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Papers by Kgaladi Maphutha

Research paper thumbnail of Exploring Grade 11 Learners’ Mathematical Connections when Solving Trigonometric Equations

Symmetry, Jun 27, 2023

In this paper, we explored the intra-mathematical connections that grade 11 learners make when so... more In this paper, we explored the intra-mathematical connections that grade 11 learners make when solving trigonometric equations. The study was guided by Mowat's theory of mathematical connections in which nodes and links are used to connect mathematical concepts and topics. We used a qualitative case study design within an interpretive paradigm to explore the intra-mathematical connections learners make as they solved trigonometric equations. The study was conducted in a high school in Mankweng Circuit, Limpopo Province, South Africa. Convenience sampling was used to select 30 learners who participated in the study. Data was collected using documents and task-based interviews. Data were analysed using inductive thematic analysis. The findings showed that learners made were able to make algebraic connections when solving trigonometric equations. They, however, were unable to make connections within trigonometry itself. This study, therefore, recommends that teachers stress the importance of connections when teaching trigonometry so that learners will not learn trigonometric concepts in isolation. In addition, it is recommended that further research be conducted on teaching strategies to improve learners' mathematical connection skills when solving trigonometric equations.

Research paper thumbnail of Learners’ Graphical Efficacy When Solving Trigonometric Problems

MEJ (Mathematics Education Journal), Aug 30, 2023

This study explored grade 12 learners' graphical efficacy when solving problems involving trigono... more This study explored grade 12 learners' graphical efficacy when solving problems involving trigonometric graphs. A structured test consisting of five trigonometric problems, with variations in context and structure, was administered to a purposefully selected group of 25 Grade 12 learners from the Sekhukhune District in South Africa. Insights into learners' graphing efficacy were obtained through task-based interviews. Data were analysed using direct interpretation which involved deductive thematic analysis of the task-based interviews and content analysis of the test scripts to match learners' responses to the themes drawn from the Meta-Representational Competence (MRC) framework. The results showed that most learners lack invention and functioning, critiquing and reflection efficacies and hence this affected their drawing and interpretation of the graphs and consequently lead to incorrect solutions. Furthermore, the results show most learners have critiquing efficacy. This indicates that learners lack graphical efficacy for solving trigonometric problems involving trigonometric functions. This finding has pedagogic implications: the apparent lack of graphical efficacy in graphical solutions may suggest inadequate mastery of the concept. Therefore, this study recommends that the teaching and learning of trigonometric graphs should consider the development of invention, functioning, critiquing and reflection efficacies.

Research paper thumbnail of Learners’ Misconceptions and Errors when Solving Inequalities

Mathematics Education Journal

This study explored Grade 12 learners’ misconceptions and errors when solving inequalities. A tes... more This study explored Grade 12 learners’ misconceptions and errors when solving inequalities. A test on Inequalities was administered to a randomly selected sample of 50 Grade 12 learners in Sekhukhune District, South Africa. A rubric was used to guide the assessment and scoring of learners’ scripts. Ten (10) learners were purposively selected based their test responses for interviews to explain their errors, misconceptions and reasoning. Results indicated that learners’ errors are due to misunderstandings from prior learning and insufficient mathematical content knowledge. Misconceptions and errors recorded from learners’ work include: learners solved inequalities as equations, treated inequality signs as an equal sign, and multiplying both sides of inequalities involving fractions by a variable. Learners had challenges in presenting solutions of inequalities using graphical and number lines. The study recommends that teachers should make an effort to understand learners’ thoug...

Research paper thumbnail of Exploring grade 11 learners’ mathematical connections when solving two-dimensional trigonometric problems in an activity-based learning environment

Journal on Mathematics Education, Apr 9, 2023

Research paper thumbnail of The effect of the activity-based approach on grade 11 learners’ performance in solving two-dimensional trigonometric problems

Eurasia Journal of Mathematics, Science and Technology Education

The study explored the effect of the activity-based approach (ABA) on grade 11 learners' performa... more The study explored the effect of the activity-based approach (ABA) on grade 11 learners' performance in solving two-dimensional (2D) trigonometric problems. A sequential explanatory design was used, starting with the quantitative, followed by the qualitative method. The experimental group (EG) and the control group (CG) were facilitated using ABA, while CG was taught using traditional teaching approach. A 2D trigonometry test was used as a pre-and posttest to measure learners' performance. EG's experiences of using ABA were captured through focus group interviews. The study findings reveal significant differences between EG and CG posttests [t(100)=.3. 95; p=.05] with Cohen d=.79. Also, ABA did not segregate between boys and girls. Despite ABA being time-consuming, learners in EG developed collaborative skills, trigonometry vocabulary, the ability to solve trigonometric problems, and learning autonomy, which improved their performance. The study recommends ABA to improve learners' performance.

Research paper thumbnail of Investigating mathematics teachers’ beliefs about the nature of mathematics and their impact on classroom practices

This study investigated Mathematics teachers' beliefs about the nature of Mathematics and their i... more This study investigated Mathematics teachers' beliefs about the nature of Mathematics and their impact on classroom practices. It was conducted in a public semi-urban school in the Capricorn District-Limpopo Province. It was a case study targeting two FET teachers with teaching experiences of 15 years or more. The central research questions addressed in this study are, namely: What are Mathematics teachers' beliefs about the nature of Mathematics? And, what is the relationship between teachers' beliefs and their classroom practices? Data were collected through pre-observation interviews, classroom observation and through post observation interviews. Pre-observation interviews were conducted once before the participants were observed. I was a complete observer during my colleagues' lessons. Interviews and observations data were analysed using categorisation and interpretation of data in terms of common themes and synthesis into an overall portrait of the case. Each case study teacher's data were analysed individually (that is within-case analysis) first and thereafter cross-case analysis was done in order to compare the two case studies. v

Research paper thumbnail of Where is the bigger picture in the teaching and learning of mathematics?

Pythagoras, 2016

This article presents an interpretive analysis of three different mathematics teaching cases to e... more This article presents an interpretive analysis of three different mathematics teaching cases to establish where the bigger picture should lie in the teaching and learning of mathematics. We use pre-existing data collected through pre-observation and post-observation interviews and passive classroom observation undertaken by the third author in two different Grade 11 classes taught by two different teachers at one high school. Another set of data was collected through participant observation of the second author’s Year 2 University class. We analyse the presence or absence of the bigger picture, especially, in the teachers’ questioning strategies and their approach to content, guided by Tall’s framework of three worlds of mathematics, namely the ‘conceptual-embodied’ world, the ‘proceptual-symbolic’ world and the ‘axiomatic-formal’ world. Within this broad framework we acknowledge Pirie and Kieren’s notion of folding back towards the attainment of an axiomatic-formal world. We argue ...

Research paper thumbnail of Exploring Grade 11 Learners’ Mathematical Connections when Solving Trigonometric Equations

Symmetry, Jun 27, 2023

In this paper, we explored the intra-mathematical connections that grade 11 learners make when so... more In this paper, we explored the intra-mathematical connections that grade 11 learners make when solving trigonometric equations. The study was guided by Mowat's theory of mathematical connections in which nodes and links are used to connect mathematical concepts and topics. We used a qualitative case study design within an interpretive paradigm to explore the intra-mathematical connections learners make as they solved trigonometric equations. The study was conducted in a high school in Mankweng Circuit, Limpopo Province, South Africa. Convenience sampling was used to select 30 learners who participated in the study. Data was collected using documents and task-based interviews. Data were analysed using inductive thematic analysis. The findings showed that learners made were able to make algebraic connections when solving trigonometric equations. They, however, were unable to make connections within trigonometry itself. This study, therefore, recommends that teachers stress the importance of connections when teaching trigonometry so that learners will not learn trigonometric concepts in isolation. In addition, it is recommended that further research be conducted on teaching strategies to improve learners' mathematical connection skills when solving trigonometric equations.

Research paper thumbnail of Learners’ Graphical Efficacy When Solving Trigonometric Problems

MEJ (Mathematics Education Journal), Aug 30, 2023

This study explored grade 12 learners' graphical efficacy when solving problems involving trigono... more This study explored grade 12 learners' graphical efficacy when solving problems involving trigonometric graphs. A structured test consisting of five trigonometric problems, with variations in context and structure, was administered to a purposefully selected group of 25 Grade 12 learners from the Sekhukhune District in South Africa. Insights into learners' graphing efficacy were obtained through task-based interviews. Data were analysed using direct interpretation which involved deductive thematic analysis of the task-based interviews and content analysis of the test scripts to match learners' responses to the themes drawn from the Meta-Representational Competence (MRC) framework. The results showed that most learners lack invention and functioning, critiquing and reflection efficacies and hence this affected their drawing and interpretation of the graphs and consequently lead to incorrect solutions. Furthermore, the results show most learners have critiquing efficacy. This indicates that learners lack graphical efficacy for solving trigonometric problems involving trigonometric functions. This finding has pedagogic implications: the apparent lack of graphical efficacy in graphical solutions may suggest inadequate mastery of the concept. Therefore, this study recommends that the teaching and learning of trigonometric graphs should consider the development of invention, functioning, critiquing and reflection efficacies.

Research paper thumbnail of Learners’ Misconceptions and Errors when Solving Inequalities

Mathematics Education Journal

This study explored Grade 12 learners’ misconceptions and errors when solving inequalities. A tes... more This study explored Grade 12 learners’ misconceptions and errors when solving inequalities. A test on Inequalities was administered to a randomly selected sample of 50 Grade 12 learners in Sekhukhune District, South Africa. A rubric was used to guide the assessment and scoring of learners’ scripts. Ten (10) learners were purposively selected based their test responses for interviews to explain their errors, misconceptions and reasoning. Results indicated that learners’ errors are due to misunderstandings from prior learning and insufficient mathematical content knowledge. Misconceptions and errors recorded from learners’ work include: learners solved inequalities as equations, treated inequality signs as an equal sign, and multiplying both sides of inequalities involving fractions by a variable. Learners had challenges in presenting solutions of inequalities using graphical and number lines. The study recommends that teachers should make an effort to understand learners’ thoug...

Research paper thumbnail of Exploring grade 11 learners’ mathematical connections when solving two-dimensional trigonometric problems in an activity-based learning environment

Journal on Mathematics Education, Apr 9, 2023

Research paper thumbnail of The effect of the activity-based approach on grade 11 learners’ performance in solving two-dimensional trigonometric problems

Eurasia Journal of Mathematics, Science and Technology Education

The study explored the effect of the activity-based approach (ABA) on grade 11 learners' performa... more The study explored the effect of the activity-based approach (ABA) on grade 11 learners' performance in solving two-dimensional (2D) trigonometric problems. A sequential explanatory design was used, starting with the quantitative, followed by the qualitative method. The experimental group (EG) and the control group (CG) were facilitated using ABA, while CG was taught using traditional teaching approach. A 2D trigonometry test was used as a pre-and posttest to measure learners' performance. EG's experiences of using ABA were captured through focus group interviews. The study findings reveal significant differences between EG and CG posttests [t(100)=.3. 95; p=.05] with Cohen d=.79. Also, ABA did not segregate between boys and girls. Despite ABA being time-consuming, learners in EG developed collaborative skills, trigonometry vocabulary, the ability to solve trigonometric problems, and learning autonomy, which improved their performance. The study recommends ABA to improve learners' performance.

Research paper thumbnail of Investigating mathematics teachers’ beliefs about the nature of mathematics and their impact on classroom practices

This study investigated Mathematics teachers' beliefs about the nature of Mathematics and their i... more This study investigated Mathematics teachers' beliefs about the nature of Mathematics and their impact on classroom practices. It was conducted in a public semi-urban school in the Capricorn District-Limpopo Province. It was a case study targeting two FET teachers with teaching experiences of 15 years or more. The central research questions addressed in this study are, namely: What are Mathematics teachers' beliefs about the nature of Mathematics? And, what is the relationship between teachers' beliefs and their classroom practices? Data were collected through pre-observation interviews, classroom observation and through post observation interviews. Pre-observation interviews were conducted once before the participants were observed. I was a complete observer during my colleagues' lessons. Interviews and observations data were analysed using categorisation and interpretation of data in terms of common themes and synthesis into an overall portrait of the case. Each case study teacher's data were analysed individually (that is within-case analysis) first and thereafter cross-case analysis was done in order to compare the two case studies. v

Research paper thumbnail of Where is the bigger picture in the teaching and learning of mathematics?

Pythagoras, 2016

This article presents an interpretive analysis of three different mathematics teaching cases to e... more This article presents an interpretive analysis of three different mathematics teaching cases to establish where the bigger picture should lie in the teaching and learning of mathematics. We use pre-existing data collected through pre-observation and post-observation interviews and passive classroom observation undertaken by the third author in two different Grade 11 classes taught by two different teachers at one high school. Another set of data was collected through participant observation of the second author’s Year 2 University class. We analyse the presence or absence of the bigger picture, especially, in the teachers’ questioning strategies and their approach to content, guided by Tall’s framework of three worlds of mathematics, namely the ‘conceptual-embodied’ world, the ‘proceptual-symbolic’ world and the ‘axiomatic-formal’ world. Within this broad framework we acknowledge Pirie and Kieren’s notion of folding back towards the attainment of an axiomatic-formal world. We argue ...