The incorporation of GeoGebra as a visualisation tool to teach calculus in teacher education institutions: the Zambian case
- Authors: Kangwa, Lemmy
- Date: 2022-10-14
- Subjects: GeoGebra , Calculus Study and teaching (Secondary) Zambia , Visual learning
- Language: English
- Type: Academic theses , Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/405470 , vital:70174 , DOI
- Description: This qualitative case study investigated teacher educators’ (lecturers) use of the dynamic mathematics software, GeoGebra, to teach calculus in three teacher education institutions (TEIs) in Zambia. Visualisation, a key characteristic of GeoGebra, is increasingly gaining recognition of playing a critical role in mathematics teaching and learning, especially in problem solving tasks. It is considered a powerful didactical tool for students to construct mental and physical representations that can enhance conceptual understanding of mathematics. GeoGebra is a visualisation tool that can be used for problem-oriented teaching and foster mathematical experiments and discoveries. GeoGebra’s inherent visualisation characteristics align well with the teaching of calculus, the mathematical domain of this study. The study (whose research methodology was underpinned by the interpretive paradigm) was undertaken with a broader goal of designing and implementing GeoGebra applets and instructional materials on various calculus topics. The study is located within the “Teaching and Learning Mathematics with GeoGebra (TLMG) project” – a project that involves mathematics teachers and lecturers in Zambia. The case in this study is the six mathematics lecturers who co-designed and used GeoGebra applets to teach derivatives and integrals to pre-service mathematics teachers in TEIs. The unit of analysis therefore is the six lecturers’ use of GeoGebra as a visualisation tool to teach calculus to enhance conceptual understanding, their perceptions and experiences of using GeoGebra and the enabling and constraining factors of using GeoGebra to teach and learn mathematics. The data for the study were video recordings of observations and interviews of lecturers. The data was analysed thematically and was guided and informed by an analytical framework adopted from the theory of constructivism – the umbrella theoretical framework of this study – and the models of Technological Pedagogical Content Knowledge (TPACK), and the Technology Acceptance Model (TAM). A detailed analysis of the lecturers’ interactions with the applets enabled me to gain insights into the participants’ experiences and perceptions of GeoGebra applets in the teaching and learning process. The findings of the study revealed that the visualisation characteristics of GeoGebra generally enhanced the conceptual understanding of calculus. It also revealed that adequate training, coupled with sufficient knowledge of the subject matter in calculus, were necessary for lecturers to use GeoGebra effectively, and that the lack of resources and expertise were major hindrances in the use of GeoGebra to teach mathematics in TEIs. It also revealed that there is a need to equip GeoGebra with other features that would make it more versatile, and suggested a teaching approach that would complement the use of conventional methods and GeoGebra to provide a link between abstract and concrete concepts of calculus. , Thesis (PhD) -- Faculty of Education, Education, 2022
- Full Text:
- Date Issued: 2022-10-14
- Authors: Kangwa, Lemmy
- Date: 2022-10-14
- Subjects: GeoGebra , Calculus Study and teaching (Secondary) Zambia , Visual learning
- Language: English
- Type: Academic theses , Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/405470 , vital:70174 , DOI
- Description: This qualitative case study investigated teacher educators’ (lecturers) use of the dynamic mathematics software, GeoGebra, to teach calculus in three teacher education institutions (TEIs) in Zambia. Visualisation, a key characteristic of GeoGebra, is increasingly gaining recognition of playing a critical role in mathematics teaching and learning, especially in problem solving tasks. It is considered a powerful didactical tool for students to construct mental and physical representations that can enhance conceptual understanding of mathematics. GeoGebra is a visualisation tool that can be used for problem-oriented teaching and foster mathematical experiments and discoveries. GeoGebra’s inherent visualisation characteristics align well with the teaching of calculus, the mathematical domain of this study. The study (whose research methodology was underpinned by the interpretive paradigm) was undertaken with a broader goal of designing and implementing GeoGebra applets and instructional materials on various calculus topics. The study is located within the “Teaching and Learning Mathematics with GeoGebra (TLMG) project” – a project that involves mathematics teachers and lecturers in Zambia. The case in this study is the six mathematics lecturers who co-designed and used GeoGebra applets to teach derivatives and integrals to pre-service mathematics teachers in TEIs. The unit of analysis therefore is the six lecturers’ use of GeoGebra as a visualisation tool to teach calculus to enhance conceptual understanding, their perceptions and experiences of using GeoGebra and the enabling and constraining factors of using GeoGebra to teach and learn mathematics. The data for the study were video recordings of observations and interviews of lecturers. The data was analysed thematically and was guided and informed by an analytical framework adopted from the theory of constructivism – the umbrella theoretical framework of this study – and the models of Technological Pedagogical Content Knowledge (TPACK), and the Technology Acceptance Model (TAM). A detailed analysis of the lecturers’ interactions with the applets enabled me to gain insights into the participants’ experiences and perceptions of GeoGebra applets in the teaching and learning process. The findings of the study revealed that the visualisation characteristics of GeoGebra generally enhanced the conceptual understanding of calculus. It also revealed that adequate training, coupled with sufficient knowledge of the subject matter in calculus, were necessary for lecturers to use GeoGebra effectively, and that the lack of resources and expertise were major hindrances in the use of GeoGebra to teach mathematics in TEIs. It also revealed that there is a need to equip GeoGebra with other features that would make it more versatile, and suggested a teaching approach that would complement the use of conventional methods and GeoGebra to provide a link between abstract and concrete concepts of calculus. , Thesis (PhD) -- Faculty of Education, Education, 2022
- Full Text:
- Date Issued: 2022-10-14
Examining mathematical reasoning through enacted visualisation
- Authors: Dongwi, Beata Lididimikeni
- Date: 2019
- Subjects: Visualization , Mathematics -- Study and teaching -- Namibia , Mathematics -- Study and teaching -- Audio-visual aids , Geometry -- Study and teaching , Reasoning , Mathematical ability
- Language: English
- Type: text , Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/68192 , vital:29217
- Description: This study sets out to analyse the co-emergence of visualisation and reasoning processes when selected learners engaged in solving word problems. The study argues that visualisation processes and mathematical reasoning processes are closely interlinked in the process of engaging in any mathematical activity. This qualitative research project adopted a case study methodology embedded within a broader interpretative orientation. The research participants were a cohort of 17 mixedgender and mixed-ability Grade 11 learners from a private school in southern Namibia. Data was collected in three phases and comprised of one-on-one task-based interviews in the first phase, focus group task-based interviews in the second, and semi-structured reflective interviews in the third. The analytical framework was informed by elements of enactivism and consisted of a hybrid of observable visualisation and mathematical reasoning indicators. The study was framed by an enactivist perspective that served as a linking mediator to bring visualisation and reasoning processes together, and as a lens through which the coemergence of these processes was observed and analysed. The key enactivist concepts of structural coupling and co-emergence were the two mediating ideas that enabled me to discuss the links between visualisation and reasoning that emerged whilst my participants solved the set word problems. The study argues that the visualisation processes enacted by the participants when solving these problems are inseparable from the reasoning processes that the participants brought to bear; that is, they co-emerged.
- Full Text:
- Date Issued: 2019
- Authors: Dongwi, Beata Lididimikeni
- Date: 2019
- Subjects: Visualization , Mathematics -- Study and teaching -- Namibia , Mathematics -- Study and teaching -- Audio-visual aids , Geometry -- Study and teaching , Reasoning , Mathematical ability
- Language: English
- Type: text , Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/68192 , vital:29217
- Description: This study sets out to analyse the co-emergence of visualisation and reasoning processes when selected learners engaged in solving word problems. The study argues that visualisation processes and mathematical reasoning processes are closely interlinked in the process of engaging in any mathematical activity. This qualitative research project adopted a case study methodology embedded within a broader interpretative orientation. The research participants were a cohort of 17 mixedgender and mixed-ability Grade 11 learners from a private school in southern Namibia. Data was collected in three phases and comprised of one-on-one task-based interviews in the first phase, focus group task-based interviews in the second, and semi-structured reflective interviews in the third. The analytical framework was informed by elements of enactivism and consisted of a hybrid of observable visualisation and mathematical reasoning indicators. The study was framed by an enactivist perspective that served as a linking mediator to bring visualisation and reasoning processes together, and as a lens through which the coemergence of these processes was observed and analysed. The key enactivist concepts of structural coupling and co-emergence were the two mediating ideas that enabled me to discuss the links between visualisation and reasoning that emerged whilst my participants solved the set word problems. The study argues that the visualisation processes enacted by the participants when solving these problems are inseparable from the reasoning processes that the participants brought to bear; that is, they co-emerged.
- Full Text:
- Date Issued: 2019
An analysis of how visualisation processes can be used by teachers participating in an intervention programme to teach for conceptual understanding of geometry
- Authors: Muhembo, Gottfried Mbundu
- Date: 2018
- Subjects: Geometry -- Study and teaching (Secondary) -- Namibia -- Kavango East , Visualization , Mathematics teachers -- Namibia -- Kavango East , Effective teaching -- Namibia -- Kavango East , Mathematics -- Study and teaching -- Activity programs
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/62439 , vital:28190
- Description: Visualisation in general and visualisation processes in particular have received much attention in the mathematics education research literature. Literature suggests that the appropriate use of visualisation helps learners to develop their conceptual understanding and skills of geometry as it allows them to visually interpret and understand fundamental mathematical and geometrical concepts. It is claimed that visual tools play an important role in communicating mathematical ideas through diagrams, gestures, images, sketches or drawings. Learning mathematics through visualisation can be a powerful tool to explore mathematical problems and give meaning to mathematical concepts and relationships between them. This interpretive case study focused on how selected teachers taught concepts in geometry through visualisation processes for conceptual understanding as a result of an intervention programme. The study was conducted at four high schools by four mathematics teachers in the Kavango East Region in Northern Namibia. The participants were involved in a three-week intervention programme and afterwards taught three lessons each on the topic of geometry. The data collection method of this research was: focus group and stimulus recall interviews, classroom observations and recorded videos. This research is located in constructivism. I used vertical and horizontal analysis strategies to analyse the data. My analytical instrument consisted of an observation schedule which I used in each lesson to identify how each of the visualisation processes was evident in each of the observed lessons. This study revealed that the participant teachers used visualisation processes in most of their lessons and these processes were used accurately in line with the requirements of the grade 8 mathematics syllabi. The visualisation processes were used through designed visual materials, posters and through the use of geometrical objects such as chalkboard ruler, protractor and compass. The results from this study also confirmed that visualisation processes can be a powerful instructional tool for enhancing learners’ conceptual understanding of geometry.
- Full Text:
- Date Issued: 2018
- Authors: Muhembo, Gottfried Mbundu
- Date: 2018
- Subjects: Geometry -- Study and teaching (Secondary) -- Namibia -- Kavango East , Visualization , Mathematics teachers -- Namibia -- Kavango East , Effective teaching -- Namibia -- Kavango East , Mathematics -- Study and teaching -- Activity programs
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/62439 , vital:28190
- Description: Visualisation in general and visualisation processes in particular have received much attention in the mathematics education research literature. Literature suggests that the appropriate use of visualisation helps learners to develop their conceptual understanding and skills of geometry as it allows them to visually interpret and understand fundamental mathematical and geometrical concepts. It is claimed that visual tools play an important role in communicating mathematical ideas through diagrams, gestures, images, sketches or drawings. Learning mathematics through visualisation can be a powerful tool to explore mathematical problems and give meaning to mathematical concepts and relationships between them. This interpretive case study focused on how selected teachers taught concepts in geometry through visualisation processes for conceptual understanding as a result of an intervention programme. The study was conducted at four high schools by four mathematics teachers in the Kavango East Region in Northern Namibia. The participants were involved in a three-week intervention programme and afterwards taught three lessons each on the topic of geometry. The data collection method of this research was: focus group and stimulus recall interviews, classroom observations and recorded videos. This research is located in constructivism. I used vertical and horizontal analysis strategies to analyse the data. My analytical instrument consisted of an observation schedule which I used in each lesson to identify how each of the visualisation processes was evident in each of the observed lessons. This study revealed that the participant teachers used visualisation processes in most of their lessons and these processes were used accurately in line with the requirements of the grade 8 mathematics syllabi. The visualisation processes were used through designed visual materials, posters and through the use of geometrical objects such as chalkboard ruler, protractor and compass. The results from this study also confirmed that visualisation processes can be a powerful instructional tool for enhancing learners’ conceptual understanding of geometry.
- Full Text:
- Date Issued: 2018
A study of mathematics teacher identity as shaped through participation in a mathematics teacher professional development programme
- Authors: Kangela, Nyameka
- Date: 2017
- Subjects: Mathematics Teacher Enrichment Programme (MTEP) (Rhodes University) , Mathematics teachers -- Psychology , Mathematics teachers -- Psychology -- Case studies , Mathematics teachers -- Training of -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/7832 , vital:21305
- Description: There is an abundance of evidence suggesting that all is not well in mathematics education in South Africa. It is also common cause that the role of mathematics teachers is central to finding sustainable solutions to what is commonly referred to as a mathematics crisis. The purpose of this study is to explore the process of change in selected mathematics teachers’ identities as they participated in a mathematics teacher Professional Development Programme (PDP) at Rhodes University. The core of the PDP was a teacher enrichment programme called the Mathematics Teacher Enrichment Programme (MTEP), under the aegis of the First Rand Foundation (FRF) Mathematics Education Chair at Rhodes University. MTEP foregrounded and emphasized the teaching of mathematics for conceptual understanding. The research approach was qualitative, and it used elements of the methods associated with educational ethnography. The data was collected from five teachers from five different schools that participated in the FRF Maths Chair project. I used Wenger’s (1998) three modes of belonging to analyse the identities of the five participants. This was achieved through analysing the teachers’ practice with a particular focus on teaching for conceptual understanding. I used Sfard & Prusak’s (2005) framework to analyse the participants’ journey from an actual to a designated identity through their participation in MTEP. The participants’ changing sense of belonging to MTEP was a key element in transforming their practice to teaching for conceptual understanding. I assumed the role of a participant observer during MTEP sessions, and of an outside observer as a researcher.The study found that the selected teachers’ participation in the MTEP community of practice strongly encouraged them to accumulate shared histories of learning and teaching. The study found that as participating teachers adopted and grew into their designated identity they partially embraced and implemented a conceptual teaching approach. The gap between their actual and their designated identity was partly closed as they sought to align their teaching with MTEP’s goal of conceptual teaching.
- Full Text:
- Date Issued: 2017
- Authors: Kangela, Nyameka
- Date: 2017
- Subjects: Mathematics Teacher Enrichment Programme (MTEP) (Rhodes University) , Mathematics teachers -- Psychology , Mathematics teachers -- Psychology -- Case studies , Mathematics teachers -- Training of -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/7832 , vital:21305
- Description: There is an abundance of evidence suggesting that all is not well in mathematics education in South Africa. It is also common cause that the role of mathematics teachers is central to finding sustainable solutions to what is commonly referred to as a mathematics crisis. The purpose of this study is to explore the process of change in selected mathematics teachers’ identities as they participated in a mathematics teacher Professional Development Programme (PDP) at Rhodes University. The core of the PDP was a teacher enrichment programme called the Mathematics Teacher Enrichment Programme (MTEP), under the aegis of the First Rand Foundation (FRF) Mathematics Education Chair at Rhodes University. MTEP foregrounded and emphasized the teaching of mathematics for conceptual understanding. The research approach was qualitative, and it used elements of the methods associated with educational ethnography. The data was collected from five teachers from five different schools that participated in the FRF Maths Chair project. I used Wenger’s (1998) three modes of belonging to analyse the identities of the five participants. This was achieved through analysing the teachers’ practice with a particular focus on teaching for conceptual understanding. I used Sfard & Prusak’s (2005) framework to analyse the participants’ journey from an actual to a designated identity through their participation in MTEP. The participants’ changing sense of belonging to MTEP was a key element in transforming their practice to teaching for conceptual understanding. I assumed the role of a participant observer during MTEP sessions, and of an outside observer as a researcher.The study found that the selected teachers’ participation in the MTEP community of practice strongly encouraged them to accumulate shared histories of learning and teaching. The study found that as participating teachers adopted and grew into their designated identity they partially embraced and implemented a conceptual teaching approach. The gap between their actual and their designated identity was partly closed as they sought to align their teaching with MTEP’s goal of conceptual teaching.
- Full Text:
- Date Issued: 2017
An analysis of the nature of visualisation objects in three Namibian grade 9 mathematics textbooks: a case study in Namibia
- Nghifimule, Selma Ndilipomwene
- Authors: Nghifimule, Selma Ndilipomwene
- Date: 2017
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/6334 , vital:21090
- Description: Textbooks are a universal and central element of teaching and learning mathematics (Namibia. Ministry of Education [MoE], 2008). Steenpaß and Steinbring (2014) state that diagrams in mathematics textbooks are often used as Visualisation Objects (VOs) to enhance learning of mathematical concepts. VOs in textbooks are thus important teaching and learning tools (Fotakopoulou and Spiliotopoulou, 2008). This Namibian interpretive case study analysed the nature of VOs used in the three approved grade 9 Namibian mathematics textbooks namely: y=mx+c to success, Maths for Life 9 and Discover Mathematics 9. The VOs were analysed by using an analytical framework adapted from Fotakopoulou and Spiliotopoulou (2008). This analytic tool was specifically used to interrogate the following categories: the type of VOs, the roles of VOs, the relation of VOs to mathematical content, the relation of VOs to reality, and their properties. The 266 VOs under study were collected from the Algebra and Geometry chapters of each book. This study also included survey questionnaires with the 50 selected mathematics teachers, which sought their views and perceptions on the use of the identified VOs. In addition, the authors’ rationale in selecting the identified VOs used in their textbooks was sought through interviews. This research study is part of the “Visualisation in Namibia and Zambia” (VISNAMZA) project which seeks to research the effective use of visualisation processes in the mathematics classroom in Namibia and Zambia (Schäfer, 2015). It is hoped that this study contributes towards improving the quality of textbook evaluations, and design of suitable and more comprehensive assessment procedures in Namibia. It is also hoped that it creates a critical awareness of the roles of VOs in textbooks amongst teachers, inspiring them to help their learners interpret VOs effectively. It should also inspire potential authors to use suitable and appropriate VOs that enhance conceptual teaching and learning of mathematics. The study discovered that most of the VOs used in the selected textbooks align well with the mathematical content. The VOs can help make abstract ideas concrete, stimulate learning, simplify and clarify written texts. In addition, VOs can also be used as a tool for reasoning and an instrument for problem solving. The findings however also indicate that some of the VOs used are not self-explanatory; they are vague, unfamiliar and confusing, leading to misinterpretations by some learners. Another interesting finding was that some of the learners found it difficult to interpret VOs on their own without the help of the teacher.
- Full Text:
- Date Issued: 2017
- Authors: Nghifimule, Selma Ndilipomwene
- Date: 2017
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/6334 , vital:21090
- Description: Textbooks are a universal and central element of teaching and learning mathematics (Namibia. Ministry of Education [MoE], 2008). Steenpaß and Steinbring (2014) state that diagrams in mathematics textbooks are often used as Visualisation Objects (VOs) to enhance learning of mathematical concepts. VOs in textbooks are thus important teaching and learning tools (Fotakopoulou and Spiliotopoulou, 2008). This Namibian interpretive case study analysed the nature of VOs used in the three approved grade 9 Namibian mathematics textbooks namely: y=mx+c to success, Maths for Life 9 and Discover Mathematics 9. The VOs were analysed by using an analytical framework adapted from Fotakopoulou and Spiliotopoulou (2008). This analytic tool was specifically used to interrogate the following categories: the type of VOs, the roles of VOs, the relation of VOs to mathematical content, the relation of VOs to reality, and their properties. The 266 VOs under study were collected from the Algebra and Geometry chapters of each book. This study also included survey questionnaires with the 50 selected mathematics teachers, which sought their views and perceptions on the use of the identified VOs. In addition, the authors’ rationale in selecting the identified VOs used in their textbooks was sought through interviews. This research study is part of the “Visualisation in Namibia and Zambia” (VISNAMZA) project which seeks to research the effective use of visualisation processes in the mathematics classroom in Namibia and Zambia (Schäfer, 2015). It is hoped that this study contributes towards improving the quality of textbook evaluations, and design of suitable and more comprehensive assessment procedures in Namibia. It is also hoped that it creates a critical awareness of the roles of VOs in textbooks amongst teachers, inspiring them to help their learners interpret VOs effectively. It should also inspire potential authors to use suitable and appropriate VOs that enhance conceptual teaching and learning of mathematics. The study discovered that most of the VOs used in the selected textbooks align well with the mathematical content. The VOs can help make abstract ideas concrete, stimulate learning, simplify and clarify written texts. In addition, VOs can also be used as a tool for reasoning and an instrument for problem solving. The findings however also indicate that some of the VOs used are not self-explanatory; they are vague, unfamiliar and confusing, leading to misinterpretations by some learners. Another interesting finding was that some of the learners found it difficult to interpret VOs on their own without the help of the teacher.
- Full Text:
- Date Issued: 2017
An analysis of visualization processes used by selected Grade 11 and 12 learners when solving algebraic problems: a Namibian case study
- Authors: Josef, Joseane
- Date: 2017
- Subjects: Visualization , Mathematics -- Study and teaching -- Namibia -- Case studies , Mathematics -- Study and teaching (Secondary) -- Activity programs , Algebra -- Study and teaching (Secondary) -- Namibia -- Case studies
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/7843 , vital:21309
- Description: Visualisation is gaining visibility in mathematics education research. It is a powerful tool for solving different types of problems in many areas of mathematics, including Algebra - the mathematical domain of this study. The aim of this case study was to analyse the visualisation processes that selected senior secondary school learners used to solve a set of ten algebraic problems.The research was conducted at a secondary school in the Erongo region of Namibia. This is the school where the researcher is teaching. The sample consisted of six selected learners, three from Grade 11 and three from Grade 12. The learners were purposefully selected to participate in this study based on their mathematics performance in class and their willingness to participate. The participants were video recorded as they worked through the ten items of an Algebraic Visualisation Tasks (AVT) worksheet. They were also interviewed about the visualisation processes they employed when solving each of the tasks. The AVT, the videos and the interviews were analysed with the aid of an adapted visualisation template. The findings of the study show that learners used visualisations in all their problem-solving processes. These visualisations were used for different purposes such as starting points, for illustrative purposes, as organizational tools and as simplification tools. Visualisations as starting points were used when the problem was wordy and had lengthy descriptions and explanations. Illustrative visualisations enabled learners to articulate in their own way mathematical notations, mathematical equations and expressions that they then used to solve the problem. Organizational pictures provided a useful structural framework for solving the problems.This research suggests that the selected participants indeed used visualisation processes to solve algebraic problems. It is thus important for teachers to harness this aid and make the most use of these visualisation processes when teaching Algebra.
- Full Text:
- Date Issued: 2017
- Authors: Josef, Joseane
- Date: 2017
- Subjects: Visualization , Mathematics -- Study and teaching -- Namibia -- Case studies , Mathematics -- Study and teaching (Secondary) -- Activity programs , Algebra -- Study and teaching (Secondary) -- Namibia -- Case studies
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/7843 , vital:21309
- Description: Visualisation is gaining visibility in mathematics education research. It is a powerful tool for solving different types of problems in many areas of mathematics, including Algebra - the mathematical domain of this study. The aim of this case study was to analyse the visualisation processes that selected senior secondary school learners used to solve a set of ten algebraic problems.The research was conducted at a secondary school in the Erongo region of Namibia. This is the school where the researcher is teaching. The sample consisted of six selected learners, three from Grade 11 and three from Grade 12. The learners were purposefully selected to participate in this study based on their mathematics performance in class and their willingness to participate. The participants were video recorded as they worked through the ten items of an Algebraic Visualisation Tasks (AVT) worksheet. They were also interviewed about the visualisation processes they employed when solving each of the tasks. The AVT, the videos and the interviews were analysed with the aid of an adapted visualisation template. The findings of the study show that learners used visualisations in all their problem-solving processes. These visualisations were used for different purposes such as starting points, for illustrative purposes, as organizational tools and as simplification tools. Visualisations as starting points were used when the problem was wordy and had lengthy descriptions and explanations. Illustrative visualisations enabled learners to articulate in their own way mathematical notations, mathematical equations and expressions that they then used to solve the problem. Organizational pictures provided a useful structural framework for solving the problems.This research suggests that the selected participants indeed used visualisation processes to solve algebraic problems. It is thus important for teachers to harness this aid and make the most use of these visualisation processes when teaching Algebra.
- Full Text:
- Date Issued: 2017
An investigation of how Visual Technology for the Autonomous Learning of Mathematics (VITALmaths) video clips on mobile phones can be used by student teachers as a visualisation tool in the teaching of Number Sense: a case study
- Authors: Kangwa, Lemmy
- Date: 2017
- Subjects: Mathematics -- Study and teaching -- Zambia -- Case studies , Visualization , Number concept , Mobile communication systems in education , Mathematics -- Study and teaching -- Software , Telecommunications in education , Educational innovations , VITALmaths
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/6930 , vital:21201
- Description: Visualisation is increasingly being recognised as having a significant role in the learning of mathematics especially when students are solving mathematical problems (Thornton, 2001). It is argued that visualisation is a powerful tool for learners to construct mental and physical representations that correctly mirror mathematical relationships and concepts. To gain a thorough understanding of the scope of visualisation, three Visual Technology for Autonomous Learning of Mathematics (VITALmaths) (www.vitalmaths.com) video clips were uploaded on mobile phones of each of the eleven participating student teachers who used them in their teaching practice. This is in cognisance of the educational potential offered by mobile phones and their current pervasiveness in the daily lives of both teachers and learners in Zambia (Zambia. Ministry of Education [M.O.E], 2013]). This study sought to investigate how VITALmaths video clips on mobile phones could be used by student teachers as a visualisation tool in the teaching of Number Sense. The videos of the lessons formed the core of my analysis. The study was conducted at four primary schools by eleven student teachers of a public university in Zambia. The study is framed as a case study and is grounded within the interpretive paradigm. The findings revealed that the student teachers’ use of the video clips in the classrooms for teaching was generally approached from two perspectives: at the beginning of the lesson or at the end. The videos were used at the beginning of the lesson as a means to introduce a topic or an idea, and at the end of the lesson to consolidate what was taught. The videos were also used to enhance the conceptual understanding of Number Sense. The findings also revealed that students encountered both enabling and constraining factors in their use of mobile phones to teach number sense. The overall findings revealed that, if well utilised, mobile phones as visualisation tools had the potential to enhance the teaching of Mathematics in general and Number Sense in particular, and therefore teachers should be encouraged to use them in their teaching.
- Full Text:
- Date Issued: 2017
- Authors: Kangwa, Lemmy
- Date: 2017
- Subjects: Mathematics -- Study and teaching -- Zambia -- Case studies , Visualization , Number concept , Mobile communication systems in education , Mathematics -- Study and teaching -- Software , Telecommunications in education , Educational innovations , VITALmaths
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/6930 , vital:21201
- Description: Visualisation is increasingly being recognised as having a significant role in the learning of mathematics especially when students are solving mathematical problems (Thornton, 2001). It is argued that visualisation is a powerful tool for learners to construct mental and physical representations that correctly mirror mathematical relationships and concepts. To gain a thorough understanding of the scope of visualisation, three Visual Technology for Autonomous Learning of Mathematics (VITALmaths) (www.vitalmaths.com) video clips were uploaded on mobile phones of each of the eleven participating student teachers who used them in their teaching practice. This is in cognisance of the educational potential offered by mobile phones and their current pervasiveness in the daily lives of both teachers and learners in Zambia (Zambia. Ministry of Education [M.O.E], 2013]). This study sought to investigate how VITALmaths video clips on mobile phones could be used by student teachers as a visualisation tool in the teaching of Number Sense. The videos of the lessons formed the core of my analysis. The study was conducted at four primary schools by eleven student teachers of a public university in Zambia. The study is framed as a case study and is grounded within the interpretive paradigm. The findings revealed that the student teachers’ use of the video clips in the classrooms for teaching was generally approached from two perspectives: at the beginning of the lesson or at the end. The videos were used at the beginning of the lesson as a means to introduce a topic or an idea, and at the end of the lesson to consolidate what was taught. The videos were also used to enhance the conceptual understanding of Number Sense. The findings also revealed that students encountered both enabling and constraining factors in their use of mobile phones to teach number sense. The overall findings revealed that, if well utilised, mobile phones as visualisation tools had the potential to enhance the teaching of Mathematics in general and Number Sense in particular, and therefore teachers should be encouraged to use them in their teaching.
- Full Text:
- Date Issued: 2017
An investigation into the nature of mathematical connections selected grade 7 teachers make when teaching fractions : a Namibian case study.
- Authors: Amupolo, Loide M
- Date: 2015
- Subjects: Mathematics -- Study and teaching -- Namibia , Fractions -- Study and teaching -- Namibia
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:2016 , http://hdl.handle.net/10962/d1016374
- Description: The general understanding of mathematics as a subject and its implications is, in reality alarmingly low. Evidence of this is evident in learners’ performance and their reaction towards the subject. Fractions as a domain of Mathematics are no exception. The majority of the learners do not learn Fractions comfortably. The causes of this may be varied. However, it is believed that one way of ensuring meaningful teaching and learning is to make use of appropriate connections. The significance and the important role of the teacher in making mathematical connections in learning for understanding are well documented in the literature. This study focuses on the nature of mathematical connections selected Grade 7 teachers make when teaching Fractions, as well as their perceptions of the importance of making such connections. This qualitative case study was conducted in three schools in the Oshana region. The purpose was to investigate how mathematics teachers make connections in fractions. Underpinned by an interpretive paradigm, the study made use of observations and interviews to generate data. The framework borrowed from Businkas’ (2008) study was used in analysing and coding the nature of connections used in the lessons observed. An individual conversation on the nature and perceptions of the connections made in the observed lessons was undertaken with each teacher followed by a focus group discussion that aimed at analysing deeper perceptions on connections. The main findings of the study revealed that teachers made use of all the different types of connections as per Businkas’s framework. The frequency of occurrence showed that Instruction-Oriented Connection and Multiple Representation connections topped the list of connections used. Teachers pointed out that connections to prior knowledge and making multiple representations were most significant, as they related to learners’ existing knowledge and pointed to different ways of solving a problem. The teachers were, however, not familiar with the other connections identified as this was their first experience of interrogating connections. They, however, agreed on the importance of making those connections. The teachers agreed that meaningful connections indeed helped with their conceptual understanding of Mathematics. They believed that connections can increase learners’ interest in school and help reduce negative views of fractions, in particular, and mathematics in general. However, they felt that the limited number of resources, poor teaching approaches and the inability of creating fraction sense may hinder them from making appropriate connections.
- Full Text:
- Date Issued: 2015
- Authors: Amupolo, Loide M
- Date: 2015
- Subjects: Mathematics -- Study and teaching -- Namibia , Fractions -- Study and teaching -- Namibia
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:2016 , http://hdl.handle.net/10962/d1016374
- Description: The general understanding of mathematics as a subject and its implications is, in reality alarmingly low. Evidence of this is evident in learners’ performance and their reaction towards the subject. Fractions as a domain of Mathematics are no exception. The majority of the learners do not learn Fractions comfortably. The causes of this may be varied. However, it is believed that one way of ensuring meaningful teaching and learning is to make use of appropriate connections. The significance and the important role of the teacher in making mathematical connections in learning for understanding are well documented in the literature. This study focuses on the nature of mathematical connections selected Grade 7 teachers make when teaching Fractions, as well as their perceptions of the importance of making such connections. This qualitative case study was conducted in three schools in the Oshana region. The purpose was to investigate how mathematics teachers make connections in fractions. Underpinned by an interpretive paradigm, the study made use of observations and interviews to generate data. The framework borrowed from Businkas’ (2008) study was used in analysing and coding the nature of connections used in the lessons observed. An individual conversation on the nature and perceptions of the connections made in the observed lessons was undertaken with each teacher followed by a focus group discussion that aimed at analysing deeper perceptions on connections. The main findings of the study revealed that teachers made use of all the different types of connections as per Businkas’s framework. The frequency of occurrence showed that Instruction-Oriented Connection and Multiple Representation connections topped the list of connections used. Teachers pointed out that connections to prior knowledge and making multiple representations were most significant, as they related to learners’ existing knowledge and pointed to different ways of solving a problem. The teachers were, however, not familiar with the other connections identified as this was their first experience of interrogating connections. They, however, agreed on the importance of making those connections. The teachers agreed that meaningful connections indeed helped with their conceptual understanding of Mathematics. They believed that connections can increase learners’ interest in school and help reduce negative views of fractions, in particular, and mathematics in general. However, they felt that the limited number of resources, poor teaching approaches and the inability of creating fraction sense may hinder them from making appropriate connections.
- Full Text:
- Date Issued: 2015
An analysis of the distribution and use of teaching aids in mathematics in selected Windhoek secondary schools
- Authors: Dzambara, Tobias Munyaradzi
- Date: 2013
- Subjects: Mathematics -- Study and teaching (Secondary) -- Namibia Teaching -- Aids and devices -- Research
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: vital:1344 , http://hdl.handle.net/10962/d1001410
- Description: This study investigates the types of mathematics teaching aids available at both public and private secondary schools in Windhoek. The study characterises their usage and source as well as teachers’ perceptions towards the use of such teaching resources in the Mathematics classroom. The study is grounded in an interpretive paradigm and employed a mixed methods approach to generate both quantitative and qualitative data in two sequential phases. Phase 1 of the research process, which involved 75 Mathematics teachers, took the form of an audit of the availability and use of teaching aids at 25 secondary schools in Windhoek. A case study methodology was adopted in Phase 2 which focused on five purposively selected schools that displayed different characteristics in terms of the availability of teaching resources. The study found that the majority of teachers at secondary schools in Windhoek have a positive attitude towards the importance and role of teaching aids in Mathematics, seeing them as promoters of hands-on engagement, visual reasoning, active participation and motivation amongst learners. However, in some instances schools are underresourced with respect to certain types of teaching aids, specifically graph boards, geoboards, geometric models and computers. A need for appropriate in-school support on the use of teaching aids was also identified
- Full Text:
- Date Issued: 2013
- Authors: Dzambara, Tobias Munyaradzi
- Date: 2013
- Subjects: Mathematics -- Study and teaching (Secondary) -- Namibia Teaching -- Aids and devices -- Research
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: vital:1344 , http://hdl.handle.net/10962/d1001410
- Description: This study investigates the types of mathematics teaching aids available at both public and private secondary schools in Windhoek. The study characterises their usage and source as well as teachers’ perceptions towards the use of such teaching resources in the Mathematics classroom. The study is grounded in an interpretive paradigm and employed a mixed methods approach to generate both quantitative and qualitative data in two sequential phases. Phase 1 of the research process, which involved 75 Mathematics teachers, took the form of an audit of the availability and use of teaching aids at 25 secondary schools in Windhoek. A case study methodology was adopted in Phase 2 which focused on five purposively selected schools that displayed different characteristics in terms of the availability of teaching resources. The study found that the majority of teachers at secondary schools in Windhoek have a positive attitude towards the importance and role of teaching aids in Mathematics, seeing them as promoters of hands-on engagement, visual reasoning, active participation and motivation amongst learners. However, in some instances schools are underresourced with respect to certain types of teaching aids, specifically graph boards, geoboards, geometric models and computers. A need for appropriate in-school support on the use of teaching aids was also identified
- Full Text:
- Date Issued: 2013
An enquiry into the formative and summative assessment procedures, and perceptions thereof, of grade 10 mathematics teachers : a Namibian case study
- Authors: Marongwe, Anesu Desmond
- Date: 2013
- Subjects: Mathematics -- Study and teaching (Secondary) -- Namibia
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1385 , http://hdl.handle.net/10962/d1001513
- Description: The purpose of this study was to gain insight into observed discrepancies between continuous assessment and final examination average marks in Grade 10 Mathematics in the Oshikoto region of Namibia. The study is framed as a case study and is grounded within the interpretive paradigm. A mixed methods approach was applied, eliciting both quantitative as well as qualitative data. The study took place in two phases. In Phase 1, continuous assessment and Grade 10 final examination average marks for 62 Junior Secondary Schools for the period 2008-2010 were gathered and analyzed. Schools were characterized in terms of the relationship between their continuous assessment and final examination average marks for each of the three years. Phase 2, which was informed by Phase 1, took the form of structured interviews with a sample of three Mathematics teachers and three principals along with a focus-group interview of twelve teachers in order to investigate more deeply the perceptions of teachers and principals toward assessment policy and practice. The study shows that Grade 10 assessment practice in Namibian schools is far from ideal. Many teachers are not fully conversant with the various continuous assessment components as outlined by policy, and teachers are not confident about setting appropriate continuous assessment tasks. There is a strong perception that continuous assessment marks can easily be inflated and those teachers who gave high continuous assessment marks to their learners were generally perceived as being either incompetent or dishonest. While continuous assessment was seen as an important component of teaching and learning, it is evident that teachers and principals would welcome greater clarity, along with standardization and moderation, with respect to continuous assessment practice.
- Full Text:
- Date Issued: 2013
- Authors: Marongwe, Anesu Desmond
- Date: 2013
- Subjects: Mathematics -- Study and teaching (Secondary) -- Namibia
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1385 , http://hdl.handle.net/10962/d1001513
- Description: The purpose of this study was to gain insight into observed discrepancies between continuous assessment and final examination average marks in Grade 10 Mathematics in the Oshikoto region of Namibia. The study is framed as a case study and is grounded within the interpretive paradigm. A mixed methods approach was applied, eliciting both quantitative as well as qualitative data. The study took place in two phases. In Phase 1, continuous assessment and Grade 10 final examination average marks for 62 Junior Secondary Schools for the period 2008-2010 were gathered and analyzed. Schools were characterized in terms of the relationship between their continuous assessment and final examination average marks for each of the three years. Phase 2, which was informed by Phase 1, took the form of structured interviews with a sample of three Mathematics teachers and three principals along with a focus-group interview of twelve teachers in order to investigate more deeply the perceptions of teachers and principals toward assessment policy and practice. The study shows that Grade 10 assessment practice in Namibian schools is far from ideal. Many teachers are not fully conversant with the various continuous assessment components as outlined by policy, and teachers are not confident about setting appropriate continuous assessment tasks. There is a strong perception that continuous assessment marks can easily be inflated and those teachers who gave high continuous assessment marks to their learners were generally perceived as being either incompetent or dishonest. While continuous assessment was seen as an important component of teaching and learning, it is evident that teachers and principals would welcome greater clarity, along with standardization and moderation, with respect to continuous assessment practice.
- Full Text:
- Date Issued: 2013
An investigation into the prevalence and use of code switching practices in grade 8 mathematics classrooms in the Ohangwena region of Namibia: a case study
- Authors: Shilamba, Julia Ndinoshisho
- Date: 2013
- Subjects: Mathematics -- Study and teaching (Secondary) -- Namibia -- Ohangwena Mathematics teachers -- Education (Secondary) -- Namibia -- Ohangwena Code switching (Linguistics) -- Research -- Namibia -- Ohangwena Education, Secondary -- Namibia -- Ohangwena
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1392 , http://hdl.handle.net/10962/d1001683
- Description: This research report focuses on an investigation of the prevalence and nature of code switching practices in grade 8 mathematics classrooms in the Ohangwena region of Namibia. The existence of code switching in these classrooms was established by administering a survey to all grade 8 teachers in the region, while the nature of these practices was explored by interviewing and observing selected teachers using a case study research methodology. The data from the survey was analysed quantitatively using descriptive statistics, while the qualitative data from the case study which comprised of audio and video transcripts was analysed within the framework of Probyn’s (2006) code switching categories. These categories looked at code switching in terms of: explaining concepts; clarifying statements or questions; emphasising points; making connections with learners’ own contexts and experiences; maintaining the learners’ attention with question tags; classroom management and maintaining discipline; and affective purposes. The study found that code switching is widespread in most of the grade 8 mathematics classrooms in the Ohangwena region. It also revealed that the teachers’ code switching practices aligned well with most of Probyn’s framework. The criterion of maintaining learner’s attention with question tags was however not found in this study. The results of the study showed that teachers code switch because the majority of the learners’ language proficiency is not good. Code switching is mostly used as a strategy to support and promote learners understanding in mathematics. The study recommends that it is high time that code switching is acknowledged as a legitimate practice and recognised as an important and meaningful teaching strategy to assist learners who are learning mathematics in their second language. Code switching needs to be de-stigmatised and teachers should be supported in using this practice effectively and efficiently.
- Full Text:
- Date Issued: 2013
- Authors: Shilamba, Julia Ndinoshisho
- Date: 2013
- Subjects: Mathematics -- Study and teaching (Secondary) -- Namibia -- Ohangwena Mathematics teachers -- Education (Secondary) -- Namibia -- Ohangwena Code switching (Linguistics) -- Research -- Namibia -- Ohangwena Education, Secondary -- Namibia -- Ohangwena
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1392 , http://hdl.handle.net/10962/d1001683
- Description: This research report focuses on an investigation of the prevalence and nature of code switching practices in grade 8 mathematics classrooms in the Ohangwena region of Namibia. The existence of code switching in these classrooms was established by administering a survey to all grade 8 teachers in the region, while the nature of these practices was explored by interviewing and observing selected teachers using a case study research methodology. The data from the survey was analysed quantitatively using descriptive statistics, while the qualitative data from the case study which comprised of audio and video transcripts was analysed within the framework of Probyn’s (2006) code switching categories. These categories looked at code switching in terms of: explaining concepts; clarifying statements or questions; emphasising points; making connections with learners’ own contexts and experiences; maintaining the learners’ attention with question tags; classroom management and maintaining discipline; and affective purposes. The study found that code switching is widespread in most of the grade 8 mathematics classrooms in the Ohangwena region. It also revealed that the teachers’ code switching practices aligned well with most of Probyn’s framework. The criterion of maintaining learner’s attention with question tags was however not found in this study. The results of the study showed that teachers code switch because the majority of the learners’ language proficiency is not good. Code switching is mostly used as a strategy to support and promote learners understanding in mathematics. The study recommends that it is high time that code switching is acknowledged as a legitimate practice and recognised as an important and meaningful teaching strategy to assist learners who are learning mathematics in their second language. Code switching needs to be de-stigmatised and teachers should be supported in using this practice effectively and efficiently.
- Full Text:
- Date Issued: 2013
Case study : using visual representations to enhance conceptual knowledge of division in mathematics
- Authors: Joel, Linea Beautty
- Date: 2013
- Subjects: Mathematics -- Study and teaching , Visual learning , Division -- Study and teaching
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1992 , http://hdl.handle.net/10962/d1013356
- Description: Literature emphasizes how important it is that procedural and conceptual knowledge of mathematics should be learned in integration. Yet, generally, the learning and teaching in mathematics classrooms relies heavily on isolated procedures. This study aims to improve teaching and learning of partitive and quotitive division, moving away from isolated procedural knowledge to that of procedures with their underlying concepts through the use of manipulatives, visual representation and questioning. Learning and teaching lessons were designed to teach partitive and quotitive division both procedurally and conceptually. The study explored the roles these manipulatives, visual representations and questioning played toward the conceptual learning of partitive and quotitive division. It was found that manipulatives and iconic visualization enhanced learning, and this could be achieved through scaffolding using a questioning approach. It was concluded that manipulatives and iconic visualization need to be properly planned and used, and integrated with questioning to achieve success in the learning of procedural and conceptual knowledge.
- Full Text:
- Date Issued: 2013
Case study : using visual representations to enhance conceptual knowledge of division in mathematics
- Authors: Joel, Linea Beautty
- Date: 2013
- Subjects: Mathematics -- Study and teaching , Visual learning , Division -- Study and teaching
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1992 , http://hdl.handle.net/10962/d1013356
- Description: Literature emphasizes how important it is that procedural and conceptual knowledge of mathematics should be learned in integration. Yet, generally, the learning and teaching in mathematics classrooms relies heavily on isolated procedures. This study aims to improve teaching and learning of partitive and quotitive division, moving away from isolated procedural knowledge to that of procedures with their underlying concepts through the use of manipulatives, visual representation and questioning. Learning and teaching lessons were designed to teach partitive and quotitive division both procedurally and conceptually. The study explored the roles these manipulatives, visual representations and questioning played toward the conceptual learning of partitive and quotitive division. It was found that manipulatives and iconic visualization enhanced learning, and this could be achieved through scaffolding using a questioning approach. It was concluded that manipulatives and iconic visualization need to be properly planned and used, and integrated with questioning to achieve success in the learning of procedural and conceptual knowledge.
- Full Text:
- Date Issued: 2013
How do teachers characterise their teaching for conceptual understanding and procedural fluency?: a case study of two teachers
- Junius, Daniel Franscius, Danie Junius
- Authors: Junius, Daniel Franscius , Danie Junius
- Date: 2013
- Subjects: Mathematics -- Study and teaching (Secondary) -- Namibia Mathematics -- Study and teaching -- Case studies
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: vital:1360 , http://hdl.handle.net/10962/d1001426
- Description: Over many years the practice or art of teaching Mathematics posed itself as, not only being different from the practice of teaching any other subject, but to have many challenges and opportunities that ask for exploration and understanding. Just after independence in 1990, Namibia has embarked upon a reform process for the entire education system. Many changes were brought about to create a uniform, equal system for all. However, many challenges still remain to be addressed. Mathematics education remains one of the key areas where Namibian teachers can contribute towards the improvement of the subject. Unsatisfactory results, under-qualified teachers, and a negative disposition towards Mathematics are some of the challenges. These challenges are not unique to Namibia. Across the globe psychologists, philosophers and educators continue to engage in debates and research projects in search of answers and solutions for the improvement of Mathematics education. Despite encountering numerous obstacles, many teachers are dedicated and achieve outstanding results with their learners. This thesis reports on a research project that focused on the Mathematics teaching practice of two teachers whose experiences can make a positive contribution to the improvement of Mathematics teaching in Namibia. Furthermore, this case study investigated and attempted to understand the Mathematics teaching practices of two proficient teachers who each claimed to have a specific and unique approach to teaching Mathematics. The one claimed to be mainly procedural in her Mathematics teaching, while the other one claimed to teach mainly in a conceptual manner. Both achieve very good results with their classes and attribute their own teaching orientations to a process of several experiences they went through as students and in their careers. The study revealed that both claims are substantiated and that each teacher was consistent in her claimed approach. Many challenges and constraints were encountered by both teachers, but in their unique and specific ways each teacher’s chosen teaching approach supported them to overcome these. It was evident from the findings that each teacher’s practice came about as an evolutionary process over an extended period of time. As many challenges and limitations are universal, it is believed that in sharing experiences, teachers can benefit from each other by improving their practice. It was clearly stated by both participants that the re-thinking of and reflecting on their own practices provided them with new insights and motivation. Peer support and sharing of practices contribute positively towards the improvement of the teachers’ classroom practices.
- Full Text:
- Date Issued: 2013
- Authors: Junius, Daniel Franscius , Danie Junius
- Date: 2013
- Subjects: Mathematics -- Study and teaching (Secondary) -- Namibia Mathematics -- Study and teaching -- Case studies
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: vital:1360 , http://hdl.handle.net/10962/d1001426
- Description: Over many years the practice or art of teaching Mathematics posed itself as, not only being different from the practice of teaching any other subject, but to have many challenges and opportunities that ask for exploration and understanding. Just after independence in 1990, Namibia has embarked upon a reform process for the entire education system. Many changes were brought about to create a uniform, equal system for all. However, many challenges still remain to be addressed. Mathematics education remains one of the key areas where Namibian teachers can contribute towards the improvement of the subject. Unsatisfactory results, under-qualified teachers, and a negative disposition towards Mathematics are some of the challenges. These challenges are not unique to Namibia. Across the globe psychologists, philosophers and educators continue to engage in debates and research projects in search of answers and solutions for the improvement of Mathematics education. Despite encountering numerous obstacles, many teachers are dedicated and achieve outstanding results with their learners. This thesis reports on a research project that focused on the Mathematics teaching practice of two teachers whose experiences can make a positive contribution to the improvement of Mathematics teaching in Namibia. Furthermore, this case study investigated and attempted to understand the Mathematics teaching practices of two proficient teachers who each claimed to have a specific and unique approach to teaching Mathematics. The one claimed to be mainly procedural in her Mathematics teaching, while the other one claimed to teach mainly in a conceptual manner. Both achieve very good results with their classes and attribute their own teaching orientations to a process of several experiences they went through as students and in their careers. The study revealed that both claims are substantiated and that each teacher was consistent in her claimed approach. Many challenges and constraints were encountered by both teachers, but in their unique and specific ways each teacher’s chosen teaching approach supported them to overcome these. It was evident from the findings that each teacher’s practice came about as an evolutionary process over an extended period of time. As many challenges and limitations are universal, it is believed that in sharing experiences, teachers can benefit from each other by improving their practice. It was clearly stated by both participants that the re-thinking of and reflecting on their own practices provided them with new insights and motivation. Peer support and sharing of practices contribute positively towards the improvement of the teachers’ classroom practices.
- Full Text:
- Date Issued: 2013
Mathematics teachers' experiences of designing and implementing a circle geometry teaching programme using the van Hiele phases of instruction as a conceptual framework: a Namibian case study
- Authors: Dongwi, Beata Lididimikeni
- Date: 2013
- Subjects: Geometry -- Study and teaching (Secondary) -- Namibia Mathematics -- Study and teaching -- Namibia
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1412 , http://hdl.handle.net/10962/d1003133
- Description: The aim of this case study was to examine, analyze and report on the findings of the experiences of selected mathematics teachers when they used the van Hiele phases of instruction in designing and implementing a Grade 11 circle geometry teaching programme. The sample consisted of three selected mathematics teachers from the school where the researcher teaches. This school is located in the Oshikoto Education Region in Namibia. The school serves a multicultural group of 759 learners from a middle-class economic background. The site and participants were selected conveniently as the researcher had unrestricted access to both the facilities and the participants. This research takes the form of a case study and is underpinned by the interpretive paradigm. Data for this research was collected using a variety of techniques such as interviews, classroom observation and document analysis. This facilitated easy triangulation of the data. The findings of this research make four claims with regard to the experiences of the mathematics teachers with designing and implementing the circle geometry teaching programme using the five van Hiele phases of instruction as a conceptual framework. The findings revealed that firstly, all three participating mathematics teachers used and implemented all the five van Hiele phases of instruction in their lessons I observed. Secondly, the teachers navigated quite freely from one phase of instruction to the next, but also returned to the earlier phases for clarification and reinforcement in their teaching. Thirdly, the teachers saw the phases of instruction as a good pedagogical tool or template for planning and presenting lessons. Fourthly, the majority of the learners followed the instructions and seemed to obtain the answers faster than expected. The lesson presentations were lively and both teachers and learners communicated at length to discover angle properties of circles while developing and nurturing the technical language of geometry.
- Full Text:
- Date Issued: 2013
- Authors: Dongwi, Beata Lididimikeni
- Date: 2013
- Subjects: Geometry -- Study and teaching (Secondary) -- Namibia Mathematics -- Study and teaching -- Namibia
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1412 , http://hdl.handle.net/10962/d1003133
- Description: The aim of this case study was to examine, analyze and report on the findings of the experiences of selected mathematics teachers when they used the van Hiele phases of instruction in designing and implementing a Grade 11 circle geometry teaching programme. The sample consisted of three selected mathematics teachers from the school where the researcher teaches. This school is located in the Oshikoto Education Region in Namibia. The school serves a multicultural group of 759 learners from a middle-class economic background. The site and participants were selected conveniently as the researcher had unrestricted access to both the facilities and the participants. This research takes the form of a case study and is underpinned by the interpretive paradigm. Data for this research was collected using a variety of techniques such as interviews, classroom observation and document analysis. This facilitated easy triangulation of the data. The findings of this research make four claims with regard to the experiences of the mathematics teachers with designing and implementing the circle geometry teaching programme using the five van Hiele phases of instruction as a conceptual framework. The findings revealed that firstly, all three participating mathematics teachers used and implemented all the five van Hiele phases of instruction in their lessons I observed. Secondly, the teachers navigated quite freely from one phase of instruction to the next, but also returned to the earlier phases for clarification and reinforcement in their teaching. Thirdly, the teachers saw the phases of instruction as a good pedagogical tool or template for planning and presenting lessons. Fourthly, the majority of the learners followed the instructions and seemed to obtain the answers faster than expected. The lesson presentations were lively and both teachers and learners communicated at length to discover angle properties of circles while developing and nurturing the technical language of geometry.
- Full Text:
- Date Issued: 2013
Student teachers' experiences in using multiple representations in the teaching of grade 6 proportion word problems : a Namibian case study
- Authors: Simasiku, Bosman Muyubano
- Date: 2013
- Subjects: Mathematics -- Study and teaching (Secondary) -- Research -- Namibia Ratio and proportion -- Study and teaching (Secondary) -- Research -- Namibia Mathematics teachers -- Training of -- Namibia Mathematics teachers -- Training of -- Namibia
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1393 , http://hdl.handle.net/10962/d1001703
- Description: This study investigated the experiences of four participating student teachers in using multiple representative approaches in the teaching of Grade 6 proportion word problems. The multiple representative approaches include the Between Comparison Method, the Within Comparison Method, the Diagrammatic Method, the Table Method, the Graph Method, the Cross-product Method, and the Oral Informal Method. An intervention programme was organised, using workshops where student teachers were prepared to teach Grade 6 proportion word problems using multiple representative approaches. The teaching practice lessons of the four participating student teachers in two primary schools were video recorded, and the focus group interview was conducted at the University Campus. With the exception of the Graph Method and the Cross-product Method, it was revealed that the multiple representative approaches were generally effective in the teaching of Grade 6 proportion word problems. The study further revealed that multiplicative relationships can be explored through using the different individual representative approaches. The study argues that the cross-product method is not the only way to teach Grade 6 proportion word problems. There are multiple representative approaches that should be used in conjunction with each other to enhance the teaching of proportion word problems. Furthermore, this study revealed that a number of challenges were encountered when using multiple representative approaches. The challenges include difficulties with the English language, different and unique abilities of the learners, lack of plotting skills and the lack of proficiency in the learners’ multiplication and division skills. This study made recommendations on the integration of multiple representative approaches in the mathematics education curriculum and textbooks. It further recommended that in-service workshops for teachers and student teachers on the integration of multiple representative approaches in the teaching of Grade 6 proportion word problems should be initiated.
- Full Text:
- Date Issued: 2013
- Authors: Simasiku, Bosman Muyubano
- Date: 2013
- Subjects: Mathematics -- Study and teaching (Secondary) -- Research -- Namibia Ratio and proportion -- Study and teaching (Secondary) -- Research -- Namibia Mathematics teachers -- Training of -- Namibia Mathematics teachers -- Training of -- Namibia
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1393 , http://hdl.handle.net/10962/d1001703
- Description: This study investigated the experiences of four participating student teachers in using multiple representative approaches in the teaching of Grade 6 proportion word problems. The multiple representative approaches include the Between Comparison Method, the Within Comparison Method, the Diagrammatic Method, the Table Method, the Graph Method, the Cross-product Method, and the Oral Informal Method. An intervention programme was organised, using workshops where student teachers were prepared to teach Grade 6 proportion word problems using multiple representative approaches. The teaching practice lessons of the four participating student teachers in two primary schools were video recorded, and the focus group interview was conducted at the University Campus. With the exception of the Graph Method and the Cross-product Method, it was revealed that the multiple representative approaches were generally effective in the teaching of Grade 6 proportion word problems. The study further revealed that multiplicative relationships can be explored through using the different individual representative approaches. The study argues that the cross-product method is not the only way to teach Grade 6 proportion word problems. There are multiple representative approaches that should be used in conjunction with each other to enhance the teaching of proportion word problems. Furthermore, this study revealed that a number of challenges were encountered when using multiple representative approaches. The challenges include difficulties with the English language, different and unique abilities of the learners, lack of plotting skills and the lack of proficiency in the learners’ multiplication and division skills. This study made recommendations on the integration of multiple representative approaches in the mathematics education curriculum and textbooks. It further recommended that in-service workshops for teachers and student teachers on the integration of multiple representative approaches in the teaching of Grade 6 proportion word problems should be initiated.
- Full Text:
- Date Issued: 2013
An investigation into Grade R teachers' experiences of implementing numeracy in Grade R
- Authors: Barnard, Elna
- Date: 2011
- Subjects: Teachers -- South Africa -- Attitudes Numeracy -- Study and teaching (Elementary) -- South Africa Teachers -- Training of -- South Africa Mathematics teachers -- In-service training -- South Africa Early childhood education -- South Africa -- History Early childhood education -- South Africa -- Political aspects
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:1855 , http://hdl.handle.net/10962/d1004529
- Description: This research study investigates how selected Grade R teachers implement numeracy in their classrooms, based on their experiences, personal beliefs and perceptions. This study adopts the view that a teacher's practice is not only informed on what she believes about her learners, but also on how she organises her classroom environment and her own teaching practice. However, the teacher cannot be divorced from the political and historical background of Early Childhood Development (ECD), as these factors have an impact on her numeracy implementation. Integrated in this research study is thus not only a comprehensive historical analysis of the historical and political background of ECD, but also an in-depth look at the complex curriculum road the Grade R teacher had to travel over the past twelve years. The aim of this case study is to understand and describe what is happening in Grade R classrooms when numeracy is implemented, as well as identifying possible barriers which Grade R teachers may experience in implementing numeracy. The author utilized an adapted Interactive Qualitative Analysis Framework to explore Grade R teachers' views and experiences. Open-ended focus group interviews were used to develop a framework for individual interviews. This interview framework guided the data collection of nine audio-video tapes of classroom activities and nine semi-structured individual interviews. Analysis of the individual interviews revealed each teacher's understanding as well as her perceptions and needs regarding the implementation of numeracy in her classroom. The transcriptions of the individual interviews were compared to the audio-video tapes of what happened in each classroom. This was done in order to determine whether the teachers' practices were consistent with what they said in the interviews. Paradoxes and inconsistencies were documented. The historical and political analysis of ECD illustrates the complex development of ECD in South Africa over the last few decades. It therefore also highlights and brings to the fore the complex journey that Grade R teachers had to navigate in adapting their practice to ever changing curriculum requirements. The empirical results show that there are inconsistencies between what selected teachers know and believe, and what they are implementing. However, "silent themes" which did not come to the fore in the focus group or individual interviews, were identified in the audiovideo tapes of classroom activities. Also, many "silent themes" indicate that there are numerous concerns, such as lack of proficiency in bridging the gap between theory and practice, regarding the implementation of numeracy in Grade R. It was found that many of the selected Grade R teachers struggle to implement numeracy in their classrooms, as they lack the skills and support to teach numeracy in a Grade R context.
- Full Text:
- Date Issued: 2011
- Authors: Barnard, Elna
- Date: 2011
- Subjects: Teachers -- South Africa -- Attitudes Numeracy -- Study and teaching (Elementary) -- South Africa Teachers -- Training of -- South Africa Mathematics teachers -- In-service training -- South Africa Early childhood education -- South Africa -- History Early childhood education -- South Africa -- Political aspects
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:1855 , http://hdl.handle.net/10962/d1004529
- Description: This research study investigates how selected Grade R teachers implement numeracy in their classrooms, based on their experiences, personal beliefs and perceptions. This study adopts the view that a teacher's practice is not only informed on what she believes about her learners, but also on how she organises her classroom environment and her own teaching practice. However, the teacher cannot be divorced from the political and historical background of Early Childhood Development (ECD), as these factors have an impact on her numeracy implementation. Integrated in this research study is thus not only a comprehensive historical analysis of the historical and political background of ECD, but also an in-depth look at the complex curriculum road the Grade R teacher had to travel over the past twelve years. The aim of this case study is to understand and describe what is happening in Grade R classrooms when numeracy is implemented, as well as identifying possible barriers which Grade R teachers may experience in implementing numeracy. The author utilized an adapted Interactive Qualitative Analysis Framework to explore Grade R teachers' views and experiences. Open-ended focus group interviews were used to develop a framework for individual interviews. This interview framework guided the data collection of nine audio-video tapes of classroom activities and nine semi-structured individual interviews. Analysis of the individual interviews revealed each teacher's understanding as well as her perceptions and needs regarding the implementation of numeracy in her classroom. The transcriptions of the individual interviews were compared to the audio-video tapes of what happened in each classroom. This was done in order to determine whether the teachers' practices were consistent with what they said in the interviews. Paradoxes and inconsistencies were documented. The historical and political analysis of ECD illustrates the complex development of ECD in South Africa over the last few decades. It therefore also highlights and brings to the fore the complex journey that Grade R teachers had to navigate in adapting their practice to ever changing curriculum requirements. The empirical results show that there are inconsistencies between what selected teachers know and believe, and what they are implementing. However, "silent themes" which did not come to the fore in the focus group or individual interviews, were identified in the audiovideo tapes of classroom activities. Also, many "silent themes" indicate that there are numerous concerns, such as lack of proficiency in bridging the gap between theory and practice, regarding the implementation of numeracy in Grade R. It was found that many of the selected Grade R teachers struggle to implement numeracy in their classrooms, as they lack the skills and support to teach numeracy in a Grade R context.
- Full Text:
- Date Issued: 2011
A critical investigation of the interpretation and implementation of the Parzival main lesson within the context of the Waldorf curriculum : a multiple case study
- Authors: Swanepoel, Elizabeth
- Date: 2010
- Subjects: Waldorf method of education Education -- Philosophy Teaching -- South Africa Perceval (Legendary character) Perceval (Legendary character) -- Study and teaching Grail Legends -- Study and teaching
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1483 , http://hdl.handle.net/10962/d1003364
- Description: The Steiner/Waldorf school movement is currently one of the fastest growing independent school movements internationally. In several countries it seems to have developed into the most popular form of alternative education. South Africa has 17 Waldorf schools and one full-time teacher training facility. This study investigated the interpretation and implementation of the Parzival main lesson within the wider context of the Waldorf curriculum. The main lesson system is an essential constituent of the Waldorf curriculum. Most academic subjects in a Waldorf school are taught in a three- or four-week main lesson block. The main lesson occupies the first two hours of the school day. A main lesson consists of a particular three-part structure, and the main lesson book is the keystone to the Waldorf evaluative process. The Parzival main lesson is specifically taught in Class 11, and most Waldorf schools consider it as one of the most important main lessons in the high school. The interpretivist model was ideally suited to this research. The investigation was conducted as a multiple case study, and the main source of data was provided by classroom observation. This was supported by interviews and classroom artifacts. The study involved two South African Waldorf schools at which the Parzival main lesson is taught. This main lesson is presented at only three South African Waldorf schools. I teach at the remaining school, and therefore conducted my research at the other two schools. The teachers who facilitated the Parzival main lesson, as well as the Class students at the selected schools voluntarily participated in the research. My research findings indicate that the possibility exists for the teacher to exercise a certain degree of freedom and creativity within the parameters of Waldorf methodology and the Waldorf curriculum. The study also determines that teachers often find it difficult to integrate the three-part structure, as indicated by Waldorf methodology, in a single main lesson. Furthermore, my research establishes that main lesson books can indeed serve as both text and as an assessment tool. I therefore conclude and maintain in this study, with particular reference to the Parzival main lesson, that despite the prescriptive structure of the Waldorf system and Steiner pedagogy, teachers need not necessarily sacrifice their freedom and creativity within the classroom.
- Full Text:
- Date Issued: 2010
- Authors: Swanepoel, Elizabeth
- Date: 2010
- Subjects: Waldorf method of education Education -- Philosophy Teaching -- South Africa Perceval (Legendary character) Perceval (Legendary character) -- Study and teaching Grail Legends -- Study and teaching
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1483 , http://hdl.handle.net/10962/d1003364
- Description: The Steiner/Waldorf school movement is currently one of the fastest growing independent school movements internationally. In several countries it seems to have developed into the most popular form of alternative education. South Africa has 17 Waldorf schools and one full-time teacher training facility. This study investigated the interpretation and implementation of the Parzival main lesson within the wider context of the Waldorf curriculum. The main lesson system is an essential constituent of the Waldorf curriculum. Most academic subjects in a Waldorf school are taught in a three- or four-week main lesson block. The main lesson occupies the first two hours of the school day. A main lesson consists of a particular three-part structure, and the main lesson book is the keystone to the Waldorf evaluative process. The Parzival main lesson is specifically taught in Class 11, and most Waldorf schools consider it as one of the most important main lessons in the high school. The interpretivist model was ideally suited to this research. The investigation was conducted as a multiple case study, and the main source of data was provided by classroom observation. This was supported by interviews and classroom artifacts. The study involved two South African Waldorf schools at which the Parzival main lesson is taught. This main lesson is presented at only three South African Waldorf schools. I teach at the remaining school, and therefore conducted my research at the other two schools. The teachers who facilitated the Parzival main lesson, as well as the Class students at the selected schools voluntarily participated in the research. My research findings indicate that the possibility exists for the teacher to exercise a certain degree of freedom and creativity within the parameters of Waldorf methodology and the Waldorf curriculum. The study also determines that teachers often find it difficult to integrate the three-part structure, as indicated by Waldorf methodology, in a single main lesson. Furthermore, my research establishes that main lesson books can indeed serve as both text and as an assessment tool. I therefore conclude and maintain in this study, with particular reference to the Parzival main lesson, that despite the prescriptive structure of the Waldorf system and Steiner pedagogy, teachers need not necessarily sacrifice their freedom and creativity within the classroom.
- Full Text:
- Date Issued: 2010
An investigation into the persistence of traditional teaching methods in grade 9 mathematics classrooms in Rundu : a case study
- Authors: Ausiku, Charity M
- Date: 2009
- Subjects: Mathematics -- Study and teaching (Secondary) -- Namibia -- Case studies Mathematics teachers -- Training of -- Namibia -- Case studies
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1852 , http://hdl.handle.net/10962/d1004461
- Description: I embarked upon this study to investigate mathematics teachers' practices that have led to the persistence of traditional teaching methods in grade 9 mathematics classrooms in Rundu. The study was conducted from a learner-centred (L-C) perspective or reform approach in the Namibian context. It is a qualitative study oriented in the interpretive paradigm- a paradigm that seeks to understand the meanings attached to human actions. The participants involved in this study were purposively selected and they are composed of two mathematics teachers and their grade 9 learners. This study was conducted at two schools in Rundu. One is an urban school while the other one is a rural school on the outskirts of Rundu. The research tools employed in this study are questionnaires, interviews and observations. The questionnaires were used to identify and select my participants while the observations were used to investigate the participants teaching strategies. The purpose of the interviews was mainly to investigate teachers' understanding, interpretation and implementation of learner-centre education (LCE). Amongst other findings, this study reveals that inadequate teacher-training, controversial educational policies and challenges such as overcrowdedness in mathematics classrooms, lack of teaching and learning materials, lack of cooperation among mathematics teachers and learners' negative attitude towards mathematics are some of the contributing factors to the persistence of traditional teaching methods in mathematics classrooms. Moreover, the study reveals that the persistence of traditional teaching methods in mathematics classes can no longer be attributed to the lack of understanding of LCE. The teachers in this study seem to be well acquainted with the theoretical aspect of the LCE framework while the implementation aspect seems to be a concern.
- Full Text:
- Date Issued: 2009
- Authors: Ausiku, Charity M
- Date: 2009
- Subjects: Mathematics -- Study and teaching (Secondary) -- Namibia -- Case studies Mathematics teachers -- Training of -- Namibia -- Case studies
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1852 , http://hdl.handle.net/10962/d1004461
- Description: I embarked upon this study to investigate mathematics teachers' practices that have led to the persistence of traditional teaching methods in grade 9 mathematics classrooms in Rundu. The study was conducted from a learner-centred (L-C) perspective or reform approach in the Namibian context. It is a qualitative study oriented in the interpretive paradigm- a paradigm that seeks to understand the meanings attached to human actions. The participants involved in this study were purposively selected and they are composed of two mathematics teachers and their grade 9 learners. This study was conducted at two schools in Rundu. One is an urban school while the other one is a rural school on the outskirts of Rundu. The research tools employed in this study are questionnaires, interviews and observations. The questionnaires were used to identify and select my participants while the observations were used to investigate the participants teaching strategies. The purpose of the interviews was mainly to investigate teachers' understanding, interpretation and implementation of learner-centre education (LCE). Amongst other findings, this study reveals that inadequate teacher-training, controversial educational policies and challenges such as overcrowdedness in mathematics classrooms, lack of teaching and learning materials, lack of cooperation among mathematics teachers and learners' negative attitude towards mathematics are some of the contributing factors to the persistence of traditional teaching methods in mathematics classrooms. Moreover, the study reveals that the persistence of traditional teaching methods in mathematics classes can no longer be attributed to the lack of understanding of LCE. The teachers in this study seem to be well acquainted with the theoretical aspect of the LCE framework while the implementation aspect seems to be a concern.
- Full Text:
- Date Issued: 2009
An exploration of mathematical concepts embedded in Xhosa beadwork artifacts through an invention programme for Grade 9 learners
- Authors: Myemane, Dumakazi Margaret
- Date: 2008
- Subjects: Mathematics -- Study and teaching -- Psychological aspects Mathematics -- Study and teaching -- Social aspects -- South Africa Mathematics -- Study and teaching (Secondary) -- South Africa Xhosa (African people) Ethnomathematics Beadwork -- South Africa -- Eastern Cape Beadwork, Xhosa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1950 , http://hdl.handle.net/10962/d1008201
- Description: Mathematics has become increasingly important, as it is a pre-requisite for careers like architecture, science, engineering and medicine. Therefore it becomes imperative for the learners to understand and love it. In other words a sound foundation of mathematical skills and knowledge in the early stages is required. Often we hear learners asking questions like "when and where are we going to use these symbols x and y in our lives? " These questions might indicate that learners cannot link mathematics with daily life occurrences or even their own background experiences. This study is an exploration through hands-on activities of mathematical concepts embedded in beadwork artifacts. Learners' background experiences on bead work artifacts are acknowledged and explored for mathematical understanding. It is a case study, consisting of 44 learners in Grade 9 in two schools in Grahamstown. An interpretive approach is used. In order for the learners to be able to explore beadwork artifacts, they visited the Albany Museum (AM) and Msithandane Women's Project (MWP) in the community. Learners gathered information from these two sources. Beadwork artifacts in this study were used as a mediation and integration tool between culture and mathematics. Beadwork artifacts are found in the learners' cultures serving different purposes. In this study the focus was on Xhosa bead work artifacts. The hands-on activities posed challenges to learners because of their different background experiences. Some were able to draw designs but were unable to thread what they designed, whereas others were able to thread beads but were unable to draw designs. In this study learners had to use both completed bead work artifacts and drawn up designs for the investigation of mathematical concepts. Learners were able to identify symmetries in dress and in South African flag designs. Number patterns discovered were linked to their prior number pattern knowledge. The economic value of beadwork artifacts linked mathematics to the economics learning area. This study ties up with the new curriculum (C2005) and RNCS, which advocate the inclusion and integration of learning areas. In this instance, art and culture were used in mathematical activities. The study also encouraged the inclusion of participants' cultural background as a starting point for motivating them towards utilizing mathematical resources existing in their real life situations. The purpose was to make them aware that mathematics is found everywhere around us.
- Full Text:
- Date Issued: 2008
- Authors: Myemane, Dumakazi Margaret
- Date: 2008
- Subjects: Mathematics -- Study and teaching -- Psychological aspects Mathematics -- Study and teaching -- Social aspects -- South Africa Mathematics -- Study and teaching (Secondary) -- South Africa Xhosa (African people) Ethnomathematics Beadwork -- South Africa -- Eastern Cape Beadwork, Xhosa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1950 , http://hdl.handle.net/10962/d1008201
- Description: Mathematics has become increasingly important, as it is a pre-requisite for careers like architecture, science, engineering and medicine. Therefore it becomes imperative for the learners to understand and love it. In other words a sound foundation of mathematical skills and knowledge in the early stages is required. Often we hear learners asking questions like "when and where are we going to use these symbols x and y in our lives? " These questions might indicate that learners cannot link mathematics with daily life occurrences or even their own background experiences. This study is an exploration through hands-on activities of mathematical concepts embedded in beadwork artifacts. Learners' background experiences on bead work artifacts are acknowledged and explored for mathematical understanding. It is a case study, consisting of 44 learners in Grade 9 in two schools in Grahamstown. An interpretive approach is used. In order for the learners to be able to explore beadwork artifacts, they visited the Albany Museum (AM) and Msithandane Women's Project (MWP) in the community. Learners gathered information from these two sources. Beadwork artifacts in this study were used as a mediation and integration tool between culture and mathematics. Beadwork artifacts are found in the learners' cultures serving different purposes. In this study the focus was on Xhosa bead work artifacts. The hands-on activities posed challenges to learners because of their different background experiences. Some were able to draw designs but were unable to thread what they designed, whereas others were able to thread beads but were unable to draw designs. In this study learners had to use both completed bead work artifacts and drawn up designs for the investigation of mathematical concepts. Learners were able to identify symmetries in dress and in South African flag designs. Number patterns discovered were linked to their prior number pattern knowledge. The economic value of beadwork artifacts linked mathematics to the economics learning area. This study ties up with the new curriculum (C2005) and RNCS, which advocate the inclusion and integration of learning areas. In this instance, art and culture were used in mathematical activities. The study also encouraged the inclusion of participants' cultural background as a starting point for motivating them towards utilizing mathematical resources existing in their real life situations. The purpose was to make them aware that mathematics is found everywhere around us.
- Full Text:
- Date Issued: 2008
Hermeneutic and empirical analyses of graphically inspired metamathematics that reflect critical consciousness within perspectives of personal and social justice
- Authors: Van Jaarsveld, Pieter Paul
- Date: 2007
- Subjects: Mathematics -- Study and teaching -- South Africa Mathematics -- Study and teaching -- Social aspects -- South Africa Algorithms -- Study and teaching -- South Africa Critical pedagogy Metacognition Hermeneutics
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:1842 , http://hdl.handle.net/10962/d1004376
- Description: My involvement with mathematics education amongst township educators and learners over the past seven years has highlighted the absence of sustained meaning and meaning making of mathematical concepts. It appears though that this instrumental rather than relational understanding of FET mathematics is not unique to township learners but is encountered amongst learners of all socio-economic classes and is representative of many FET mathematics learners. Given that the language of learning and teaching is a major contributory factor in the South African education system, it appears that the language of mathematics itself is a greater exacerbating factor for many learners of mathematics. The exclusive algorithmic approach to classroom mathematics further seems to alienate many learners from the essence of the meaning of mathematical tasks. This research undertakes to determine whether metateaching and metalearning as forerunners to metacognition facilitates the acquisition of the sustained meaning of mathematical concepts. Metateaching and metalearning refer to the acute and deliberate awareness by educator and learner as to what constitutes concepts. Teaching and learning therefore presupposes the deconstruction of concepts into its subsumed derivative roots. It also assumes an awareness of the tacit degrees of abstraction that characterise tasks and the content of tasks. This in turn has implications for the educator's adopted sequence of topics for instruction. Metacognition implies awareness on the part of the learner (and educator) as to how material is learned and a further awareness as to how that learning can be sustained. Whether we ascribe meaningful learning to radical or social constructivism, or to associationist didactive approaches, or a combination of these, we are making assumptions about how learners acquire and sustain mathematical meaning because mathematics is, by and large a symbolic language often devoid of affective connotation. Furthermore our assessments of learners' tasks amount to clinical corrections of austere formulae wrapped in algorithmic procedures which manifest nothing of a learner's experience of mathematics or the deeper understanding (or misunderstandings) which characterise a learning and/or assessment episode. To this end the research design of this interpretive case study requires learners to expound in textual accounts their thoughts as they describe the evolution of a mathematical process as they approach a solution and eventually interpret it. The textual account exposes the concept definition for what it really is in a learner's understanding of it and it is the expressiveness of language that indicates whether the understanding of a learner is approaching the concept image. The textual accounts vary in richness in terms of mathematical register and this in turn reflects the conceptual depth. The mechanism which seems to promote the conversion from concept definition to concept image is the graphical representation of the mathematical task or procedure, possibly because of its greater concreteness as opposed to the abstraction of its algebraic form.
- Full Text:
- Date Issued: 2007
- Authors: Van Jaarsveld, Pieter Paul
- Date: 2007
- Subjects: Mathematics -- Study and teaching -- South Africa Mathematics -- Study and teaching -- Social aspects -- South Africa Algorithms -- Study and teaching -- South Africa Critical pedagogy Metacognition Hermeneutics
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:1842 , http://hdl.handle.net/10962/d1004376
- Description: My involvement with mathematics education amongst township educators and learners over the past seven years has highlighted the absence of sustained meaning and meaning making of mathematical concepts. It appears though that this instrumental rather than relational understanding of FET mathematics is not unique to township learners but is encountered amongst learners of all socio-economic classes and is representative of many FET mathematics learners. Given that the language of learning and teaching is a major contributory factor in the South African education system, it appears that the language of mathematics itself is a greater exacerbating factor for many learners of mathematics. The exclusive algorithmic approach to classroom mathematics further seems to alienate many learners from the essence of the meaning of mathematical tasks. This research undertakes to determine whether metateaching and metalearning as forerunners to metacognition facilitates the acquisition of the sustained meaning of mathematical concepts. Metateaching and metalearning refer to the acute and deliberate awareness by educator and learner as to what constitutes concepts. Teaching and learning therefore presupposes the deconstruction of concepts into its subsumed derivative roots. It also assumes an awareness of the tacit degrees of abstraction that characterise tasks and the content of tasks. This in turn has implications for the educator's adopted sequence of topics for instruction. Metacognition implies awareness on the part of the learner (and educator) as to how material is learned and a further awareness as to how that learning can be sustained. Whether we ascribe meaningful learning to radical or social constructivism, or to associationist didactive approaches, or a combination of these, we are making assumptions about how learners acquire and sustain mathematical meaning because mathematics is, by and large a symbolic language often devoid of affective connotation. Furthermore our assessments of learners' tasks amount to clinical corrections of austere formulae wrapped in algorithmic procedures which manifest nothing of a learner's experience of mathematics or the deeper understanding (or misunderstandings) which characterise a learning and/or assessment episode. To this end the research design of this interpretive case study requires learners to expound in textual accounts their thoughts as they describe the evolution of a mathematical process as they approach a solution and eventually interpret it. The textual account exposes the concept definition for what it really is in a learner's understanding of it and it is the expressiveness of language that indicates whether the understanding of a learner is approaching the concept image. The textual accounts vary in richness in terms of mathematical register and this in turn reflects the conceptual depth. The mechanism which seems to promote the conversion from concept definition to concept image is the graphical representation of the mathematical task or procedure, possibly because of its greater concreteness as opposed to the abstraction of its algebraic form.
- Full Text:
- Date Issued: 2007