’ achievement in drawing graphs of linear functions and interpretation of the representations of linear functions. These aspects of linear functions tend to pose a challenge to many students. The non-equivalent control group pre-test-post-test quasi-experimental research design was used in the study. The sample was 94 Grade 9 students from three secondary schools in a province in South Africa. Two schools formed the control groups and one school was the experimental group. Data were collected using achievement tests. The tests results were analysed using inferential statistics (Kruskal-Wallis and Mann-Whitney U comparison tests) at 0.05 level of significance. Statistically significant differences were found between the groups with respect to drawing and interpretation of linear functions graphs with the experimental group obtaining the highest mean scores. The findings suggest that...
The coronavirus pandemic (COVID-19) has brought another dimension to teaching and learning across the levels of education. The lockdown imposed in many countries to curtail the pandemic forced many institutions of learning to shift to the... more
The coronavirus pandemic (COVID-19) has brought another dimension to teaching and learning across the levels of education. The lockdown imposed in many countries to curtail the pandemic forced many institutions of learning to shift to the online mode of teaching and learning. Using a descriptive survey research design, this study explored the online learning experiences of pre-service teachers at a Ghanaian university during the COVID-19 lockdown. The study focused on the pre-service teachers’ preparedness for online learning in terms of their digital literacy and technological devices used for online learning, their positive online learning experiences, and the challenges they encountered learning online. The findings suggested that the pre-service teachers were digitally literate and mostly accessed online learning using smartphones. Besides, online learning enabled them to communicate and collaborate actively with their course mates and lecturers. It was found that the flexibilit...
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Social media networks are fundamentally changing the way we socialize, communicate, and perhaps the way students learn. This paper explored the patterns of pre-service teachers’ adoption and their perceived usefulness of social media. The... more
Social media networks are fundamentally changing the way we socialize, communicate, and perhaps the way students learn. This paper explored the patterns of pre-service teachers’ adoption and their perceived usefulness of social media. The participants were 388 pre-service teachers from one tertiary institution in Nigeria. The social constructivist theory, the Theory of Planned Behaviour and the Technology Acceptance Model were used to underpin the study. The result revealed that Facebook and WhatsApp were the most common social media applications used by the participants and they use the media chiefly for socialising. With respect to the time they spent on social media daily, 310 (80%) spent at least one hour on social media on average daily while 196 (50%) spent over two hours on average every day. The relationships between social media subscriptions, and perceived usefulness of social media for socialising and for communication, were found to be positive and statistically signific...
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Learners’ underachievement in mathematics is one major challenge in South Africa. Reports show that one of the topics that learners struggle with is functions. Many teachers also struggle to teach the topic effectively. The foundation of... more
Learners’ underachievement in mathematics is one major challenge in South Africa. Reports show that one of the topics that learners struggle with is functions. Many teachers also struggle to teach the topic effectively. The foundation of functions in the school mathematics curriculum is in the senior phase of schooling (Grades 7-9). Functions need to be taught effectively at the foundation level in order to ensure smooth content progression into the higher grades. Several studies globally have advocated the integration of graphing software with the teaching of some topics in mathematics including functions to enhance students’ learning of the topics. This study investigated the effect of in-tegrating GeoGebra with the teaching of linear functions on Grade 9 learners’ achievement. The study was guided by the constructivist theory of learning and followed a pre-test post-test, non-equivalent groups and quasi-experimental de-sign. The participants were 62 learners from two schools in L...
The Student Evaluation of Teaching (SET), although controversial, is a common practice at the higher education level for faculty appraisals and promotions, but seldom at secondary school level. Concerns have been raised as to whether... more
The Student Evaluation of Teaching (SET), although controversial, is a common practice at the higher education level for faculty appraisals and promotions, but seldom at secondary school level. Concerns have been raised as to whether students are informed and experienced enough to evaluate teachers’ teaching practices in a reliable way and arrive at valid outcomes. The purpose of this research was to explore the reliability of students’ evaluations of mathematics teaching at secondary school level. This research involved eight teachers, and 194 Grade 11 students from eight secondary schools in Bojanala District, North West province in South Africa. A SET questionnaire was developed, validated and used for data collection. The data were analysed by calculating the average deviation index of the students’ evaluations of each teacher per item and the Intraclass Correlation Coefficient (ICC) with SPSS. This was done using one-way random effects, absolute agreement and a multiple raters/...
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This study explores the use of alternative methods of solution to enhance low performing learners' achievement in finding the general term of quadratic sequence. A convenience sample of twenty-five low-performing grade twelve learners... more
This study explores the use of alternative methods of solution to enhance low performing learners' achievement in finding the general term of quadratic sequence. A convenience sample of twenty-five low-performing grade twelve learners from a secondary school in Capricorn District in Limpopo Province took part in the study which adopted repeated measures research design. The learners were exposed to four methods of finding the general term of quadratics sequence. Data was collected using an achievement test and the data was analysed using one-way repeated measures analysis of variance. Findings indicate significant differences in the learners' average scores due to the methods used. The study therefore concludes that the achievement of low performing learners in finding the general term of quadratic sequence can be enhanced by offering them opportunities to explore a wide range of alternative methods of solving mathematics problems.
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This study investigated the relationship between students' achievement in mathematics and teacher qualification and subject major. A self report instrument was used to collect data from Form C (Grade 10) mathematics teachers in the... more
This study investigated the relationship between students' achievement in mathematics and teacher qualification and subject major. A self report instrument was used to collect data from Form C (Grade 10) mathematics teachers in the Maseru District in Lesotho, Southern Africa. The stratified random sampling technique was adopted for the study in the selection of 40 participants screened on the basis of type of ownership of schools. Out of the 40 teachers, 18 (45.0%) were males while 22(55.0%) were female. The simple correlation and regression statistics at the 0.01 and 0.05 significant levels were utilized for data analysis as well as the statistical inference. Findings indicated a significant positive relationship between students' academic achievement in mathematics and teacher qualification and subject majors. The findings therefore suggest that the policies adopted by the Ministry of Education concerning qualifications and subject majors of teachers that are employed make important difference in the students academic achievement in mathematics in Lesotho. African Journal of Cross-Cultural psychology and sport facilitation (AJCPSF) Vol. 9 2007: pp. 37-48
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This study investigated lecturers’ adoption of ICT tools in Ghanaian colleges of education. The participants of this study were 390 lecturers from 25 colleges of education in Ghana. Data was collected using a questionnaire and lesson... more
This study investigated lecturers’ adoption of ICT tools in Ghanaian colleges of education. The participants of this study were 390 lecturers from 25 colleges of education in Ghana. Data was collected using a questionnaire and lesson observation, and the results were analysed quantitatively and qualitatively using descriptive statistics and thematic analysis. The study revealed that more than two-thirds of the participants/respondents used personal computers, projectors, social media, and LMSs in their education. The lecturers asserted that they utilise ICT tools for research, for storing, retrieving, and sharing files and information in addition to utilising them to teach their courses. The respondents/participants recounted that they grow professionally as a result of using these ICT tools. Additionally, it was discovered that the respondents/participants employed ICT tools in their instruction due to its mobility, time-saving qualities, accessibility, and user-friendliness whi...
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Although many scholars support the Lakatosian method of mathematics education for enhancing students learning, the use of the method to foster students’ transition from alternative to scientific conceptions in mathematics does not seem to... more
Although many scholars support the Lakatosian method of mathematics education for enhancing students learning, the use of the method to foster students’ transition from alternative to scientific conceptions in mathematics does not seem to have been a focus of any research. This study explored if the Lakatosian heuristic method of teaching could foster a students’ transition from alternative to scientific conceptions of the surface area of a cone. The study used a qualitative, exploratory single case study design to undertake an in-depth study of a student in the 11th grade at a secondary school in Cyprus. Data was collected through lesson observation and analyzed using deductive content analysis. The study found that beginning from informal conjectures and proofs to more formal proofs the student was able to transit from alternative conception to the scientific conception of the surface area of a cone. The finding suggests that the Lakatosian method of mathematics can foster studen...
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Abstract This paper reports a study on the use of ICT to teach parabolic functions to secondary school students. The project was informed by the need to find better ways of presenting parabolic functions to secondary school students in... more
Abstract This paper reports a study on the use of ICT to teach parabolic functions to secondary school students. The project was informed by the need to find better ways of presenting parabolic functions to secondary school students in order to improve their learning of the concepts and improve their interest and performance in mathematics. The study was also influenced by the global call for the integration of ICT into teaching and learning, the enormous investments by the South African government and other stakeholders in ICT in education, and the increasing demand for academic excellence in mathematics. In the study, computer graphing software (Graphmatica) was used by students to explore parabolic functions. This paper addresses the questions: Can ICT help students to have a better learning of parabolic functions compared to traditional teaching and learning and how can ICT help students to have a better learning of parabolic functions compared to traditional teaching and learning? The study employed a mixed method research design in the light of a practical action research paradigm. Data was collected from two grade 11 mathematics classes at a secondary school in the North-West Province of South Africa using teaching and learning documents (students' assignments and test scripts), classroom observation and formal/informal interviews. Data from students' performances on the assignments and test, classroom observations and interviews were analysed using descriptive narrative. The study found that ICT could help students learn parabolic functions and may also make the lessons enjoyable to students. The findings imply that integrating ICT into the teaching and learning of parabolic functions and perhaps other topics in mathematics will likely help to improve students' attitude towards mathematics and consequently improve their performances in this learning area.
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Survey is one of the most widely used methods of investigation into educational systems and practices. While the results from surveys might give insight into what goes on in the educational system, important questions arise: how reliable... more
Survey is one of the most widely used methods of investigation into educational systems and practices. While the results from surveys might give insight into what goes on in the educational system, important questions arise: how reliable are the results of surveys in evaluating educational systems and practices? And can the results be used to take high-stakes decisions about teaching and learning? This study examines the reliability of surveys in evaluating teaching by comparing the degree of agreement between mathematics teachers' self-evaluation of their teaching and their peers' evaluation of it. A sample of 31 grade 11 mathematics teachers took part in the study. The result shows that teachers' self-evaluations of their teaching generally did not agree significantly with their peers' evaluations. This finding suggests caution in the use of self and peer evaluations in taking high-stakes decisions on teaching and learning. DOI: 10.5901/mjss.2014.v5n9p370
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This paper reports a study on the effect of using the Lakatosian heuristic method to teach the surface area of a cone (SAC) on students’ achievement according to Bloom's taxonomy levels. Two groups of students (experimental and... more
This paper reports a study on the effect of using the Lakatosian heuristic method to teach the surface area of a cone (SAC) on students’ achievement according to Bloom's taxonomy levels. Two groups of students (experimental and control) participated in the study. The experimental group (n = 20) was taught using the Lakatosian heuristic method while the control group (n = 36) was taught using the Euclidean deductive method. Both groups were given a pre-test and a post-test. Data analysis using two-way Analysis of Varianceshows that both groups increased their scores within times (pre- and post-test) at α = 0.05. However, the experimental group scored higher than the control group within time and also displayed more positive higher-order thinking skills than the control group. It was concluded that the Lakatosian heuristic method would, in all likelihood, help students to learn the SAC better than the Euclidean method does.
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The main purpose of this study was to assess the relationship between students' achievement in mathematics and teacher factors. The study was conducted in the in Lesotho, Southern Africa. Stratified random sampling based on school... more
The main purpose of this study was to assess the relationship between students' achievement in mathematics and teacher factors. The study was conducted in the in Lesotho, Southern Africa. Stratified random sampling based on school ownership was used to draw a sample of 40 teachers from the population of Grade 10 Mathematics teachers. Of the 40 teachers, 18 (45%) were male while 22 (55%) were female. A self report questionnaire was used to collect data from the teachers. The students' achievement scores in mathematics were collected from the JC 2006 examination result list. Results indicated significant positive association between students' achievement in mathematics and teacher factors. International Journal of emotiaonl psychology and sport ethics Vol. 9 2007: pp. 64-72
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لم يكن تحصيل طلبة المرحلة الثانوية في جنوب أفريقيا في الرياضيات مثيرا للإعجاب، ويعزا ضعف التحصيل هذا إلى عدة عوامل. وقد حاولت هذه الدراسة استكشاف العوامل التي تساهم في تدني تحصيل طلبة المرحلة الثانوية في الرياضيات، فجمعت البيانات من (135)... more
لم يكن تحصيل طلبة المرحلة الثانوية في جنوب أفريقيا في الرياضيات مثيرا للإعجاب، ويعزا ضعف التحصيل هذا إلى عدة عوامل. وقد حاولت هذه الدراسة استكشاف العوامل التي تساهم في تدني تحصيل طلبة المرحلة الثانوية في الرياضيات، فجمعت البيانات من (135) معلما من معلمي الرياضيات للمرحلة الثانوية. وقد تبين من تحليل البيانات أن من العوامل التي تؤدي إلى ضعف تحصيل الطلبة في الرياضيات: معرفة المعلم، وضعف الخلفية المعرفية لدى الطلبة في الرياضيات، ونقص مصادر التعليم والتعلم، وعدم مشاركة الآباء في تعليم الطلاب، واتجاهات الطلبة السلبية نحو الرياضيات ، وعدم انضباط الطلبة في أثناء التدريس، وكثرة تغيير مناهج الرياضيات المدرسية، وارتفاع نسبة الطلبة إلى المعلمين، والمعيق اللغوي. وعلى ضوء التوصيات، يوصي الباحث بضرورة البدء بإصلاح السياسات المدرسية بشكل عام، وسياسات تعليم الرياضيات على وجه الخصوص.