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
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
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
A critical investigation into the process of negotiating a mathematics education curriculum with pre-service teachers
- Authors: Westaway, Lise
- Date: 2005
- Subjects: Teacher participation in curriculum planning -- South Africa Curriculum planning -- South Africa Curriculum change -- South Africa Mathematics -- Study and teaching -- South Africa Teachers -- Training of -- South Africa Mathematics teachers -- Training of -- South Africa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1826 , http://hdl.handle.net/10962/d1003712
- Description: It's almost like a dinner party and a buffet. A dinner party you get dished up stuff and you eat it and a buffet you can choose what you want out of a range of stuff. I mean think about it when you go to a dinner party- they always dish up something you don't like and you don't want to eat it anyway. It's the same if you have a lecturer in the front that just dishes out what you're going to learn, ... you have to learn it. But in terms of the curriculum negotiation process, I've got to choose what I wanted to leam. (Melissa II 27/11/01: 3) This thesis focuses on the process of negotiating the curriculum with twelve pre-service teachers registered for the Bachelor of Education (Primary) Degree during their Mathematics Education Course in their third year of study. The research is presented methodologically as an action research located within two paradigmatic positions, interpretive and critical. The research attempted to understand, interpret and critique the process of curriculum negotiation within the context of teacher education in South Africa In order to understand the negotiated curriculum process, experiences of the participants are presented through the use of their voices within the thesis. The interpretation is based on the construction and reconstruction of meaning during the enactment of the negotiated curriculum process and during the writing and reviewing of this thesis. The critique is rooted in the historical, cultural and social contexts of both the students and the author. The main contention of this thesis is that curriculum negotiation is not necessarily a suitable vehicle for developing a critical pedagogy in pre-service teacher education when all the participants form a homogenous group in this case, white middle-class women. The democratic values promoted within the context of our curriculum negotiation were fraught with dilemmas and entrenched the values of western liberalism. At most, the curriculum negotiation process and the development of a democratic learning environment, promoted a conscientisation at an individual level, namely a ' transformation of consciousness' . The democratic values promoted in our pedagogy were not sufficient in bringing about social change, a 'transformation for social action'.
- Full Text:
- Date Issued: 2005
- Authors: Westaway, Lise
- Date: 2005
- Subjects: Teacher participation in curriculum planning -- South Africa Curriculum planning -- South Africa Curriculum change -- South Africa Mathematics -- Study and teaching -- South Africa Teachers -- Training of -- South Africa Mathematics teachers -- Training of -- South Africa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1826 , http://hdl.handle.net/10962/d1003712
- Description: It's almost like a dinner party and a buffet. A dinner party you get dished up stuff and you eat it and a buffet you can choose what you want out of a range of stuff. I mean think about it when you go to a dinner party- they always dish up something you don't like and you don't want to eat it anyway. It's the same if you have a lecturer in the front that just dishes out what you're going to learn, ... you have to learn it. But in terms of the curriculum negotiation process, I've got to choose what I wanted to leam. (Melissa II 27/11/01: 3) This thesis focuses on the process of negotiating the curriculum with twelve pre-service teachers registered for the Bachelor of Education (Primary) Degree during their Mathematics Education Course in their third year of study. The research is presented methodologically as an action research located within two paradigmatic positions, interpretive and critical. The research attempted to understand, interpret and critique the process of curriculum negotiation within the context of teacher education in South Africa In order to understand the negotiated curriculum process, experiences of the participants are presented through the use of their voices within the thesis. The interpretation is based on the construction and reconstruction of meaning during the enactment of the negotiated curriculum process and during the writing and reviewing of this thesis. The critique is rooted in the historical, cultural and social contexts of both the students and the author. The main contention of this thesis is that curriculum negotiation is not necessarily a suitable vehicle for developing a critical pedagogy in pre-service teacher education when all the participants form a homogenous group in this case, white middle-class women. The democratic values promoted within the context of our curriculum negotiation were fraught with dilemmas and entrenched the values of western liberalism. At most, the curriculum negotiation process and the development of a democratic learning environment, promoted a conscientisation at an individual level, namely a ' transformation of consciousness' . The democratic values promoted in our pedagogy were not sufficient in bringing about social change, a 'transformation for social action'.
- Full Text:
- Date Issued: 2005
Exploring learners' mathematical understanding through an analysis of their solution strategies
- Authors: Penlington, Thomas Helm
- Date: 2005
- Subjects: Mathematics -- Study and teaching (Elementary) Mathematics -- Problems, exercises, etc. Problem solving -- Study and teaching Reasoning Mathematical ability
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1934 , http://hdl.handle.net/10962/d1007642
- Description: The purpose of this study is to investigate various solution strategies employed by Grade 7 learners and their teachers when solving a given set of mathematical tasks. This study is oriented in an interpretive paradigm and is characterised by qualitative methods. The research, set in nine schools in the Eastern Cape, was carried out with nine learners and their mathematics teachers and was designed around two phases. The research tools consisted of a set of 12 tasks that were modelled after the Third International Mathematics and Science Study (TIMSS), and a process of clinical interviews that interrogated the solution strategies that were used in solving the 12 tasks. Aspects of grounded theory were used in the analysis of the data. The study reveals that in most tasks, learners relied heavily on procedural understanding at the expense of conceptual understanding. It also emphasises that the solution strategies adopted by learners, particularly whole number operations, were consistent with those strategies used by their teachers. Both learners and teachers favoured using the traditional, standard algorithm strategies and appeared to have learned these algorithms in isolation from concepts, failing to relate them to understanding. Another important finding was that there was evidence to suggest that some learners and teachers did employ their own constructed solution strategies. They were able to make sense of the problems and to 'mathematize' effectively and reason mathematically. An interesting outcome of the study shows that participants were more proficient in solving word problems than mathematical computations. This is in contrast to existing research on word problems, where it is shown that teachers find them difficult to teach and learners find them difficult to understand. The findings of this study also highlight issues for mathematics teachers to consider when dealing with computations and word problems involving number sense and other problem solving type problems.
- Full Text:
- Date Issued: 2005
- Authors: Penlington, Thomas Helm
- Date: 2005
- Subjects: Mathematics -- Study and teaching (Elementary) Mathematics -- Problems, exercises, etc. Problem solving -- Study and teaching Reasoning Mathematical ability
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1934 , http://hdl.handle.net/10962/d1007642
- Description: The purpose of this study is to investigate various solution strategies employed by Grade 7 learners and their teachers when solving a given set of mathematical tasks. This study is oriented in an interpretive paradigm and is characterised by qualitative methods. The research, set in nine schools in the Eastern Cape, was carried out with nine learners and their mathematics teachers and was designed around two phases. The research tools consisted of a set of 12 tasks that were modelled after the Third International Mathematics and Science Study (TIMSS), and a process of clinical interviews that interrogated the solution strategies that were used in solving the 12 tasks. Aspects of grounded theory were used in the analysis of the data. The study reveals that in most tasks, learners relied heavily on procedural understanding at the expense of conceptual understanding. It also emphasises that the solution strategies adopted by learners, particularly whole number operations, were consistent with those strategies used by their teachers. Both learners and teachers favoured using the traditional, standard algorithm strategies and appeared to have learned these algorithms in isolation from concepts, failing to relate them to understanding. Another important finding was that there was evidence to suggest that some learners and teachers did employ their own constructed solution strategies. They were able to make sense of the problems and to 'mathematize' effectively and reason mathematically. An interesting outcome of the study shows that participants were more proficient in solving word problems than mathematical computations. This is in contrast to existing research on word problems, where it is shown that teachers find them difficult to teach and learners find them difficult to understand. The findings of this study also highlight issues for mathematics teachers to consider when dealing with computations and word problems involving number sense and other problem solving type problems.
- Full Text:
- Date Issued: 2005
Research projects
- Authors: Thomas, Chacko
- Date: 2002
- Subjects: Mathematics -- Study and teaching -- South Africa Competency-based education -- South Africa Mathematics teachers -- Training of -- South Africa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1856 , http://hdl.handle.net/10962/d1004531
- Description: The South African education is undergoing transformation. The introduction of Curriculum 2005 and Outcome Based Education (OBE) are important aspects of this transformation process. The implementation of the new curriculum however, has not been smooth. A lack of adequately qualified and trained teachers and effective learning support materials have been identified as some of the major problems facing the implementation of OBE at school level. Even though the colleges of education in the country were not brought on board in the planning and implementation levels of the new curriculum, they could have played an important role in training of educators and developing learning materials for the successful take off of the new curriculum. In the first research project I look into the preparedness of the Mathematics Department of a college of education in the Eastern Cape towards the implementation of Outcome Based Education. The first part of the research project consists of a literature review on Curriculum 2005, Outcome Based Education and the expectations of teachers in the new curriculum and the research methodologies used. The findings revealed that the department, as a whole, was not adequately prepared for the implementation of outcome-based education even though there were some indications that the department effected some modifications in its curriculum and practice teaching. As an OBE facilitator and a college lecturer, I developed some learning materials in Linear Programming. These activity-oriented materials were based on constructivist principles and were used by my first year Secondary Teachers Diploma students. In the second research project, I reflect on the results of using these learning materials by my students. In the first chapter of the project, the context and background of the research and the reasons for selecting Linear Programming as the topic for preparing the learning material are described. This is followed by a brief overview of constructivism together with a brief explanation of the reasons for considering the material to be constructivist. The research paradigm followed in the project, the research techniques employed in evaluating the learning material and the strengths and weaknesses of the evaluation techniques are given in the next chapter. In the following chapter, the findings from the various data gathering methods and the results of the implementation of the material are described. The concluding chapter presents a critical reflection on the whole process involved in the material development. The post 1994 government in South Africa seems to attach much importance to mathematics, science and technology education. The majority of the population who were previously denied access to these subjects is given more opportunities to learn them. The international Mathematics Union declared 2000 as the World Mathematical Year. One of the aims of the activities organized as part of the celebrations was improving the public image of mathematics to realize the vision of "Mathematics For All". The South African government shows keen interest to improve mathematics education in the country in an attempt to realize the vision of Mathematics For All. Even though the accessibility rate to mathematics has increased, the success rate has not yet increased as anticipated. In this context I, as a post-graduate student in Mathematics Education, thought of /reviewing the concept of Mathematics For All in the South African context. In the third research project, which is a literature review, initially an attempt is made to unpack the concept of Mathematics for ALL. In analyzing the concept, answers are sought for questions like: What is mathematics and why should it be taught? It is followed by a brief review of some goals of mathematics education. Then the current situation of mathematics education in South Africa and the efforts to improve it are also looked at. This is followed by an analysis pf the reasons for the general unpopularity of mathematics. In the concluding part some suggestions for improving mathematics education in the country are given.
- Full Text:
- Date Issued: 2002
- Authors: Thomas, Chacko
- Date: 2002
- Subjects: Mathematics -- Study and teaching -- South Africa Competency-based education -- South Africa Mathematics teachers -- Training of -- South Africa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1856 , http://hdl.handle.net/10962/d1004531
- Description: The South African education is undergoing transformation. The introduction of Curriculum 2005 and Outcome Based Education (OBE) are important aspects of this transformation process. The implementation of the new curriculum however, has not been smooth. A lack of adequately qualified and trained teachers and effective learning support materials have been identified as some of the major problems facing the implementation of OBE at school level. Even though the colleges of education in the country were not brought on board in the planning and implementation levels of the new curriculum, they could have played an important role in training of educators and developing learning materials for the successful take off of the new curriculum. In the first research project I look into the preparedness of the Mathematics Department of a college of education in the Eastern Cape towards the implementation of Outcome Based Education. The first part of the research project consists of a literature review on Curriculum 2005, Outcome Based Education and the expectations of teachers in the new curriculum and the research methodologies used. The findings revealed that the department, as a whole, was not adequately prepared for the implementation of outcome-based education even though there were some indications that the department effected some modifications in its curriculum and practice teaching. As an OBE facilitator and a college lecturer, I developed some learning materials in Linear Programming. These activity-oriented materials were based on constructivist principles and were used by my first year Secondary Teachers Diploma students. In the second research project, I reflect on the results of using these learning materials by my students. In the first chapter of the project, the context and background of the research and the reasons for selecting Linear Programming as the topic for preparing the learning material are described. This is followed by a brief overview of constructivism together with a brief explanation of the reasons for considering the material to be constructivist. The research paradigm followed in the project, the research techniques employed in evaluating the learning material and the strengths and weaknesses of the evaluation techniques are given in the next chapter. In the following chapter, the findings from the various data gathering methods and the results of the implementation of the material are described. The concluding chapter presents a critical reflection on the whole process involved in the material development. The post 1994 government in South Africa seems to attach much importance to mathematics, science and technology education. The majority of the population who were previously denied access to these subjects is given more opportunities to learn them. The international Mathematics Union declared 2000 as the World Mathematical Year. One of the aims of the activities organized as part of the celebrations was improving the public image of mathematics to realize the vision of "Mathematics For All". The South African government shows keen interest to improve mathematics education in the country in an attempt to realize the vision of Mathematics For All. Even though the accessibility rate to mathematics has increased, the success rate has not yet increased as anticipated. In this context I, as a post-graduate student in Mathematics Education, thought of /reviewing the concept of Mathematics For All in the South African context. In the third research project, which is a literature review, initially an attempt is made to unpack the concept of Mathematics for ALL. In analyzing the concept, answers are sought for questions like: What is mathematics and why should it be taught? It is followed by a brief review of some goals of mathematics education. Then the current situation of mathematics education in South Africa and the efforts to improve it are also looked at. This is followed by an analysis pf the reasons for the general unpopularity of mathematics. In the concluding part some suggestions for improving mathematics education in the country are given.
- Full Text:
- Date Issued: 2002
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