Visual representations of linear algebraic expressions: a case study in a Grade 9 after-school mathematics club
- Authors: Herbert, Sindisiwe
- Date: 2023-10-13
- Subjects: Visual learning , Algebra Study and teaching (Secondary) South Africa , Algebras, Linear , After-school programs , Kinaesthetic learning
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/424019 , vital:72116
- Description: Visualisation is commonly used as a tool in introducing algebra through visual or kinaesthetic sequences designed to prompt learners' development of a general rule for moving from a term's position to its output value. Fluency in both the concepts and the conventions of elementary algebra are essential to learners, as algebra forms the language in which many advanced mathematical ideas are encoded. Moreover, algebraic fluency is often associated with an ability to think abstractly about arithmetic processes. In many classrooms, however, research has shown that learners often focus on fluency in algebraic conventions rather than concepts, learning how to manipulate expressions without understanding the algorithms they are taught to follow. This trend can be linked to several causes, including teacher-centred mathematics classrooms in which learners are – whether implicitly or explicitly – encouraged to copy formulae and methods in order to ‘get it right in a test’ without necessarily grasping the underlying logical relationships. This case study, therefore, aimed to determine whether there was value in using visual, kinaesthetic models to broaden and deepen learners' use of algebra. To that end, in the context of an extra-curricular mathematics club that aimed to decentre the teachers and demand innovative ideas of the participants, six pairs of Grade 9 learners were tasked with creating visual representations of a linear algebraic expression using coloured building cubes. The responses to this task over the course of five assignments were many and varied and almost universally displayed a sustained internal logic that the learners were able to explain and develop. Most pairs began with a visual list of terms arranged in sets of towers, pyramids or, in one case, a spiral. At the end of the study, all but one of the pairs had settled on a Visual Expression, in which various colours were used to represent elements of the algebra such as the values of the coefficient, the variable and the constant term. The participants' representations grew in complexity over the course of the study and the conformity of the final responses showed that the club was a collaborative space in which learners shared ideas. However, the structure of the Visual Expressions and their own confessions of nerves about ‘getting it wrong’ in the interviews suggest that the participants were stuck in a mindset that led them to seek out and idealise the representation closest to the original algebra, even though that representation revealed little about the structural relationship underlying the expression. , Thesis (MEd) -- Faculty of Education, Secondary and Post-School Education, 2023
- Full Text:
- Date Issued: 2023-10-13
- Authors: Herbert, Sindisiwe
- Date: 2023-10-13
- Subjects: Visual learning , Algebra Study and teaching (Secondary) South Africa , Algebras, Linear , After-school programs , Kinaesthetic learning
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/424019 , vital:72116
- Description: Visualisation is commonly used as a tool in introducing algebra through visual or kinaesthetic sequences designed to prompt learners' development of a general rule for moving from a term's position to its output value. Fluency in both the concepts and the conventions of elementary algebra are essential to learners, as algebra forms the language in which many advanced mathematical ideas are encoded. Moreover, algebraic fluency is often associated with an ability to think abstractly about arithmetic processes. In many classrooms, however, research has shown that learners often focus on fluency in algebraic conventions rather than concepts, learning how to manipulate expressions without understanding the algorithms they are taught to follow. This trend can be linked to several causes, including teacher-centred mathematics classrooms in which learners are – whether implicitly or explicitly – encouraged to copy formulae and methods in order to ‘get it right in a test’ without necessarily grasping the underlying logical relationships. This case study, therefore, aimed to determine whether there was value in using visual, kinaesthetic models to broaden and deepen learners' use of algebra. To that end, in the context of an extra-curricular mathematics club that aimed to decentre the teachers and demand innovative ideas of the participants, six pairs of Grade 9 learners were tasked with creating visual representations of a linear algebraic expression using coloured building cubes. The responses to this task over the course of five assignments were many and varied and almost universally displayed a sustained internal logic that the learners were able to explain and develop. Most pairs began with a visual list of terms arranged in sets of towers, pyramids or, in one case, a spiral. At the end of the study, all but one of the pairs had settled on a Visual Expression, in which various colours were used to represent elements of the algebra such as the values of the coefficient, the variable and the constant term. The participants' representations grew in complexity over the course of the study and the conformity of the final responses showed that the club was a collaborative space in which learners shared ideas. However, the structure of the Visual Expressions and their own confessions of nerves about ‘getting it wrong’ in the interviews suggest that the participants were stuck in a mindset that led them to seek out and idealise the representation closest to the original algebra, even though that representation revealed little about the structural relationship underlying the expression. , Thesis (MEd) -- Faculty of Education, Secondary and Post-School Education, 2023
- Full Text:
- Date Issued: 2023-10-13
An investigation of how a visual teaching approach can possibly address issues of mathematics anxiety at a selected school in the Oshikoto region of Namibia
- Ngonga, Daniel Nghifikepunye
- Authors: Ngonga, Daniel Nghifikepunye
- Date: 2022-04-08
- Subjects: Visual learning Namibia , Math anxiety Namibia , Mathematics Study and teaching Namibia , After-school programs Namibia , Mathematics Study and teaching Activity programs
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/290637 , vital:56770
- Description: This Namibian case study aimed to explore a visual teaching approach (VTA) used by three selected teachers to address issues of mathematics anxiety (MA). The three teachers took part in an intervention program that was looking at how a VTA could be grown in the context of an after-school club (ASC) at my school. The selected teachers were the senior primary teachers at my school. The focus of the research was on how they taught mathematics using visuals after participating in an intervention programme. Their VTA made use of manipulatives, visuals, and concrete materials. The learners of the participating teachers completed a big MA pre-test, small MA tests, and a big MA post-test to determine their levels of MA as the teaching programme unfolded. The study hoped to create awareness amongst teachers and education researchers about the significant use of a VTA in the teaching and learning of mathematics to address issues of MA among the learners. It aimed to answer three research questions. One was on teachers’ use of a VTA in the context of an ASC; the second one was on comparisons of learners’ MA big pre and post-tests to detect any change of MA, and the last was on the enabling and constraining factors encountered when using a VTA. The main argument was that a VTA can encourage learners to be more confident and less anxious about doing mathematics. This study was framed by a constructivist perspective and its design and methodology were underpinned by an interpretive paradigm. This mixed-method research study employed video-recorded observations and stimulated recall interviews, learners’ MA test results, and the teachers’ focus group interviews as the means of collecting data. To generate rich data and support validity, four lessons per selected teacher were observed and video recorded; 54 learners completed the MA tests of 16 questions, and three teachers answered seven questions each in the focus group interview (FGI) after the stimulus recall interviews (SRI) which were done immediately after the lesson presentations. The study found that the participating teachers incorporated a variety of visuals into their lessons to make the mathematics fun, inspiring, visible, hands-on, and activity-oriented. They engaged the learners and also found that the use of visuals motivated learners and reduced their MA. , Thesis (MED) -- Faculty of Education, Education, 2022
- Full Text:
- Date Issued: 2022-04-08
- Authors: Ngonga, Daniel Nghifikepunye
- Date: 2022-04-08
- Subjects: Visual learning Namibia , Math anxiety Namibia , Mathematics Study and teaching Namibia , After-school programs Namibia , Mathematics Study and teaching Activity programs
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/290637 , vital:56770
- Description: This Namibian case study aimed to explore a visual teaching approach (VTA) used by three selected teachers to address issues of mathematics anxiety (MA). The three teachers took part in an intervention program that was looking at how a VTA could be grown in the context of an after-school club (ASC) at my school. The selected teachers were the senior primary teachers at my school. The focus of the research was on how they taught mathematics using visuals after participating in an intervention programme. Their VTA made use of manipulatives, visuals, and concrete materials. The learners of the participating teachers completed a big MA pre-test, small MA tests, and a big MA post-test to determine their levels of MA as the teaching programme unfolded. The study hoped to create awareness amongst teachers and education researchers about the significant use of a VTA in the teaching and learning of mathematics to address issues of MA among the learners. It aimed to answer three research questions. One was on teachers’ use of a VTA in the context of an ASC; the second one was on comparisons of learners’ MA big pre and post-tests to detect any change of MA, and the last was on the enabling and constraining factors encountered when using a VTA. The main argument was that a VTA can encourage learners to be more confident and less anxious about doing mathematics. This study was framed by a constructivist perspective and its design and methodology were underpinned by an interpretive paradigm. This mixed-method research study employed video-recorded observations and stimulated recall interviews, learners’ MA test results, and the teachers’ focus group interviews as the means of collecting data. To generate rich data and support validity, four lessons per selected teacher were observed and video recorded; 54 learners completed the MA tests of 16 questions, and three teachers answered seven questions each in the focus group interview (FGI) after the stimulus recall interviews (SRI) which were done immediately after the lesson presentations. The study found that the participating teachers incorporated a variety of visuals into their lessons to make the mathematics fun, inspiring, visible, hands-on, and activity-oriented. They engaged the learners and also found that the use of visuals motivated learners and reduced their MA. , Thesis (MED) -- Faculty of Education, Education, 2022
- Full Text:
- Date Issued: 2022-04-08
The use of smartphones and visualisation processes for conceptual understanding of mensuration: a case study of the Mathcitymap Project in Namibia
- Authors: Shimakeleni, Liina
- Date: 2022-04-08
- Subjects: Mathematics Study and teaching (Secondary) Namibia Oshana , Smartphones , Visual learning , Measurement , Concept learning , MathCityMap (MCM) project
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/290649 , vital:56771
- Description: The aim of this study was to investigate and analyse the potential use of smartphones as visualisation tools by learners to enhance conceptual understanding through mathematics trails developed using the MathCityMap (MCM) project. This research study is part of the VIPROmaths project which seeks to research the effective use of visualisation processes in mathematics classrooms in South Africa, Namibia, Zambia, Switzerland and Germany. This study adopted a case of twelve purposively selected Grade 9 learners from a school in the Eheke circuit of the Oshana region, Namibia. This study was framed within a social constructivist perspective and sought to investigate visualisation processes as well as conceptual understanding of learners as they conceptualised the MCM tasks in new, outdoor and collaborative learning situations. The MCM app was installed on selected learners’ smartphones to access and to walk the MCM trails located in various places in the schoolyard. Three MCM trails based on three key themes of mensuration (perimeter, area and volume) were created. Each consisted of four tasks that were sourced and developed in line with the Grade 9 Namibian mathematics syllabus. This study is oriented in an interpretive paradigm and employed video-recorded observations and focus group interviews as qualitative data collection methods. Data collected were analysed first using the themes developed from Ho’s (2010) work on visualisation processes and Kilpatrick, Swafford, and Findell’s (2001) conceptual understanding. During analysis, some themes emerged from the data and were considered. Findings from this study revealed that smartphones afforded learners ample opportunities to enhance the visualisation processes that they went through as they learned the concepts of measurement. In addition to this, some learners were initially pessimistic regarding the use of smartphones for learning purposes. This study recommends that resources such as MCM be effectively be used in formal school settings. The learning of measurement can be advanced in outdoor settings where learners have physical and spatial access to the learning content. Smartphone technology can be used as an additional tool to integrate Information and Communication Technology (ICT) in learning mathematics within the Namibian context. , Thesis (MED) -- Faculty of Education, Education, 2022
- Full Text:
- Date Issued: 2022-04-08
- Authors: Shimakeleni, Liina
- Date: 2022-04-08
- Subjects: Mathematics Study and teaching (Secondary) Namibia Oshana , Smartphones , Visual learning , Measurement , Concept learning , MathCityMap (MCM) project
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/290649 , vital:56771
- Description: The aim of this study was to investigate and analyse the potential use of smartphones as visualisation tools by learners to enhance conceptual understanding through mathematics trails developed using the MathCityMap (MCM) project. This research study is part of the VIPROmaths project which seeks to research the effective use of visualisation processes in mathematics classrooms in South Africa, Namibia, Zambia, Switzerland and Germany. This study adopted a case of twelve purposively selected Grade 9 learners from a school in the Eheke circuit of the Oshana region, Namibia. This study was framed within a social constructivist perspective and sought to investigate visualisation processes as well as conceptual understanding of learners as they conceptualised the MCM tasks in new, outdoor and collaborative learning situations. The MCM app was installed on selected learners’ smartphones to access and to walk the MCM trails located in various places in the schoolyard. Three MCM trails based on three key themes of mensuration (perimeter, area and volume) were created. Each consisted of four tasks that were sourced and developed in line with the Grade 9 Namibian mathematics syllabus. This study is oriented in an interpretive paradigm and employed video-recorded observations and focus group interviews as qualitative data collection methods. Data collected were analysed first using the themes developed from Ho’s (2010) work on visualisation processes and Kilpatrick, Swafford, and Findell’s (2001) conceptual understanding. During analysis, some themes emerged from the data and were considered. Findings from this study revealed that smartphones afforded learners ample opportunities to enhance the visualisation processes that they went through as they learned the concepts of measurement. In addition to this, some learners were initially pessimistic regarding the use of smartphones for learning purposes. This study recommends that resources such as MCM be effectively be used in formal school settings. The learning of measurement can be advanced in outdoor settings where learners have physical and spatial access to the learning content. Smartphone technology can be used as an additional tool to integrate Information and Communication Technology (ICT) in learning mathematics within the Namibian context. , Thesis (MED) -- Faculty of Education, Education, 2022
- Full Text:
- Date Issued: 2022-04-08
An analysis of selected Grade 8 mathematics teachers’ use of gestures as visualisation tools to support mathematical meaning-making
- Authors: Haipinge, David Tuhafeni
- Date: 2021-10-29
- Subjects: Gesture , Gesture in mathematics education , Visual learning , Visualization , Mathematics Study and teaching (Secondary) Namibia
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/191969 , vital:45184
- Description: The purpose of this Namibian case study was to investigate how different types of gestures are used to support the construction of mathematical meaning making in teaching and learning. Gestures of three selected Grade 8 mathematics teachers were observed and analysed. This study was intended to answer the following research question: how do selected Grade 8 mathematics teachers use gestures as visualisation tools to support mathematical meaning making? The study was framed by an enactivist perspective and the research was oriented in the interpretive paradigm. Data were collected through video-recorded observations of three selected teachers and through stimulus recall interviews. In order to generate rich data and support validity, five lessons per selected teacher were video recorded. The study found that the participating teachers incorporated a variety of mathematical gestures into their lessons in order to support and provide mathematical meaning. Further, this study found that gestures facilitated meaning making in mathematics. The findings in the study suggest a need for mathematics teachers to be trained in using gestures appropriately to communicate mathematically in their lessons. In addition, this study discovered a new type of gesture – the overlapping gesture in addition to McNeill's (1992) types, namely: pointing gestures, metaphor gestures, beating gestures and iconic gestures. This case study also showed that the more experienced the teachers are, the more mathematical gestures they produce during their mathematics lessons. , Thesis (MEd) -- Faculty of Education, Education, 2021
- Full Text:
- Date Issued: 2021-10-29
- Authors: Haipinge, David Tuhafeni
- Date: 2021-10-29
- Subjects: Gesture , Gesture in mathematics education , Visual learning , Visualization , Mathematics Study and teaching (Secondary) Namibia
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/191969 , vital:45184
- Description: The purpose of this Namibian case study was to investigate how different types of gestures are used to support the construction of mathematical meaning making in teaching and learning. Gestures of three selected Grade 8 mathematics teachers were observed and analysed. This study was intended to answer the following research question: how do selected Grade 8 mathematics teachers use gestures as visualisation tools to support mathematical meaning making? The study was framed by an enactivist perspective and the research was oriented in the interpretive paradigm. Data were collected through video-recorded observations of three selected teachers and through stimulus recall interviews. In order to generate rich data and support validity, five lessons per selected teacher were video recorded. The study found that the participating teachers incorporated a variety of mathematical gestures into their lessons in order to support and provide mathematical meaning. Further, this study found that gestures facilitated meaning making in mathematics. The findings in the study suggest a need for mathematics teachers to be trained in using gestures appropriately to communicate mathematically in their lessons. In addition, this study discovered a new type of gesture – the overlapping gesture in addition to McNeill's (1992) types, namely: pointing gestures, metaphor gestures, beating gestures and iconic gestures. This case study also showed that the more experienced the teachers are, the more mathematical gestures they produce during their mathematics lessons. , Thesis (MEd) -- Faculty of Education, Education, 2021
- Full Text:
- Date Issued: 2021-10-29
An evaluation of the impact of the Rhodes University Master of Education in Mathematics Education Programme in Namibia from the perspectives of its graduates
- Authors: David, Johannes
- Date: 2021-10-29
- Subjects: Master of education degree Namibia , Rhodes University. Department of Education , Mathematics Study and teaching , Critical thinking , Master of education degree Evaluation , Career development Namibia , Educational change Namibia , College students Attitudes
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/191942 , vital:45181
- Description: Rhodes University (RU) has been offering a MEdME (Masters in Education, Mathematics Education) degree in Namibia for over 12 years without evaluating its success and impact. This study aimed to evaluate the MEdME programme’s impact on the graduates and on mathematics education in Namibia from the perspectives of its graduates. The study also evaluated the factors that enabled or limited the impact of the programme from the perspective of RU staff members. A three-phased research study was implemented to achieve this. Phase I was a MEdME theses audit to analyze what each graduate researched which then guided the sampling process. Phase II was a distribution of a questionnaire to willing MEdME graduates to elicit their views about the programme's impact. In Phase III, selected graduates were interviewed to follow up on the questionnaire. The RU academic staff members were also interviewed about the programme's design and rationale, as well as their perspectives on its impact on graduates' professional lives. The study found that graduates believed that the programme made them more critical reflexive practitioners (CRPs) who: are now self-introspective, can reflect in context and are competent researchers. This is a sign of the programme attaining its objectives of developing and growing CRPs and graduates, who have advanced in their fields, including their ability to do research. The programme also created opportunities for graduates to study further and/or publish papers. The programme further opened up opportunities for graduates’ promotion into positions of influence in the Ministry of Education where they can positively impact on mathematics education transformation in Namibia (METN). The graduates consequently noticed improvements in some areas but they also noticed room for improvement in other areas of mathematics education in Namibia. This study therefore suggests that more mathematics teachers study further, improve their research capacity and contribute more to METN. The study also suggests a national campaign to increase mathematics teachers' content knowledge. Furthermore, the programme should reintroduce coursework to address students’ subject content knowledge. RU is also advised to explore offering a Professional MEd in Namibia for students who want to focus more on improving their mathematics content knowledge. It is also proposed that Namibia establish a research bank where researchers can upload their theses for wider dissemination. , Thesis (MEd) -- Faculty of Education, Education, 2021
- Full Text:
- Date Issued: 2021-10-29
- Authors: David, Johannes
- Date: 2021-10-29
- Subjects: Master of education degree Namibia , Rhodes University. Department of Education , Mathematics Study and teaching , Critical thinking , Master of education degree Evaluation , Career development Namibia , Educational change Namibia , College students Attitudes
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/191942 , vital:45181
- Description: Rhodes University (RU) has been offering a MEdME (Masters in Education, Mathematics Education) degree in Namibia for over 12 years without evaluating its success and impact. This study aimed to evaluate the MEdME programme’s impact on the graduates and on mathematics education in Namibia from the perspectives of its graduates. The study also evaluated the factors that enabled or limited the impact of the programme from the perspective of RU staff members. A three-phased research study was implemented to achieve this. Phase I was a MEdME theses audit to analyze what each graduate researched which then guided the sampling process. Phase II was a distribution of a questionnaire to willing MEdME graduates to elicit their views about the programme's impact. In Phase III, selected graduates were interviewed to follow up on the questionnaire. The RU academic staff members were also interviewed about the programme's design and rationale, as well as their perspectives on its impact on graduates' professional lives. The study found that graduates believed that the programme made them more critical reflexive practitioners (CRPs) who: are now self-introspective, can reflect in context and are competent researchers. This is a sign of the programme attaining its objectives of developing and growing CRPs and graduates, who have advanced in their fields, including their ability to do research. The programme also created opportunities for graduates to study further and/or publish papers. The programme further opened up opportunities for graduates’ promotion into positions of influence in the Ministry of Education where they can positively impact on mathematics education transformation in Namibia (METN). The graduates consequently noticed improvements in some areas but they also noticed room for improvement in other areas of mathematics education in Namibia. This study therefore suggests that more mathematics teachers study further, improve their research capacity and contribute more to METN. The study also suggests a national campaign to increase mathematics teachers' content knowledge. Furthermore, the programme should reintroduce coursework to address students’ subject content knowledge. RU is also advised to explore offering a Professional MEd in Namibia for students who want to focus more on improving their mathematics content knowledge. It is also proposed that Namibia establish a research bank where researchers can upload their theses for wider dissemination. , Thesis (MEd) -- Faculty of Education, Education, 2021
- Full Text:
- Date Issued: 2021-10-29
Exploring visual probability teaching strategies for enhancing mathematical thinking in grade 11 classrooms
- Nghidinwa, Lavinia Tangi-Jehova
- Authors: Nghidinwa, Lavinia Tangi-Jehova
- Date: 2021-10-29
- Subjects: Mathematics Study and teaching (Secondary) Namibia , Probabilities , Visualization , Learning models (Stochastic processes) , VIPROMaths project
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/192002 , vital:45187
- Description: This Namibian case study aimed to explore the use of visualisation tools associated with different teaching strategies in the teaching of probability concepts in Grade 11 by selected teachers, to promote mathematical thinking. This research project is an integral component of the VIPROMaths project whose goal is to research the effective use of visualisation strategies in the mathematics classroom in the Southern African region. As a mathematics teacher, I have observed that mathematics teaching practices in our classrooms have relatively little connection with actual mathematics and as a result, teaching misses opportunities to promote mathematical thinking. This qualitative case study is underpinned by an interpretive paradigm and it is informed by the dual coding theory. Data was collected through survey questionnaires, reflective journals, field notes, observation schedules and stimulus-recall interviews. Firstly, I piloted my study by conducting a survey with the Grade 10-12 mathematics teachers in the Khomas region. The aim of this survey was to understand and explore how teachers in the Khomas region taught probability prior to the intervention programme. The data was analysed quantitatively using descriptive statistics such as tables and bar graphs. The findings from the survey necessitated the need for an intervention programme with some teachers in the region, focused on the use of visual tools to promote mathematical thinking. Lastly, three schools were selected from which three Grade 11 mathematics teachers were chosen to take part in an intervention programme. The goal was to observe how these three teachers use visual probability teaching strategies to enhance mathematical thinking after participating in an intervention programme. Lesson observations showed that all observed teachers used visual models to generate images and used models to develop a probability idea as well as to create platforms for classroom discussions. Interviews revealed that teachers’ views towards probability have shifted from that of being the centre of knowledge to that of a facilitator. As a result, teachers used different models to build on learners’ prior knowledge, to assess whether they grasped the probability concept and extend their teaching to real-life situations. This study concluded that the teachers need to consider using mathematical models for creating a platform for discussion to ensure that their verbal explanations are in line with the visuals incorporated. Coupled with that, the teachers’ correct use of visual probability teaching strategies has the potential of enhancing learners’ mathematical thinking. Therefore, teachers need to teach the learners how to create visuals for enhancing maximise understanding of probability concepts in mathematics. Furthermore, it is hoped that the findings will be useful to mathematics teachers, scholars and educators to improve the teaching of probability. , Thesis (MEd) -- Faculty of Education, Education, 2021
- Full Text:
- Date Issued: 2021-10-29
- Authors: Nghidinwa, Lavinia Tangi-Jehova
- Date: 2021-10-29
- Subjects: Mathematics Study and teaching (Secondary) Namibia , Probabilities , Visualization , Learning models (Stochastic processes) , VIPROMaths project
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/192002 , vital:45187
- Description: This Namibian case study aimed to explore the use of visualisation tools associated with different teaching strategies in the teaching of probability concepts in Grade 11 by selected teachers, to promote mathematical thinking. This research project is an integral component of the VIPROMaths project whose goal is to research the effective use of visualisation strategies in the mathematics classroom in the Southern African region. As a mathematics teacher, I have observed that mathematics teaching practices in our classrooms have relatively little connection with actual mathematics and as a result, teaching misses opportunities to promote mathematical thinking. This qualitative case study is underpinned by an interpretive paradigm and it is informed by the dual coding theory. Data was collected through survey questionnaires, reflective journals, field notes, observation schedules and stimulus-recall interviews. Firstly, I piloted my study by conducting a survey with the Grade 10-12 mathematics teachers in the Khomas region. The aim of this survey was to understand and explore how teachers in the Khomas region taught probability prior to the intervention programme. The data was analysed quantitatively using descriptive statistics such as tables and bar graphs. The findings from the survey necessitated the need for an intervention programme with some teachers in the region, focused on the use of visual tools to promote mathematical thinking. Lastly, three schools were selected from which three Grade 11 mathematics teachers were chosen to take part in an intervention programme. The goal was to observe how these three teachers use visual probability teaching strategies to enhance mathematical thinking after participating in an intervention programme. Lesson observations showed that all observed teachers used visual models to generate images and used models to develop a probability idea as well as to create platforms for classroom discussions. Interviews revealed that teachers’ views towards probability have shifted from that of being the centre of knowledge to that of a facilitator. As a result, teachers used different models to build on learners’ prior knowledge, to assess whether they grasped the probability concept and extend their teaching to real-life situations. This study concluded that the teachers need to consider using mathematical models for creating a platform for discussion to ensure that their verbal explanations are in line with the visuals incorporated. Coupled with that, the teachers’ correct use of visual probability teaching strategies has the potential of enhancing learners’ mathematical thinking. Therefore, teachers need to teach the learners how to create visuals for enhancing maximise understanding of probability concepts in mathematics. Furthermore, it is hoped that the findings will be useful to mathematics teachers, scholars and educators to improve the teaching of probability. , Thesis (MEd) -- Faculty of Education, Education, 2021
- Full Text:
- Date Issued: 2021-10-29
Re-imagining the use of the abacus as a visualization tool to develop number sense in Grade 3 learners
- Authors: Elifas, Taimi Ndinelago
- Date: 2021-10-29
- Subjects: Abacus , Mathematics Study and teaching (Elementary) Namibia , Visual learning , Teaching Aids and devices , Constructivism (Education) , Effective teaching Namibia
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/191953 , vital:45182
- Description: The poor performance of learners in mathematics has long been a matter of concern in Namibia. After more than three decades after independence, the country's education system is still seeking ways of addressing the high rate of poor performance in mathematics. Research previously conducted pointed out the lack of number sense in learners, as one of the contributing factors to the poor performance in mathematics. This research study is a contribution towards using the abacus as a visualization tool to develop number sense in the Foundation Phase. The study was premised on the thought – supported by literature – that effective use of concrete equipment and manipulatives, of which the abacus is part of, does affect the teaching and learning of number sense. The study further examines the use of the abacus as a visualization tool to develop number sense by the four selected Grade 3 teachers. The study argues that the effective use of the abacus develops number sense in learners. This study was framed as a multiple case study that was grounded within an interpretive paradigm and informed by the constructivist learning theory. The qualitative data of this study were collected using questionnaires, observation, reflective journals, and semi-structured interviews. The data were then analyzed using thematic analysis and an analytical tool developed from relevant literature. A survey was conducted using 50 Foundation Phase teachers in the //Kharas region, while the intervention programme consisted of four purposively selected teachers from the four primary schools in the Kalahari circuit in the Keetmanshoop district. The findings of this study revealed that the majority of teachers were not aware of abacus use in teaching mathematics before the intervention programme. It was also revealed that the few teachers that use the abacus as a visualization tool to develop number sense, employ it as a counting tool for explaining certain concepts and as well as for teaching simple arithmetic. In this research study, the selected teachers use the abacus to link the abstract mathematics content to a concrete way of doing mathematics. In the absence of the abacus in classrooms, various manipulatives are used to develop learners’ number sense. Mathematical games, verbalizing mathematics concepts, and drawing pictures to visualize abstract concepts among others are used by the selected teachers to enhance the development of number sense in the Foundation Phase. The use of the abacus by the selected teachers effectively fostered the visualization process and the conceptual understanding of number sense in learners. Through the abacus, teachers led their learners into visualizing number sense concepts such as subitizing, computing, performing mental mathematics and physical representation of numbers in different ways. The abacus was used by teachers to enhance listening skills, improve concentration and strengthen the memory of learners. On the other hand, the study also revealed that despite the various benefits of the abacus, it is time consuming. The lack of abacus use in previous grades has a huge impact on the use of it and the development of learners’ number sense in the grades being studied in this research study. Teachers are recommended to make their own abacuses, encourage learners to make their own abacuses from the readily available materials, and to allow the learners to realize that the mathematics they are doing in classrooms is around them. The use of re-imagining, re-envisioning, re-conceptualizing and re-examining of so-called ‘old teaching tools’ such as the abacus, needs to be encouraged through in-service and pre-service teacher training programmes. The study concludes that the use of traditional algorithm methods do not promote conceptual understanding and visual strategies for Foundation Phase learners and should be discouraged. It is hoped that this study will contribute towards improving the practices of mathematics teachers primarily in the Keetmanshoop district, //Kharas Region and in the rest our Namibian schools. , Thesis (MEd) -- Faculty of Education, Education, 2021
- Full Text:
- Date Issued: 2021-10-29
- Authors: Elifas, Taimi Ndinelago
- Date: 2021-10-29
- Subjects: Abacus , Mathematics Study and teaching (Elementary) Namibia , Visual learning , Teaching Aids and devices , Constructivism (Education) , Effective teaching Namibia
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/191953 , vital:45182
- Description: The poor performance of learners in mathematics has long been a matter of concern in Namibia. After more than three decades after independence, the country's education system is still seeking ways of addressing the high rate of poor performance in mathematics. Research previously conducted pointed out the lack of number sense in learners, as one of the contributing factors to the poor performance in mathematics. This research study is a contribution towards using the abacus as a visualization tool to develop number sense in the Foundation Phase. The study was premised on the thought – supported by literature – that effective use of concrete equipment and manipulatives, of which the abacus is part of, does affect the teaching and learning of number sense. The study further examines the use of the abacus as a visualization tool to develop number sense by the four selected Grade 3 teachers. The study argues that the effective use of the abacus develops number sense in learners. This study was framed as a multiple case study that was grounded within an interpretive paradigm and informed by the constructivist learning theory. The qualitative data of this study were collected using questionnaires, observation, reflective journals, and semi-structured interviews. The data were then analyzed using thematic analysis and an analytical tool developed from relevant literature. A survey was conducted using 50 Foundation Phase teachers in the //Kharas region, while the intervention programme consisted of four purposively selected teachers from the four primary schools in the Kalahari circuit in the Keetmanshoop district. The findings of this study revealed that the majority of teachers were not aware of abacus use in teaching mathematics before the intervention programme. It was also revealed that the few teachers that use the abacus as a visualization tool to develop number sense, employ it as a counting tool for explaining certain concepts and as well as for teaching simple arithmetic. In this research study, the selected teachers use the abacus to link the abstract mathematics content to a concrete way of doing mathematics. In the absence of the abacus in classrooms, various manipulatives are used to develop learners’ number sense. Mathematical games, verbalizing mathematics concepts, and drawing pictures to visualize abstract concepts among others are used by the selected teachers to enhance the development of number sense in the Foundation Phase. The use of the abacus by the selected teachers effectively fostered the visualization process and the conceptual understanding of number sense in learners. Through the abacus, teachers led their learners into visualizing number sense concepts such as subitizing, computing, performing mental mathematics and physical representation of numbers in different ways. The abacus was used by teachers to enhance listening skills, improve concentration and strengthen the memory of learners. On the other hand, the study also revealed that despite the various benefits of the abacus, it is time consuming. The lack of abacus use in previous grades has a huge impact on the use of it and the development of learners’ number sense in the grades being studied in this research study. Teachers are recommended to make their own abacuses, encourage learners to make their own abacuses from the readily available materials, and to allow the learners to realize that the mathematics they are doing in classrooms is around them. The use of re-imagining, re-envisioning, re-conceptualizing and re-examining of so-called ‘old teaching tools’ such as the abacus, needs to be encouraged through in-service and pre-service teacher training programmes. The study concludes that the use of traditional algorithm methods do not promote conceptual understanding and visual strategies for Foundation Phase learners and should be discouraged. It is hoped that this study will contribute towards improving the practices of mathematics teachers primarily in the Keetmanshoop district, //Kharas Region and in the rest our Namibian schools. , Thesis (MEd) -- Faculty of Education, Education, 2021
- Full Text:
- Date Issued: 2021-10-29
How selected Grade 7 participants develop conceptual understanding in solving algebraic problems as a result of participating in a screencast intervention
- Authors: Wienekus, George Renier
- Date: 2021-04
- Subjects: Algebra -- Study and teaching -- South Africa , Mathematics -- Study and teaching (Elementary) -- South Africa , Problem solving in children , Algebra -- Ability testing , Algebra -- Computer-assisted instruction
- Language: English
- Type: thesis , text , Masters , MEd
- Identifier: http://hdl.handle.net/10962/176833 , vital:42763
- Description: This research project is an interventionist case study, oriented in the interpretive paradigm, which aims to investigate how selected Grade 7 participants develop conceptual understanding in solving algebraic problems as a result of participating in screencast interventions. The aim of my screencast intervention programme, which lies at the heart of this study, is to develop practices, inter alia, of how such devices and software may be “used to develop conceptual rather than procedural or decorative knowledge” (Larkin & Calder, 2015:1) in solving linear equations. The planned intervention was delivered in the form of a series of screencasts: these take the form of audio-video lessons with an emphasis on the visual impact, and were recorded using an application called Explain Everything. The screencast interventions were delivered via Google Classroom and included animations supported by such conceptual explanations of early algebra as are relevant to Grade 7 students, and in line with the South African Curriculum and Assessment Policy Statements - Department of Education, 2011. The fundamental components of an early algebraic equation that would be relevant to a Grade 7 student were considered and used to develop an analytic framework. This was based on a taxonomy designed according to four identified “clusters” in order to analyse the workings of the purposefully selected Grade 7 participants who were video recorded and questioned in a talk-aloud interview while they completed a post-intervention pencil-and-paper test. What emerges from this research project is that there is a significant need for specific and concentrated technology-based techniques, such as the interventions undertaken here, and that exploration and development in the field could benefit the delivery of a pedagogy for algebra. The pedagogical methods implemented and studied in the form of screencasts proved to be successful and were well received by the learners particularly in relation to the conceptualisation of “symbol sense” and transformation in early algebra. The structure and design of the screencast interventions were important in supporting the acquisition of these concepts and were demonstrated to be worthwhile tools for an epistemological application in a classroom or teaching context. , Thesis (MEd) -- Rhodes University, Faculty of Education, Education, 2021
- Full Text:
- Date Issued: 2021-04
- Authors: Wienekus, George Renier
- Date: 2021-04
- Subjects: Algebra -- Study and teaching -- South Africa , Mathematics -- Study and teaching (Elementary) -- South Africa , Problem solving in children , Algebra -- Ability testing , Algebra -- Computer-assisted instruction
- Language: English
- Type: thesis , text , Masters , MEd
- Identifier: http://hdl.handle.net/10962/176833 , vital:42763
- Description: This research project is an interventionist case study, oriented in the interpretive paradigm, which aims to investigate how selected Grade 7 participants develop conceptual understanding in solving algebraic problems as a result of participating in screencast interventions. The aim of my screencast intervention programme, which lies at the heart of this study, is to develop practices, inter alia, of how such devices and software may be “used to develop conceptual rather than procedural or decorative knowledge” (Larkin & Calder, 2015:1) in solving linear equations. The planned intervention was delivered in the form of a series of screencasts: these take the form of audio-video lessons with an emphasis on the visual impact, and were recorded using an application called Explain Everything. The screencast interventions were delivered via Google Classroom and included animations supported by such conceptual explanations of early algebra as are relevant to Grade 7 students, and in line with the South African Curriculum and Assessment Policy Statements - Department of Education, 2011. The fundamental components of an early algebraic equation that would be relevant to a Grade 7 student were considered and used to develop an analytic framework. This was based on a taxonomy designed according to four identified “clusters” in order to analyse the workings of the purposefully selected Grade 7 participants who were video recorded and questioned in a talk-aloud interview while they completed a post-intervention pencil-and-paper test. What emerges from this research project is that there is a significant need for specific and concentrated technology-based techniques, such as the interventions undertaken here, and that exploration and development in the field could benefit the delivery of a pedagogy for algebra. The pedagogical methods implemented and studied in the form of screencasts proved to be successful and were well received by the learners particularly in relation to the conceptualisation of “symbol sense” and transformation in early algebra. The structure and design of the screencast interventions were important in supporting the acquisition of these concepts and were demonstrated to be worthwhile tools for an epistemological application in a classroom or teaching context. , Thesis (MEd) -- Rhodes University, Faculty of Education, Education, 2021
- Full Text:
- Date Issued: 2021-04
A critical analysis of selected teachers’ perceptions and experiences of the role that visualisation processes play in their Van Hiele level 1 teaching to migrate their learners to the next Van Hiele level
- Authors: Munichinga, Ben Muyambango
- Date: 2019
- Subjects: Hiele, Pierre M. van. Structure and insight , Visualization , Mathematics -- Study and teaching (Secondary) -- Namibia , Geometry -- Study and teaching (Secondary) -- Namibia , Mathematics -- Study and teaching (Secondary) -- Activity programs -- Namibia
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/96735 , vital:31313
- Description: Learning is a process that involves building on prior knowledge, enriching and exchanging existing understanding where learners’ knowledge base is scaffolded in the construction of knowledge. Research on the teaching and learning of geometry in mathematics suggests that physical manipulation experiences, especially of shapes, is an important process in learning at all ages. The focus of the study was the migration of Grade 8 learners from one Van Hiele level to the next as a result of teachers incorporating visualisation processes and Van Hiele phases of instructions in their teaching. The study underpinned by the social constructivist’s theory, therefore aimed at teachers developing visual materials and using Van Hiele’s phases of instruction to teach two dimensional figures in Geometry. The study was carried out in Namibia, Zambezi region in Bukalo circuit. It involved four schools, with 93 learners and three teacher participants. The research is an interpretive case study of a planned intervention programme, which took a four weeks to complete. Participating learners wrote a Van Hiele Geometric test prior and post the intervention programme to determine their geometric level of thought. Participating teachers all received training on visualisation in mathematics and the Van Hiele theory before the intervention. During the intervention, teacher planned and each taught three lessons on two-dimensional figures. Qualitative data was collected from classroom observation, stimulus recall interviews and focus group interviews. Quantitative data came from the pre and post-test of learners. This study found that on average, Grade 8 learners who participated in the study were operating at levels lower than expected of pupils at their stage of schooling. This study also found that, visualisation processes and the Van Hiele phases are effective when used in geometry lessons to migrate learners from lower Van Hiele levels to higher. For teachers in the same circuit, partnership and planning of difficult topics on an agreed regular basis is recommended. When planning lessons teachers are encouraged to take advantage of the Van Hiele phases of instructions. This study thus recommends the incorporation of visualisation strategies of teaching geometry in particular at primary and lower secondary levels. Mathematics teachers are further encouraged to design visual materials such as Geoboards to use for every topic in geometry. Such visual materials should be carefully developed and evaluated to ensure that their use in the classroom is effectively linked to concepts under discussion in a given lesson.
- Full Text:
- Date Issued: 2019
- Authors: Munichinga, Ben Muyambango
- Date: 2019
- Subjects: Hiele, Pierre M. van. Structure and insight , Visualization , Mathematics -- Study and teaching (Secondary) -- Namibia , Geometry -- Study and teaching (Secondary) -- Namibia , Mathematics -- Study and teaching (Secondary) -- Activity programs -- Namibia
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/96735 , vital:31313
- Description: Learning is a process that involves building on prior knowledge, enriching and exchanging existing understanding where learners’ knowledge base is scaffolded in the construction of knowledge. Research on the teaching and learning of geometry in mathematics suggests that physical manipulation experiences, especially of shapes, is an important process in learning at all ages. The focus of the study was the migration of Grade 8 learners from one Van Hiele level to the next as a result of teachers incorporating visualisation processes and Van Hiele phases of instructions in their teaching. The study underpinned by the social constructivist’s theory, therefore aimed at teachers developing visual materials and using Van Hiele’s phases of instruction to teach two dimensional figures in Geometry. The study was carried out in Namibia, Zambezi region in Bukalo circuit. It involved four schools, with 93 learners and three teacher participants. The research is an interpretive case study of a planned intervention programme, which took a four weeks to complete. Participating learners wrote a Van Hiele Geometric test prior and post the intervention programme to determine their geometric level of thought. Participating teachers all received training on visualisation in mathematics and the Van Hiele theory before the intervention. During the intervention, teacher planned and each taught three lessons on two-dimensional figures. Qualitative data was collected from classroom observation, stimulus recall interviews and focus group interviews. Quantitative data came from the pre and post-test of learners. This study found that on average, Grade 8 learners who participated in the study were operating at levels lower than expected of pupils at their stage of schooling. This study also found that, visualisation processes and the Van Hiele phases are effective when used in geometry lessons to migrate learners from lower Van Hiele levels to higher. For teachers in the same circuit, partnership and planning of difficult topics on an agreed regular basis is recommended. When planning lessons teachers are encouraged to take advantage of the Van Hiele phases of instructions. This study thus recommends the incorporation of visualisation strategies of teaching geometry in particular at primary and lower secondary levels. Mathematics teachers are further encouraged to design visual materials such as Geoboards to use for every topic in geometry. Such visual materials should be carefully developed and evaluated to ensure that their use in the classroom is effectively linked to concepts under discussion in a given lesson.
- Full Text:
- Date Issued: 2019
An analysis of how the use of geoboards as visualisation tools can be utilised in the teaching of quadrilaterals
- Authors: Matengu, Given Kahale
- Date: 2019
- Subjects: Manipulatives (Education) , Information visualization , Visualization , Mathematics -- Study and teaching , Mathematics -- Study and teaching -- Activity programs , Geometry -- Study and teaching
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/96724 , vital:31312
- Description: The relationship between visualisation processes and using manipulatives in the teaching and learning of mathematics is apparent and yet not so vocal in the literature. This could be because of the common mistaken understanding that because manipulatives are visual in nature, then visualisation processes should be obvious. Literature warns that just because something is visual therefore it is transparent, is incorrect. This study argues that the effective use of manipulatives in the teaching of mathematics helps learners to effectively understand mathematical concepts. Research on the teaching and learning of mathematics suggests that physical manipulation experiences, especially of concrete materials concerning shapes, is an important process in learning at all ages. One such teaching tool, the Geoboard, a physical manipulative that employs visualisation processes when correctly used, is explored in this study. The aim of this interpretive case study was to investigate and analyse the use of Geoboards as a visualisation tool in the teaching of the properties of quadrilaterals. The study focused on visualisation processes and the use of Geoboards through a teaching framework that was informed by the Van Hiele phases of teaching geometry. The study was conducted in the Opuwo circuit of the Kunene region, Namibia, and it involved three selected Grade 7 mathematics teachers, each from a different primary school. It was underpinned by a constructivist theory using the Van Hiele phases of teaching geometry and framed within visualisation processes. The study employed the use of qualitative data collection techniques such as observations and interviews. The analysis of the findings of this study revealed that Geoboards were very useful in demonstrating the visual representations of the properties of quadrilaterals in a cheap and yet novel way in the selected teachers’ classes. Moreover, the use of Geoboards by the selected teachers effectively fostered visualisation processes such as concrete pictorial imagery, dynamic imagery, perceptual apprehension, sequential apprehension, discursive apprehension and operative apprehension. It was also revealed that Geoboards enabled the selected teachers to structure and teach their lessons in a well-planned manner according to the Van Hiele phases, although it was difficult for them to adhere strictly to the hierarchy of the phases.
- Full Text:
- Date Issued: 2019
- Authors: Matengu, Given Kahale
- Date: 2019
- Subjects: Manipulatives (Education) , Information visualization , Visualization , Mathematics -- Study and teaching , Mathematics -- Study and teaching -- Activity programs , Geometry -- Study and teaching
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/96724 , vital:31312
- Description: The relationship between visualisation processes and using manipulatives in the teaching and learning of mathematics is apparent and yet not so vocal in the literature. This could be because of the common mistaken understanding that because manipulatives are visual in nature, then visualisation processes should be obvious. Literature warns that just because something is visual therefore it is transparent, is incorrect. This study argues that the effective use of manipulatives in the teaching of mathematics helps learners to effectively understand mathematical concepts. Research on the teaching and learning of mathematics suggests that physical manipulation experiences, especially of concrete materials concerning shapes, is an important process in learning at all ages. One such teaching tool, the Geoboard, a physical manipulative that employs visualisation processes when correctly used, is explored in this study. The aim of this interpretive case study was to investigate and analyse the use of Geoboards as a visualisation tool in the teaching of the properties of quadrilaterals. The study focused on visualisation processes and the use of Geoboards through a teaching framework that was informed by the Van Hiele phases of teaching geometry. The study was conducted in the Opuwo circuit of the Kunene region, Namibia, and it involved three selected Grade 7 mathematics teachers, each from a different primary school. It was underpinned by a constructivist theory using the Van Hiele phases of teaching geometry and framed within visualisation processes. The study employed the use of qualitative data collection techniques such as observations and interviews. The analysis of the findings of this study revealed that Geoboards were very useful in demonstrating the visual representations of the properties of quadrilaterals in a cheap and yet novel way in the selected teachers’ classes. Moreover, the use of Geoboards by the selected teachers effectively fostered visualisation processes such as concrete pictorial imagery, dynamic imagery, perceptual apprehension, sequential apprehension, discursive apprehension and operative apprehension. It was also revealed that Geoboards enabled the selected teachers to structure and teach their lessons in a well-planned manner according to the Van Hiele phases, although it was difficult for them to adhere strictly to the hierarchy of the phases.
- Full Text:
- Date Issued: 2019
An analysis of the roles and functions of teachers’ gestures as visualisation tools in the teaching of mathematics at the junior primary phase (Grades 0 –3)
- Authors: Namakalu, Dietlinde Nelao
- Date: 2019
- Subjects: Gesture , Gesture in mathematics education , Visual learning , Visualization , Education, Elementary -- Namibia
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/96713 , vital:31311
- Description: There is ample evidence in the literature that gestures are important hand and bodily actions that play vital roles during interactions between learners and teachers in the mathematics classroom. These gestures enable both the teacher and the learner to visualise mathematical concepts and ideas. The aim of this Namibian interpretive case study, located in enactivist theory, was to analyse the types of gestures that three selected teachers at the junior primary phase (Grades 0–3) used in their teaching of mathematics. The study also interrogated the roles that these gestures played in the teaching process of the three teachers. As I intended to analyse the types of gestures the selected teachers used and understand their views and perceptions of the roles and functions their gestures played as visualisation tools in the teaching of mathematics, I observed ten lessons of each teacher and video recorded them. I then interviewed them (one-on-one stimulus-recall interviews) and interpreted the gestures they used and utterances they made about using these gestures. The types of gestures that the participating teachers used are classified according to McNeill‘s (1992) framework, namely pointing (deictic) gestures, iconic (illustrators) gestures, metaphoric gestures, beat (motor) gestures and symbolic (emblems) gestures. The study found that the participating teachers incorporated a variety of gestures into their lessons and used them strategically. According to the teachers, gestures made the lessons interesting and encouraged active participation of the learners in the lessons. The teachers also revealed that gestures assist in explaining mathematical concepts and thus affected the learners‘ understanding positively. This study strongly suggests that the usefulness and efficacy of employing gestures as visualisation tools in mathematics education should be strategically harnessed.
- Full Text:
- Date Issued: 2019
- Authors: Namakalu, Dietlinde Nelao
- Date: 2019
- Subjects: Gesture , Gesture in mathematics education , Visual learning , Visualization , Education, Elementary -- Namibia
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/96713 , vital:31311
- Description: There is ample evidence in the literature that gestures are important hand and bodily actions that play vital roles during interactions between learners and teachers in the mathematics classroom. These gestures enable both the teacher and the learner to visualise mathematical concepts and ideas. The aim of this Namibian interpretive case study, located in enactivist theory, was to analyse the types of gestures that three selected teachers at the junior primary phase (Grades 0–3) used in their teaching of mathematics. The study also interrogated the roles that these gestures played in the teaching process of the three teachers. As I intended to analyse the types of gestures the selected teachers used and understand their views and perceptions of the roles and functions their gestures played as visualisation tools in the teaching of mathematics, I observed ten lessons of each teacher and video recorded them. I then interviewed them (one-on-one stimulus-recall interviews) and interpreted the gestures they used and utterances they made about using these gestures. The types of gestures that the participating teachers used are classified according to McNeill‘s (1992) framework, namely pointing (deictic) gestures, iconic (illustrators) gestures, metaphoric gestures, beat (motor) gestures and symbolic (emblems) gestures. The study found that the participating teachers incorporated a variety of gestures into their lessons and used them strategically. According to the teachers, gestures made the lessons interesting and encouraged active participation of the learners in the lessons. The teachers also revealed that gestures assist in explaining mathematical concepts and thus affected the learners‘ understanding positively. This study strongly suggests that the usefulness and efficacy of employing gestures as visualisation tools in mathematics education should be strategically harnessed.
- Full Text:
- Date Issued: 2019
Investigating how the use of visual models can enhance the teaching of common fractions for conceptual understanding to Grade 8 learners
- Authors: Katenda, Aune Kashikuka
- Date: 2019
- Subjects: Fractions -- Study and teaching (Secondary)-- Namibia , Mathematics -- Study and teaching (Secondary)-- Namibia , Information visualization , Visual learning -- Case studies
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/96746 , vital:31314
- Description: The intention of this study was to explore how selected mathematics teachers used visual models to improve the teaching of common fractions for conceptual understanding to Grade 8 learners as a result of an intervention programme. This research study is part of the VIPROmaths project which seeks to research the effective use of visualisation processes in the mathematics classroom in South Africa, Namibia, Zambia, Switzerland and Germany. This study which adopted a case study of teachers in Khomas Region, Namibia, is informed by constructivist learning theory. The study is situated within the interpretive paradigm and a multi-phase mixed method research approach was used. It focussed on analysing the use of visual models when teaching fractions namely: area model, number line model and a set model. The data were collected through survey questionnaires, observation and recall interview. The survey was conducted with the forty three mathematics teachers, from twenty secondary schools in Khomas region. The survey gave an overview of the nature and the use of visual models in schools. Three teachers purposively selected from the survey participated in the intervention program and were observed while teaching and interviewed after their teaching. Data were qualitatively and quantitatively analysed. The findings of this study reveal that visualising fractions is one of the methods that can improve both teaching and learning by providing concrete evidence of otherwise abstract ideas and concepts. The teachers highlighted that models themselves guide learners through to the answer, as compared to working out solutions using symbols only. They further indicated that visual models improve learners’ motivation, enhances understanding of fractions and encourages full participation of learners in the lesson. The study also found that use of visual models encouraged participation and it also boosted learners thinking capability. Teachers in this study preferred to use the area model as they found this model easier and more user-friendly in comparison with the number line and the set models. Teachers did not use the set model because of its complexity. This study concludes that the use of visual models can help enhance the conceptual teaching and understanding of common fractions. It is hoped that the study contributes towards improving the quality teaching and learning of fractions in Namibia. Furthermore, it informs the teacher-training institutions in Namibia to integrate the use of visualisation in their training programmes to promote conceptual understanding of mathematics.
- Full Text:
- Date Issued: 2019
- Authors: Katenda, Aune Kashikuka
- Date: 2019
- Subjects: Fractions -- Study and teaching (Secondary)-- Namibia , Mathematics -- Study and teaching (Secondary)-- Namibia , Information visualization , Visual learning -- Case studies
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/96746 , vital:31314
- Description: The intention of this study was to explore how selected mathematics teachers used visual models to improve the teaching of common fractions for conceptual understanding to Grade 8 learners as a result of an intervention programme. This research study is part of the VIPROmaths project which seeks to research the effective use of visualisation processes in the mathematics classroom in South Africa, Namibia, Zambia, Switzerland and Germany. This study which adopted a case study of teachers in Khomas Region, Namibia, is informed by constructivist learning theory. The study is situated within the interpretive paradigm and a multi-phase mixed method research approach was used. It focussed on analysing the use of visual models when teaching fractions namely: area model, number line model and a set model. The data were collected through survey questionnaires, observation and recall interview. The survey was conducted with the forty three mathematics teachers, from twenty secondary schools in Khomas region. The survey gave an overview of the nature and the use of visual models in schools. Three teachers purposively selected from the survey participated in the intervention program and were observed while teaching and interviewed after their teaching. Data were qualitatively and quantitatively analysed. The findings of this study reveal that visualising fractions is one of the methods that can improve both teaching and learning by providing concrete evidence of otherwise abstract ideas and concepts. The teachers highlighted that models themselves guide learners through to the answer, as compared to working out solutions using symbols only. They further indicated that visual models improve learners’ motivation, enhances understanding of fractions and encourages full participation of learners in the lesson. The study also found that use of visual models encouraged participation and it also boosted learners thinking capability. Teachers in this study preferred to use the area model as they found this model easier and more user-friendly in comparison with the number line and the set models. Teachers did not use the set model because of its complexity. This study concludes that the use of visual models can help enhance the conceptual teaching and understanding of common fractions. It is hoped that the study contributes towards improving the quality teaching and learning of fractions in Namibia. Furthermore, it informs the teacher-training institutions in Namibia to integrate the use of visualisation in their training programmes to promote conceptual understanding of mathematics.
- Full Text:
- Date Issued: 2019
An investigation into teaching mathematics using a visualisation approach to recontextualise indigenous knowledge
- Authors: Tshithigona, Gaus
- Date: 2018
- Subjects: Ethnoscience Namibia , Mathematics Study and teaching (Elementary) Namibia , Visual learning , Visualization , Interdisciplinary approach to knowledge , Teacher effectiveness Namibia , Traditional ecological knowledge Namibia
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/62461 , vital:28195
- Description: It can be argued that the Namibian curriculum is largely influenced by a Western epistemology. However, many studies suggest that learners make powerful meanings of mathematical concepts they are learning if they visualise these and experience them in relation to what they already know from their own cultural backgrounds. According to the Namibian National Curriculum for Basic Education (NNCBE, 2010), it is not only important for learners to acquire mathematical knowledge and skills, but also to develop and grow their identities, cultures and values as individuals. The aim of this study was to explore and investigate how selected mathematics teachers employ visualisation as a teaching approach to re-contextualise indigenous knowledge (IK). The study set out to explore how conceptual understanding is enhanced by participation in an intervention programme. The use of visualisation is considered an important mediating and pedagogical tool in the mathematics classroom to enhance the mathematics learning of learners. The research is informed by a socio-cultural theory of learning and is located within an interpretive paradigm. The study was conducted at four schools in the Oshana region of Namibia and involved four mathematics teachers who were purposefully selected due to their willingness to use visualisation-IK approaches in their teaching, based on their responses to the survey. The methodologies used are qualitative and quantitative case study. To gather data, document analysis, a survey, lesson observations and focus group interviews were used. The study found that most teachers in the Oshana region have an understanding of the effective use of visualisation-IK approaches. However, the study revealed that visualisation- IK approaches are mostly used in grades 4 to 7 mathematics classrooms. It also discovered that most of the visualisation approaches that teachers employed aligned well with the curriculum and promoted conceptual understanding in the teaching of mathematics. The results of the study showed that teachers have experience of the enabling and constraining factors in using a visualisation-IK approach to teaching mathematics.
- Full Text:
- Date Issued: 2018
- Authors: Tshithigona, Gaus
- Date: 2018
- Subjects: Ethnoscience Namibia , Mathematics Study and teaching (Elementary) Namibia , Visual learning , Visualization , Interdisciplinary approach to knowledge , Teacher effectiveness Namibia , Traditional ecological knowledge Namibia
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/62461 , vital:28195
- Description: It can be argued that the Namibian curriculum is largely influenced by a Western epistemology. However, many studies suggest that learners make powerful meanings of mathematical concepts they are learning if they visualise these and experience them in relation to what they already know from their own cultural backgrounds. According to the Namibian National Curriculum for Basic Education (NNCBE, 2010), it is not only important for learners to acquire mathematical knowledge and skills, but also to develop and grow their identities, cultures and values as individuals. The aim of this study was to explore and investigate how selected mathematics teachers employ visualisation as a teaching approach to re-contextualise indigenous knowledge (IK). The study set out to explore how conceptual understanding is enhanced by participation in an intervention programme. The use of visualisation is considered an important mediating and pedagogical tool in the mathematics classroom to enhance the mathematics learning of learners. The research is informed by a socio-cultural theory of learning and is located within an interpretive paradigm. The study was conducted at four schools in the Oshana region of Namibia and involved four mathematics teachers who were purposefully selected due to their willingness to use visualisation-IK approaches in their teaching, based on their responses to the survey. The methodologies used are qualitative and quantitative case study. To gather data, document analysis, a survey, lesson observations and focus group interviews were used. The study found that most teachers in the Oshana region have an understanding of the effective use of visualisation-IK approaches. However, the study revealed that visualisation- IK approaches are mostly used in grades 4 to 7 mathematics classrooms. It also discovered that most of the visualisation approaches that teachers employed aligned well with the curriculum and promoted conceptual understanding in the teaching of mathematics. The results of the study showed that teachers have experience of the enabling and constraining factors in using a visualisation-IK approach to teaching mathematics.
- Full Text:
- Date Issued: 2018
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