Exploring outdoor mathematics learning for conceptual understanding through smartphones
- Authors: Pop, Vuyani Samuel
- Date: 2024-04-05
- Subjects: Mathematics Study and teaching (Secondary) South Africa Lejweleputswa District Municipality , Educational technology , Mobile communication systems in education , Math walk , Concept learning
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/436477 , vital:73275
- Description: This study investigated how selected grade 11 mathematics learners used smartphones with the MathCityMap application to learn trigonometry outdoors for conceptual understanding. The aim of this research project was to explore outdoor mathematics learning for conceptual understanding using smartphones. This case study of grade 11 mathematics learners in Lejweleputswa District in the Free State Province, was informed by the Realistic Mathematics Education theory. The study is grounded within an interpretive paradigm and used the explanatory sequential mixed-method design. Forty-two grade 11 mathematics learners participated in the survey and from these 12 were purposively selected to participate in walking the mathematics trails and interviews. The findings revealed that, while the grade 11 mathematics learners acknowledged the significance and value of using smartphones for learning mathematics, they were prohibited from carrying or using smartphones on the school premises, as part of the school code of conduct. The preferred use of smartphones for learning mathematics was understandable, as the survey was conducted at a time when the COVID-19 pandemic and associated restrictions were still in place. The survey unearthed that among applications for learning mathematics, the MathCityMap application was not known by the learners who participated in the survey. Mathematics trails observations indicated that outdoor tasks were a source of mathematical concepts or formal mathematical knowledge, and enabled learners to reinvent mathematical ideas and concepts with adult guidance. Learners were able to make use of appropriate mathematical models and connections. The mathematics trails ignited robust discussions among learners, and prompted learners to draw from prior knowledge, and recognise and identify suitable mathematical models and shapes from the real-world objects. Learners were able to use multiple representations, make necessary mathematical links, and use their prior knowledge to enhance their trigonometry conceptual understanding. This study concluded that using smartphones with the MathCityMap application could enhance conceptual understanding of trigonometry. The implications for teachers are that learners should be exposed to outdoor mathematics learning using smartphones with the MathCityMap application to improve their conceptual understanding. It is hoped that the results of this study can be used by various stakeholders, who include, inter alia, mathematics subject advisors and teacher training institutions, to enhance learners’ conceptual understanding of mathematics. , Thesis (MEd) -- Faculty of Education, Secondary and Post School Education, 2024
- Full Text:
- Date Issued: 2024-04-05
- Authors: Pop, Vuyani Samuel
- Date: 2024-04-05
- Subjects: Mathematics Study and teaching (Secondary) South Africa Lejweleputswa District Municipality , Educational technology , Mobile communication systems in education , Math walk , Concept learning
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/436477 , vital:73275
- Description: This study investigated how selected grade 11 mathematics learners used smartphones with the MathCityMap application to learn trigonometry outdoors for conceptual understanding. The aim of this research project was to explore outdoor mathematics learning for conceptual understanding using smartphones. This case study of grade 11 mathematics learners in Lejweleputswa District in the Free State Province, was informed by the Realistic Mathematics Education theory. The study is grounded within an interpretive paradigm and used the explanatory sequential mixed-method design. Forty-two grade 11 mathematics learners participated in the survey and from these 12 were purposively selected to participate in walking the mathematics trails and interviews. The findings revealed that, while the grade 11 mathematics learners acknowledged the significance and value of using smartphones for learning mathematics, they were prohibited from carrying or using smartphones on the school premises, as part of the school code of conduct. The preferred use of smartphones for learning mathematics was understandable, as the survey was conducted at a time when the COVID-19 pandemic and associated restrictions were still in place. The survey unearthed that among applications for learning mathematics, the MathCityMap application was not known by the learners who participated in the survey. Mathematics trails observations indicated that outdoor tasks were a source of mathematical concepts or formal mathematical knowledge, and enabled learners to reinvent mathematical ideas and concepts with adult guidance. Learners were able to make use of appropriate mathematical models and connections. The mathematics trails ignited robust discussions among learners, and prompted learners to draw from prior knowledge, and recognise and identify suitable mathematical models and shapes from the real-world objects. Learners were able to use multiple representations, make necessary mathematical links, and use their prior knowledge to enhance their trigonometry conceptual understanding. This study concluded that using smartphones with the MathCityMap application could enhance conceptual understanding of trigonometry. The implications for teachers are that learners should be exposed to outdoor mathematics learning using smartphones with the MathCityMap application to improve their conceptual understanding. It is hoped that the results of this study can be used by various stakeholders, who include, inter alia, mathematics subject advisors and teacher training institutions, to enhance learners’ conceptual understanding of mathematics. , Thesis (MEd) -- Faculty of Education, Secondary and Post School Education, 2024
- Full Text:
- Date Issued: 2024-04-05
Exploring senior phase teachers’ use of Kahoot! Gamification as a formative assessment tool to scaffold mathematical understanding
- Authors: Balele, Silence
- Date: 2024-04
- Subjects: Kahoot! Algebra by DragonBox , Mathematics Computer-assisted instruction , Pedagogical content knowledge , Mathematics Study and teaching (Secondary) South Africa , Gamification , Educational technology , Mathematics teachers Training of South Africa
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/423891 , vital:72102
- Description: In South Africa, digital technology, particularly gamification, continues to become an important teaching and learning tool. Its importance lies in scaffolding mathematical understanding, improving the quality of assessment, and developing twenty-first-century technological skills for effective mathematics assessment. To explore this importance, senior phase mathematics teachers are encouraged to adopt gamification technology such as Kahoot! in assessment. The study adopted a case study research design with a interpretivist research paradigm, as this method allows detailed exploration and understanding of a specific context through a close connection with the participants. Data was collected using semi-structured questionnaires, focus group interviews, non-participant observations, and reflective journals. The research involved ten purposively selected senior-phase mathematics teachers from two schools in the Sarah Baartman District, Eastern Cape Province, South Africa. The study drew upon Vygoysky's Sociocultural Theory for its theoretical framework, while the Technological, Pedagogical, and Content Knowledge was used for analysis. The data analysis pursued an inductive approach. Adopting a thematic analysis included coding participant responses, organizing codes into concepts and categories, and developing a theoretical framework from the resultant categories. A four-phase process was involved: coding, conceptualizing, categorizing, and theorizing, was employed. This process and using NVivo software for data organization and management helped identify patterns, themes, and significant concerns surrounding the study's core subject. The findings from the study were as follows: Firstly, it was revealed that most teachers have a positive perception and attitude towards using Kahoot! for formative assessment, believing that it enhances teaching and learning quality. However, they showed scepticism due to insufficient Information and Communication Technologies knowledge and training. Second, teachers' pedagogical and technological experiences were predominantly enjoyable. Kahoot! was accepted as beneficial for promoting collaboration, interaction, and immediate feedback. Third, the study identified enabling and constraining factors in using Kahoot! for formative assessment. The enabling factors include Kahoot!, which was convenient and accessible, promoted immediate feedback and fostered collaboration and interaction. The constraining factors include Information and Communication Technologies and network interference, which posed limitations. The research concluded that Kahoot! as a platform for formative assessment indeed scaffold mathematical understanding. The study recommends increasing teachers' access to educational technology, incorporating continuous professional development programs, providing subject-specific training, and encouraging teachers to adapt to emerging technologies. The study also provided recommendations for future research to explore learner perceptions, employ a mixed methods approach to help quantify learner performance and investigate the pedagogical and technological experiences of senior phase mathematics teachers regarding formative assessment. , Thesis (MEd) -- Faculty of Education, Secondary and Post-School Education, 2024
- Full Text:
- Date Issued: 2024-04
- Authors: Balele, Silence
- Date: 2024-04
- Subjects: Kahoot! Algebra by DragonBox , Mathematics Computer-assisted instruction , Pedagogical content knowledge , Mathematics Study and teaching (Secondary) South Africa , Gamification , Educational technology , Mathematics teachers Training of South Africa
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/423891 , vital:72102
- Description: In South Africa, digital technology, particularly gamification, continues to become an important teaching and learning tool. Its importance lies in scaffolding mathematical understanding, improving the quality of assessment, and developing twenty-first-century technological skills for effective mathematics assessment. To explore this importance, senior phase mathematics teachers are encouraged to adopt gamification technology such as Kahoot! in assessment. The study adopted a case study research design with a interpretivist research paradigm, as this method allows detailed exploration and understanding of a specific context through a close connection with the participants. Data was collected using semi-structured questionnaires, focus group interviews, non-participant observations, and reflective journals. The research involved ten purposively selected senior-phase mathematics teachers from two schools in the Sarah Baartman District, Eastern Cape Province, South Africa. The study drew upon Vygoysky's Sociocultural Theory for its theoretical framework, while the Technological, Pedagogical, and Content Knowledge was used for analysis. The data analysis pursued an inductive approach. Adopting a thematic analysis included coding participant responses, organizing codes into concepts and categories, and developing a theoretical framework from the resultant categories. A four-phase process was involved: coding, conceptualizing, categorizing, and theorizing, was employed. This process and using NVivo software for data organization and management helped identify patterns, themes, and significant concerns surrounding the study's core subject. The findings from the study were as follows: Firstly, it was revealed that most teachers have a positive perception and attitude towards using Kahoot! for formative assessment, believing that it enhances teaching and learning quality. However, they showed scepticism due to insufficient Information and Communication Technologies knowledge and training. Second, teachers' pedagogical and technological experiences were predominantly enjoyable. Kahoot! was accepted as beneficial for promoting collaboration, interaction, and immediate feedback. Third, the study identified enabling and constraining factors in using Kahoot! for formative assessment. The enabling factors include Kahoot!, which was convenient and accessible, promoted immediate feedback and fostered collaboration and interaction. The constraining factors include Information and Communication Technologies and network interference, which posed limitations. The research concluded that Kahoot! as a platform for formative assessment indeed scaffold mathematical understanding. The study recommends increasing teachers' access to educational technology, incorporating continuous professional development programs, providing subject-specific training, and encouraging teachers to adapt to emerging technologies. The study also provided recommendations for future research to explore learner perceptions, employ a mixed methods approach to help quantify learner performance and investigate the pedagogical and technological experiences of senior phase mathematics teachers regarding formative assessment. , Thesis (MEd) -- Faculty of Education, Secondary and Post-School Education, 2024
- Full Text:
- Date Issued: 2024-04
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
Visualisation processes in teaching patterns and their generalisation: perceptions and experiences from senior phase mathematics teachers
- Authors: Chatima, Simon
- Date: 2022-04-08
- Subjects: Visual learning South Africa Eastern Cape , Mathematics Study and teaching (Secondary) South Africa Eastern Cape , Mathematics teachers South Africa Eastern Cape Attitudes , Sequences (Mathematics) Study and teaching (Secondary) South Africa Eastern Cape , Constructivism (Education) South Africa Eastern Cape , Mathematics teachers In-service training South Africa Eastern Cape , VIPRO MATHS Project
- Language: English
- Type: Master's thesis , text
- Identifier: http://hdl.handle.net/10962/232936 , vital:50039
- Description: This study investigated how senior phase mathematics teachers used visualisation approaches to teach patterns and their generalisation as a result of an intervention programme. This project is an integral component of the VIPRO MATHS Project and one of a number of post-graduate research projects which has a particular focus on visualisation processes in mathematics education in the Southern African region. This case study of Senior Phase mathematics teachers in the Chris Hani West District (CHW) in the Eastern Cape Province of South Africa used a social constructivist theory. The study is grounded within an interpretive paradigm explanatory qualitative method design. It surveyed thirty-seven Senior Phase mathematics teachers from schools in the CHW district to get an idea of how teachers teach patterns and their generalisation, prior to an intervention process. After the survey, nine teachers were purposively selected to take part in an intervention programme. They were then observed (teaching) and interviewed to get their perceptions about what factors enable and/or constrain the teaching of patterns and their generalisation when visualisation approaches were used. The data from the survey questionnaire responses, the lesson observations and the interviews were analysed qualitatively. The findings from the survey questionnaire responses revealed that teachers in CHW district value the use of visualisation approaches, although they used visuals to teach patterns in a way that lacked depth, skill and rigor prior to the intervention. Challenges such as difficulty in keeping abreast with the prescribed syllabus, the lack of resources, time constraints, and the limited knowledge of algebra learners have for successfully transferring pictorial representations to symbolic presentations, emerged from the survey data. This necessitated the need for an intervention which focused on the use of a variety of visual strategies and tools to teach patterns and their generalisation effectively. Data from lesson observations showed that all observed participant teachers used visuals to generate image- related questions and created platforms for lively classroom discussions. The teachers used the generated questions to build on learners’ prior knowledge and to promote learner understanding of pattern dynamics that stem from pictorial representations. The data from the interviews revealed that teachers’ perceptions had drastically changed after the intervention. This was because they were now equipped and empowered to effectively make use of visual strategies that enabled them to: build on learners’ prior knowledge, to manipulate visuals for the purpose of prompting learning, develop cognitive perception in learners, cultivate learner innovation and originality and enhance problem solving techniques. This study concludes that the use of visuals enhanced conceptual teaching of patterns and their generalisation in the observed participants. This has the potential to provide mathematics education researchers and curriculum developers with a strong basis to include visualisation processes and strategies into the design of policy documents and to initiate further research efforts. The implications for the teachers are that learners need to be taught ways to create and interpret visual representations in order to understand the dynamics of transferring a pictorial pattern to its resultant symbolic representation expressing pattern regularity. It is also hoped that the results of this study will be utilised by mathematics subject advisers and teacher training institutions to improve the teaching of patterns and their generalisation. , Thesis (MEd) -- Faculty of Education, Education, 2022
- Full Text:
- Date Issued: 2022-04-08
- Authors: Chatima, Simon
- Date: 2022-04-08
- Subjects: Visual learning South Africa Eastern Cape , Mathematics Study and teaching (Secondary) South Africa Eastern Cape , Mathematics teachers South Africa Eastern Cape Attitudes , Sequences (Mathematics) Study and teaching (Secondary) South Africa Eastern Cape , Constructivism (Education) South Africa Eastern Cape , Mathematics teachers In-service training South Africa Eastern Cape , VIPRO MATHS Project
- Language: English
- Type: Master's thesis , text
- Identifier: http://hdl.handle.net/10962/232936 , vital:50039
- Description: This study investigated how senior phase mathematics teachers used visualisation approaches to teach patterns and their generalisation as a result of an intervention programme. This project is an integral component of the VIPRO MATHS Project and one of a number of post-graduate research projects which has a particular focus on visualisation processes in mathematics education in the Southern African region. This case study of Senior Phase mathematics teachers in the Chris Hani West District (CHW) in the Eastern Cape Province of South Africa used a social constructivist theory. The study is grounded within an interpretive paradigm explanatory qualitative method design. It surveyed thirty-seven Senior Phase mathematics teachers from schools in the CHW district to get an idea of how teachers teach patterns and their generalisation, prior to an intervention process. After the survey, nine teachers were purposively selected to take part in an intervention programme. They were then observed (teaching) and interviewed to get their perceptions about what factors enable and/or constrain the teaching of patterns and their generalisation when visualisation approaches were used. The data from the survey questionnaire responses, the lesson observations and the interviews were analysed qualitatively. The findings from the survey questionnaire responses revealed that teachers in CHW district value the use of visualisation approaches, although they used visuals to teach patterns in a way that lacked depth, skill and rigor prior to the intervention. Challenges such as difficulty in keeping abreast with the prescribed syllabus, the lack of resources, time constraints, and the limited knowledge of algebra learners have for successfully transferring pictorial representations to symbolic presentations, emerged from the survey data. This necessitated the need for an intervention which focused on the use of a variety of visual strategies and tools to teach patterns and their generalisation effectively. Data from lesson observations showed that all observed participant teachers used visuals to generate image- related questions and created platforms for lively classroom discussions. The teachers used the generated questions to build on learners’ prior knowledge and to promote learner understanding of pattern dynamics that stem from pictorial representations. The data from the interviews revealed that teachers’ perceptions had drastically changed after the intervention. This was because they were now equipped and empowered to effectively make use of visual strategies that enabled them to: build on learners’ prior knowledge, to manipulate visuals for the purpose of prompting learning, develop cognitive perception in learners, cultivate learner innovation and originality and enhance problem solving techniques. This study concludes that the use of visuals enhanced conceptual teaching of patterns and their generalisation in the observed participants. This has the potential to provide mathematics education researchers and curriculum developers with a strong basis to include visualisation processes and strategies into the design of policy documents and to initiate further research efforts. The implications for the teachers are that learners need to be taught ways to create and interpret visual representations in order to understand the dynamics of transferring a pictorial pattern to its resultant symbolic representation expressing pattern regularity. It is also hoped that the results of this study will be utilised by mathematics subject advisers and teacher training institutions to improve the teaching of patterns and their generalisation. , Thesis (MEd) -- Faculty of Education, Education, 2022
- Full Text:
- Date Issued: 2022-04-08
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
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