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:
- 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:
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:
- 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.
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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:
- 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.
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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:
- 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.
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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:
- 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.
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An analysis of how geogebra can be used as a visualisation tool by selected teachers to develop conceptual understanding of the properties of geometric shapes in grade 9 learners: a case study in Namibia
- Authors: Mwiikeni, Eramus
- Date: 2017
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/6989 , vital:21207
- Description: According to Rosken & Rolka (2006), learning mathematics through visualisations can be a powerful tool to explore mathematical problems and give meaning to mathematical concepts and relationships between them. “Visualisation can reduce the complexity of mathematical problems when dealing with a multitude of information” (p.458). This case study focused on using GeoGebra as a visualisation tool to teach angle properties in Grade 9 geometry. This study set out to analyse how GeoGebra visualisations can be used by selected teachers to teach for conceptual understanding. The research is based on a constructivist view of learning and is oriented within an interpretive paradigm. The methodology used is a qualitative case study. The study was conducted in one school and involved 3 mathematics teachers who were purposefully selected because they showed willingness to use technology in their teaching. I used classroom observations and interviews to collect the data. The study identified a number of factors from the participants that related to using GeoGebra in teaching for conceptual understanding. These include the effective use of dynamic visuals to build on prior knowledge, using multiple representations through image generation and image transformation to make connections and using visuals to justify mathematics ideas. The results from this study indicated that GeoGebra can indeed be used effectively as a teaching tool to teach for conceptual understanding in mathematics.
- Full Text:
- Authors: Mwiikeni, Eramus
- Date: 2017
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/6989 , vital:21207
- Description: According to Rosken & Rolka (2006), learning mathematics through visualisations can be a powerful tool to explore mathematical problems and give meaning to mathematical concepts and relationships between them. “Visualisation can reduce the complexity of mathematical problems when dealing with a multitude of information” (p.458). This case study focused on using GeoGebra as a visualisation tool to teach angle properties in Grade 9 geometry. This study set out to analyse how GeoGebra visualisations can be used by selected teachers to teach for conceptual understanding. The research is based on a constructivist view of learning and is oriented within an interpretive paradigm. The methodology used is a qualitative case study. The study was conducted in one school and involved 3 mathematics teachers who were purposefully selected because they showed willingness to use technology in their teaching. I used classroom observations and interviews to collect the data. The study identified a number of factors from the participants that related to using GeoGebra in teaching for conceptual understanding. These include the effective use of dynamic visuals to build on prior knowledge, using multiple representations through image generation and image transformation to make connections and using visuals to justify mathematics ideas. The results from this study indicated that GeoGebra can indeed be used effectively as a teaching tool to teach for conceptual understanding in mathematics.
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An analysis of selected grade 11 learners’ interactions with geometry tasks using visualization processes: a case study in Namibia
- Authors: Kabuku, Brian S
- Date: 2017
- Subjects: Mathematics -- Study and teaching -- Activity programs , Geometry -- Study and teaching (Secondary) -- Namibia , Geometry -- Study and teaching (Secondary) -- Namibia -- Cast studies , Visualization
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/5949 , vital:20997
- Description: This case study was conducted at a secondary school where I teach, situated in the semi-rural setting of Bukalo village in Namibia, and sought to gain insights into the nature and role of visualisation processes employed when selected grade 11 learners interacted with selected geometry problems. According to Mariotti and Pensci (1994), visualisation takes place when "thinking is spontaneously accompanied and supported by images”, and helps students to understand the problem at hand. Visualisation is regarded as "making the unseen visible and imagery as the power to imagine the possible and the impossible” (Mason 1992). The study is located within an interpretive research paradigm in order to obtain in-depth understanding of the participants’ visualisation processes. Within this paradigm, both quantitative and qualitative approaches were adopted. The eight Grade 11 participants engaged with 12 items of the Geometry Visualisation Tasks (GVT) worksheets. Data was collected using video-recorded learners’ interactions with the GVT, observations, stimulated recall interviews and post-GVT interviews with the learners. During the data analysis stage, I used inductive analysis to determine patterns evident in learners ‘thinking processes’. My analytical framework consisted of indicators that were used to identify and classify visualisation processes for each task of the GVT for each participant. I adapted this framework from Ho (2010) and Ho, Ramful and Lowrie’s (2015) clarification of the representations. The findings from this study revealed that the use of visualisations facilitated meaningful learning when learners made use of these to develop and scaffold their conceptual understanding. The findings revealed that most learners used visualisation processes fairly to very accurately when solving geometry problems. They used visualisation processes by using sketches and diagrams that transformed a mathematical problem pictorially, connected their thinking to previous knowledge and experience, clarified the algebraic task and assisted them to understand the spatial relationships within each task.
- Full Text:
- Authors: Kabuku, Brian S
- Date: 2017
- Subjects: Mathematics -- Study and teaching -- Activity programs , Geometry -- Study and teaching (Secondary) -- Namibia , Geometry -- Study and teaching (Secondary) -- Namibia -- Cast studies , Visualization
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/5949 , vital:20997
- Description: This case study was conducted at a secondary school where I teach, situated in the semi-rural setting of Bukalo village in Namibia, and sought to gain insights into the nature and role of visualisation processes employed when selected grade 11 learners interacted with selected geometry problems. According to Mariotti and Pensci (1994), visualisation takes place when "thinking is spontaneously accompanied and supported by images”, and helps students to understand the problem at hand. Visualisation is regarded as "making the unseen visible and imagery as the power to imagine the possible and the impossible” (Mason 1992). The study is located within an interpretive research paradigm in order to obtain in-depth understanding of the participants’ visualisation processes. Within this paradigm, both quantitative and qualitative approaches were adopted. The eight Grade 11 participants engaged with 12 items of the Geometry Visualisation Tasks (GVT) worksheets. Data was collected using video-recorded learners’ interactions with the GVT, observations, stimulated recall interviews and post-GVT interviews with the learners. During the data analysis stage, I used inductive analysis to determine patterns evident in learners ‘thinking processes’. My analytical framework consisted of indicators that were used to identify and classify visualisation processes for each task of the GVT for each participant. I adapted this framework from Ho (2010) and Ho, Ramful and Lowrie’s (2015) clarification of the representations. The findings from this study revealed that the use of visualisations facilitated meaningful learning when learners made use of these to develop and scaffold their conceptual understanding. The findings revealed that most learners used visualisation processes fairly to very accurately when solving geometry problems. They used visualisation processes by using sketches and diagrams that transformed a mathematical problem pictorially, connected their thinking to previous knowledge and experience, clarified the algebraic task and assisted them to understand the spatial relationships within each task.
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Observing and evaluating creative mathematical reasoning through selected VITALmaths video clips and collaborative argumentation
- Authors: Kellen, Matthew Earl
- Date: 2017
- Subjects: Mathematics Study and teaching (Secondary) South Africa Grahamstown , Mathematics Study and teaching (Secondary) Audio-visual aids , Reasoning , Mathematical ability
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/6107 , vital:21032
- Description: Creative mathematical reasoning is a definition that the NCS policies allude to when they indicate the necessity for students to, “identify and solve problems and make decisions using critical and creative thinking.”(NCS, 2011: 9). Silver (1997) and Lithner (2008) focus on creativity of reasoning in terms of the flexibility, fluency and novelty in which one approaches a mathematical problem. Learners who can creatively select appropriate strategies that are mathematically founded, and justify their answers use creative mathematical reasoning. This research uses Visual Technology for the Autonomous Learning of Mathematics (VITALmaths) video clips that pose mathematics problems to stimulate articulated reasoning among small multi-age, multi-ability Grade 9 peer groups. Using VITALmaths clips that pose visual and open-ended task, set the stage for collaborative argumentation between peers. This study observes creative mathematical reasoning in two ways: Firstly by observing the interaction between peers in the process of arriving at an answer, and secondly by examining the end product of the peer group’s justification of their solution. (Ball & Bass, 2003) Six grade 8 and 9 learners from no-fee public schools in the township of Grahamstown, South Africa were selected for this case study. Participants were a mixed ability, mixed gendered, sample group from an after-school programme which focused on creating a space for autonomous learning. The six participants were split into two groups and audio and video recorded as they solved selected VITALmaths tasks and presented their evidence and solutions to the tasks. Audio and video recordings and written work were used to translate, transcribe, and code participant interactions according to a framework adapted from Krummheuer (2007) and Lithner (2008) and Silver (1997) and Toulmin (1954). This constituted the analysis of the process of creative mathematical reasoning. Group presentations of evidence and solutions to the VITALmaths tasks, were used in conjunction with an evaluation framework adapted from Lithner (2008) and Campos (2010). This was the product analysis of creative mathematical reasoning. This research found that there was significant evidence of creative mathematical reasoning in the process and product evaluation of group interactions and solutions. Process analysis showed that participants were very active, engaged, and creative in their participation, but struggled to integrate and implement ideas cohesively. Product analysis similarly showed that depth and concentration of strategies implemented are key to correct and exhaustive mathematically grounded solutions.
- Full Text:
- Authors: Kellen, Matthew Earl
- Date: 2017
- Subjects: Mathematics Study and teaching (Secondary) South Africa Grahamstown , Mathematics Study and teaching (Secondary) Audio-visual aids , Reasoning , Mathematical ability
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/6107 , vital:21032
- Description: Creative mathematical reasoning is a definition that the NCS policies allude to when they indicate the necessity for students to, “identify and solve problems and make decisions using critical and creative thinking.”(NCS, 2011: 9). Silver (1997) and Lithner (2008) focus on creativity of reasoning in terms of the flexibility, fluency and novelty in which one approaches a mathematical problem. Learners who can creatively select appropriate strategies that are mathematically founded, and justify their answers use creative mathematical reasoning. This research uses Visual Technology for the Autonomous Learning of Mathematics (VITALmaths) video clips that pose mathematics problems to stimulate articulated reasoning among small multi-age, multi-ability Grade 9 peer groups. Using VITALmaths clips that pose visual and open-ended task, set the stage for collaborative argumentation between peers. This study observes creative mathematical reasoning in two ways: Firstly by observing the interaction between peers in the process of arriving at an answer, and secondly by examining the end product of the peer group’s justification of their solution. (Ball & Bass, 2003) Six grade 8 and 9 learners from no-fee public schools in the township of Grahamstown, South Africa were selected for this case study. Participants were a mixed ability, mixed gendered, sample group from an after-school programme which focused on creating a space for autonomous learning. The six participants were split into two groups and audio and video recorded as they solved selected VITALmaths tasks and presented their evidence and solutions to the tasks. Audio and video recordings and written work were used to translate, transcribe, and code participant interactions according to a framework adapted from Krummheuer (2007) and Lithner (2008) and Silver (1997) and Toulmin (1954). This constituted the analysis of the process of creative mathematical reasoning. Group presentations of evidence and solutions to the VITALmaths tasks, were used in conjunction with an evaluation framework adapted from Lithner (2008) and Campos (2010). This was the product analysis of creative mathematical reasoning. This research found that there was significant evidence of creative mathematical reasoning in the process and product evaluation of group interactions and solutions. Process analysis showed that participants were very active, engaged, and creative in their participation, but struggled to integrate and implement ideas cohesively. Product analysis similarly showed that depth and concentration of strategies implemented are key to correct and exhaustive mathematically grounded solutions.
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An investigation into how cell phones can be used in the teaching of mathematics using VITALmaths video clips: a case study of 2 schools in Grahamstown, South Africa
- Authors: Ndafenongo, Gerhard
- Date: 2012
- Subjects: Mathematics -- Study and teaching (Secondary) -- South Africa -- Grahamstown Educational innovations -- South Africa -- Grahamstown Telecommunication in education -- South Africa -- Grahamstown Teaching -- Aids and devices -- South Africa -- Grahamstown Mathematics Software -- South Africa -- Grahamstown Mobile communication systems in education -- South Africa -- Grahamstown
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1596 , http://hdl.handle.net/10962/d1003478
- Description: Cell phones have become a ubiquitous part of daily life for both teachers and learners alike. The educational potential afforded by cell phones is diverse. The challenge for teachers is to capitalise on this ubiquity and make use of cell phones for educational purposes. This study investigates how cell phones can be used in the teaching of Mathematics using VITALmaths video clips. Five VITALmaths video clips were uploaded onto cell phones which were used in the classroom to explore the Theorem of Pythagoras in a visually appealing way that supported a conceptual understanding of the basis of the theorem. The study was conducted in two high schools in Grahamstown, South Africa. It involved two teachers from each school and a total number of 47 Grade 10 Mathematics students. The participating teachers were chosen from a group of Mathematics teachers taking part in the Mathematics Teacher Enrichment Programme (MTEP) of the FirstRand Foundation Mathematics Education Chair hosted by Rhodes University. This study is framed as a case study and is grounded within the interpretive paradigm. The study captures teachers’ and learners’ experiences in using cell phones as instructional aids within the pedagogical context of the classroom. This research suggests that cell phones can be a useful resource to support teaching and learning in the classroom, particularly in under-resourced schools. The use of VITALmaths video clips as mathematical content, and cell phones as a vehicle of delivery, enhanced active participation and concentration, sped up lessons, encouraged collaboration as well as interaction and hands-on exploration, and promoted both student autonomy as well as teacher enrichment.
- Full Text:
- Authors: Ndafenongo, Gerhard
- Date: 2012
- Subjects: Mathematics -- Study and teaching (Secondary) -- South Africa -- Grahamstown Educational innovations -- South Africa -- Grahamstown Telecommunication in education -- South Africa -- Grahamstown Teaching -- Aids and devices -- South Africa -- Grahamstown Mathematics Software -- South Africa -- Grahamstown Mobile communication systems in education -- South Africa -- Grahamstown
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1596 , http://hdl.handle.net/10962/d1003478
- Description: Cell phones have become a ubiquitous part of daily life for both teachers and learners alike. The educational potential afforded by cell phones is diverse. The challenge for teachers is to capitalise on this ubiquity and make use of cell phones for educational purposes. This study investigates how cell phones can be used in the teaching of Mathematics using VITALmaths video clips. Five VITALmaths video clips were uploaded onto cell phones which were used in the classroom to explore the Theorem of Pythagoras in a visually appealing way that supported a conceptual understanding of the basis of the theorem. The study was conducted in two high schools in Grahamstown, South Africa. It involved two teachers from each school and a total number of 47 Grade 10 Mathematics students. The participating teachers were chosen from a group of Mathematics teachers taking part in the Mathematics Teacher Enrichment Programme (MTEP) of the FirstRand Foundation Mathematics Education Chair hosted by Rhodes University. This study is framed as a case study and is grounded within the interpretive paradigm. The study captures teachers’ and learners’ experiences in using cell phones as instructional aids within the pedagogical context of the classroom. This research suggests that cell phones can be a useful resource to support teaching and learning in the classroom, particularly in under-resourced schools. The use of VITALmaths video clips as mathematical content, and cell phones as a vehicle of delivery, enhanced active participation and concentration, sped up lessons, encouraged collaboration as well as interaction and hands-on exploration, and promoted both student autonomy as well as teacher enrichment.
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An investigation into the use of traditional Xhosa dance to teach mathematics: a case study in a Grade 7 class
- Authors: Mbusi, Nokwanda Princess
- Date: 2012
- Subjects: Mathematics -- Study and teaching (Primary) Teaching -- Aids and devices -- Research Xhosa (African people) -- Music Education, Primary -- South Africa -- Eastern Cape , Music in mathematics education
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1617 , http://hdl.handle.net/10962/d1003499
- Description: This study seeks to explore mathematical concepts embedded in traditional Xhosa dance and how these concepts can be incorporated into a learning programme for the teaching and learning of mathematics. The study seeks to gain insight into whether learners could benefit from the implementation of such a learning programme. Learners from a Grade 7 class in a rural school performed traditional Xhosa dances and their performances were captured through video recording. The video recordings were then observed and analysed to determine the mathematical concepts embedded in the dances. These concepts were then linked to those found in the Grade 7 mathematics curriculum. A learning programme integrating mathematical concepts from the dance activities with mathematical concepts from the Grade 7 curriculum was then designed. The learning programme contained mathematical problem solving activities that required learners to re-enact the dance performances in order to find the required solutions. The learning programme was then implemented with the learners over a period of three weeks. During the implementation, learners’ behaviour towards the learning experience was observed, their engagement with the problem solving activities as well as their strategies for solving the problems, were carefully observed. Also, their interactions with each other were noted. After the implementation of the learning programme, focus group interviews were held with learners to determine their opinions, attitudes and feelings about their experience of learning mathematics through traditional Xhosa dance. Key findings indicated that traditional Xhosa dance can be used as a medium for learning many concepts in the mathematics curriculum; the use of the dance gave learners an opportunity to learn mathematics from a familiar context and to participate actively and collaboratively in their learning. Also, it emerged that the use of dance to teach mathematics had potential to help improve learners’ attitudes towards mathematics. Conclusions were reached that the dance had potential for use as a means for the meaningful learning of mathematics. However, limitations and challenges with the study were identified, such as its limited replicability in other mathematics classrooms.
- Full Text:
- Authors: Mbusi, Nokwanda Princess
- Date: 2012
- Subjects: Mathematics -- Study and teaching (Primary) Teaching -- Aids and devices -- Research Xhosa (African people) -- Music Education, Primary -- South Africa -- Eastern Cape , Music in mathematics education
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1617 , http://hdl.handle.net/10962/d1003499
- Description: This study seeks to explore mathematical concepts embedded in traditional Xhosa dance and how these concepts can be incorporated into a learning programme for the teaching and learning of mathematics. The study seeks to gain insight into whether learners could benefit from the implementation of such a learning programme. Learners from a Grade 7 class in a rural school performed traditional Xhosa dances and their performances were captured through video recording. The video recordings were then observed and analysed to determine the mathematical concepts embedded in the dances. These concepts were then linked to those found in the Grade 7 mathematics curriculum. A learning programme integrating mathematical concepts from the dance activities with mathematical concepts from the Grade 7 curriculum was then designed. The learning programme contained mathematical problem solving activities that required learners to re-enact the dance performances in order to find the required solutions. The learning programme was then implemented with the learners over a period of three weeks. During the implementation, learners’ behaviour towards the learning experience was observed, their engagement with the problem solving activities as well as their strategies for solving the problems, were carefully observed. Also, their interactions with each other were noted. After the implementation of the learning programme, focus group interviews were held with learners to determine their opinions, attitudes and feelings about their experience of learning mathematics through traditional Xhosa dance. Key findings indicated that traditional Xhosa dance can be used as a medium for learning many concepts in the mathematics curriculum; the use of the dance gave learners an opportunity to learn mathematics from a familiar context and to participate actively and collaboratively in their learning. Also, it emerged that the use of dance to teach mathematics had potential to help improve learners’ attitudes towards mathematics. Conclusions were reached that the dance had potential for use as a means for the meaningful learning of mathematics. However, limitations and challenges with the study were identified, such as its limited replicability in other mathematics classrooms.
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An investigation into the use of Visual Technology for the Autonomous Learning of mathematics (VITALmaths) video clips through the medium of cell phones in the teaching of mathematics in selected South African Grade 9 classes: a case study
- Authors: Hyde, Janet Catherine
- Date: 2012
- Subjects: Mathematics -- Study and teaching (Secondary) -- South Africa Educational innovations -- South Africa Telecommunication in education -- South Africa Teaching -- South Africa -- Aids and devices
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1618 , http://hdl.handle.net/10962/d1003500
- Description: This qualitative study examines the use of Visual Technology for the Autonomous Learning of mathematics (VITALmaths) video clips in three Grade 9 classrooms in the Eastern Cape, South Africa, two of which are in well-resourced ex-Model C schools and one in a semi-rural township school. The rapid development of mobile technology, especially in Africa, has opened up previously unexplored avenues in economy, communication and education (Aker & Mbiti, 2010), with a number of mobile learning initiatives being launched in South Africa (Botha & Ford, 2007; Vosloo & Botha, 2009). The VITALmaths project was developed collaboratively between the University of Applied Sciences Northwestern Switzerland and Rhodes University in South Africa (Linneweber-Lammerskitten, Schäfer and Samson, 2010). As the main platform for dissemination of the video clips is the cell phone, the study looked at the various aspects involved in the use of cell phones by learners in the classroom, as well as the incorporation of the clips into the teaching of three teachers. Consideration was given to whether or not the clips assisted the teachers in teaching, as well as whether or not they encouraged further exploration. The study was divided into six stages during which data was collected and analysed using an interpretive approach throughout. Data collection methods included semistructured interviews, questionnaires, observation, journals and reflective essays. The study revealed the participating teachers, having incorporated the clips into several lessons, found that these had a meaningful effect on their teaching practice, as well as on the engagement of the learners in the lessons. The majority of the learners involved in the study had access to cell phones, either their own or borrowed, and were able to download the video clips onto their phones from the website (www.ru.ac.za/vitalmaths). A number of learners found that the clips helped them find examples of specific mathematical concepts outside of the classroom, thus leading to further enquiry and exploration, while several learners downloaded and viewed additional clips. Overall findings showed that the VITALmaths video clips could be incorporated into teaching with relative ease.
- Full Text:
- Authors: Hyde, Janet Catherine
- Date: 2012
- Subjects: Mathematics -- Study and teaching (Secondary) -- South Africa Educational innovations -- South Africa Telecommunication in education -- South Africa Teaching -- South Africa -- Aids and devices
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1618 , http://hdl.handle.net/10962/d1003500
- Description: This qualitative study examines the use of Visual Technology for the Autonomous Learning of mathematics (VITALmaths) video clips in three Grade 9 classrooms in the Eastern Cape, South Africa, two of which are in well-resourced ex-Model C schools and one in a semi-rural township school. The rapid development of mobile technology, especially in Africa, has opened up previously unexplored avenues in economy, communication and education (Aker & Mbiti, 2010), with a number of mobile learning initiatives being launched in South Africa (Botha & Ford, 2007; Vosloo & Botha, 2009). The VITALmaths project was developed collaboratively between the University of Applied Sciences Northwestern Switzerland and Rhodes University in South Africa (Linneweber-Lammerskitten, Schäfer and Samson, 2010). As the main platform for dissemination of the video clips is the cell phone, the study looked at the various aspects involved in the use of cell phones by learners in the classroom, as well as the incorporation of the clips into the teaching of three teachers. Consideration was given to whether or not the clips assisted the teachers in teaching, as well as whether or not they encouraged further exploration. The study was divided into six stages during which data was collected and analysed using an interpretive approach throughout. Data collection methods included semistructured interviews, questionnaires, observation, journals and reflective essays. The study revealed the participating teachers, having incorporated the clips into several lessons, found that these had a meaningful effect on their teaching practice, as well as on the engagement of the learners in the lessons. The majority of the learners involved in the study had access to cell phones, either their own or borrowed, and were able to download the video clips onto their phones from the website (www.ru.ac.za/vitalmaths). A number of learners found that the clips helped them find examples of specific mathematical concepts outside of the classroom, thus leading to further enquiry and exploration, while several learners downloaded and viewed additional clips. Overall findings showed that the VITALmaths video clips could be incorporated into teaching with relative ease.
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An investigation of the role of physical manipulatives in the teaching and learning of measurement in Grade 8 : a case study using surface area and volume
- Authors: Chiphambo, Shakespear M E K
- Date: 2012
- Subjects: Measurement -- Study and teaching -- Research Mathematics -- Education (Secondary) -- Study and teaching Teaching -- Aids and devices -- Research
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1657 , http://hdl.handle.net/10962/d1003540
- Description: The purpose of this study is to investigate the role of physical manipulatives in the teaching and learning of measurement in Grade 8. The study focuses on how the use of physical manipulatives promotes learners' mathematical proficiency in relation to the five strands of Kilpatrick, Swafford and Findell (2001). The basis of the research is a case study in the interpretive paradigm involving 18 out of a cohort of 270 Grade 8 learners in the school where I teach. The data was collected using a range of methods including: (i) baseline assessment tasks, first piloted using 7 Grade 8 learners and then given to the target group; (ii) an intervention programme with intervention tasks; (iii) a post-intervention task; (iv) observations during the intervention; and (v) individual interviews. The results of the baseline assessment and the post-intervention tasks were analysed both quantitatively and qualitatively. My research findings indicate an overall improvement of the performance after learners engaged in using physical manipulatives. The average mark of the learners in the baseline assessment task was 23% and after the intervention programme the average mark was 31 %. The responses from the learners interviewed showed that they were motivated and that the use of physical manipulatives assisted them in understanding the concepts of measurement, in particular surface area and volume. The results of my study thus reveal that the use of physical manipulatives in teaching and learning mathematics has a positive role to play in learners' understanding of surface area and volume at the Grade 8 level. The fmdings of this case study support other research regarding the importance of using physical manipulatives in teaching and learning mathematics. They align with other findings that assert that manipulatives are essential mediating tools in the development of the conceptual and procedural understanding of mathematical concepts, clarifying and helping learners to visualize abstract mathematical concepts.
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- Authors: Chiphambo, Shakespear M E K
- Date: 2012
- Subjects: Measurement -- Study and teaching -- Research Mathematics -- Education (Secondary) -- Study and teaching Teaching -- Aids and devices -- Research
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1657 , http://hdl.handle.net/10962/d1003540
- Description: The purpose of this study is to investigate the role of physical manipulatives in the teaching and learning of measurement in Grade 8. The study focuses on how the use of physical manipulatives promotes learners' mathematical proficiency in relation to the five strands of Kilpatrick, Swafford and Findell (2001). The basis of the research is a case study in the interpretive paradigm involving 18 out of a cohort of 270 Grade 8 learners in the school where I teach. The data was collected using a range of methods including: (i) baseline assessment tasks, first piloted using 7 Grade 8 learners and then given to the target group; (ii) an intervention programme with intervention tasks; (iii) a post-intervention task; (iv) observations during the intervention; and (v) individual interviews. The results of the baseline assessment and the post-intervention tasks were analysed both quantitatively and qualitatively. My research findings indicate an overall improvement of the performance after learners engaged in using physical manipulatives. The average mark of the learners in the baseline assessment task was 23% and after the intervention programme the average mark was 31 %. The responses from the learners interviewed showed that they were motivated and that the use of physical manipulatives assisted them in understanding the concepts of measurement, in particular surface area and volume. The results of my study thus reveal that the use of physical manipulatives in teaching and learning mathematics has a positive role to play in learners' understanding of surface area and volume at the Grade 8 level. The fmdings of this case study support other research regarding the importance of using physical manipulatives in teaching and learning mathematics. They align with other findings that assert that manipulatives are essential mediating tools in the development of the conceptual and procedural understanding of mathematical concepts, clarifying and helping learners to visualize abstract mathematical concepts.
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An investigation into parental involvements in the learning of mathematics : a case study involving grade 5 San learners and their parents
- Hamukwaya, Shemunyenge Taleiko
- Authors: Hamukwaya, Shemunyenge Taleiko
- Date: 2010
- Subjects: Mathematics (Elementary) -- Study and teaching -- Namibia , Mathematics (Elementary) -- Study and teaching -- Activity programs -- Namibia , Mathematics (Elementary) -- Study and teaching -- Parent participation -- Namibia , Parent-teacher relationships -- Namibia , Marginality, Social -- Namibia , Literacy -- Social aspects -- Namibia , Khoisan (African people) -- Namibia
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1598 , http://hdl.handle.net/10962/d1003480 , Mathematics (Elementary) -- Study and teaching -- Namibia , Mathematics (Elementary) -- Study and teaching -- Activity programs -- Namibia , Mathematics (Elementary) -- Study and teaching -- Parent participation -- Namibia , Parent-teacher relationships -- Namibia , Marginality, Social -- Namibia , Literacy -- Social aspects -- Namibia , Khoisan (African people) -- Namibia
- Description: The purpose of this study was to investigate and document parental involvement in a San community in Namibia over a period of two months. The emphasis was to investigate whether San parents in the Omusati region were involved in the learning of mathematics of their children. The learner participants were selected according to those who were open to sharing their ideas. An interpretive approach was used to collect and analyse data. The collected data was gathered from 9 participants (4 learners in grade 5 together with their parents, plus their mathematics teacher). Semi-structured interviews, parental contributions and home visit observations were the three tools that I used to collect data. The selected school is located in a rural area in the Omusati region of northern Namibia. The interviews were conducted in Oshiwambo (the participants‟ mother tongue) and translated into English and then analyzed. I discovered that the selected San parents were involved in some but limited school activities. The findings of this study emphasizes that illiteracy may be one of the contributing factors of low or non-involvement of parents among the San community. Other factors which I found caused parents not to assist their children with homework was parents spending much of their time at the local cuca shops during the day until late in the evenings. The study also highlights possible strategies that can be carried out by teachers to encourage parental involvement in school activities.
- Full Text:
- Authors: Hamukwaya, Shemunyenge Taleiko
- Date: 2010
- Subjects: Mathematics (Elementary) -- Study and teaching -- Namibia , Mathematics (Elementary) -- Study and teaching -- Activity programs -- Namibia , Mathematics (Elementary) -- Study and teaching -- Parent participation -- Namibia , Parent-teacher relationships -- Namibia , Marginality, Social -- Namibia , Literacy -- Social aspects -- Namibia , Khoisan (African people) -- Namibia
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1598 , http://hdl.handle.net/10962/d1003480 , Mathematics (Elementary) -- Study and teaching -- Namibia , Mathematics (Elementary) -- Study and teaching -- Activity programs -- Namibia , Mathematics (Elementary) -- Study and teaching -- Parent participation -- Namibia , Parent-teacher relationships -- Namibia , Marginality, Social -- Namibia , Literacy -- Social aspects -- Namibia , Khoisan (African people) -- Namibia
- Description: The purpose of this study was to investigate and document parental involvement in a San community in Namibia over a period of two months. The emphasis was to investigate whether San parents in the Omusati region were involved in the learning of mathematics of their children. The learner participants were selected according to those who were open to sharing their ideas. An interpretive approach was used to collect and analyse data. The collected data was gathered from 9 participants (4 learners in grade 5 together with their parents, plus their mathematics teacher). Semi-structured interviews, parental contributions and home visit observations were the three tools that I used to collect data. The selected school is located in a rural area in the Omusati region of northern Namibia. The interviews were conducted in Oshiwambo (the participants‟ mother tongue) and translated into English and then analyzed. I discovered that the selected San parents were involved in some but limited school activities. The findings of this study emphasizes that illiteracy may be one of the contributing factors of low or non-involvement of parents among the San community. Other factors which I found caused parents not to assist their children with homework was parents spending much of their time at the local cuca shops during the day until late in the evenings. The study also highlights possible strategies that can be carried out by teachers to encourage parental involvement in school activities.
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The use of the van Hiele theory in investigating teaching strategies used by grade 10 geometry teachers in Namibia
- Authors: Muyeghu, Augustinus
- Date: 2009
- Subjects: Hiele, Pierre M. van Kilpatrick, Jeremy Geometry -- Study and teaching (Secondary) -- Namibia Mathematics -- Study and teaching (Secondary) -- Namibia Mathematics teachers -- Training of -- Namibia
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1817 , http://hdl.handle.net/10962/d1003703
- Description: This study reports on the extent to which selected mathematics teachers facilitate the teaching and learning of geometry at the van Hiele levels 1 and 2 at a Grade 10 level in selected schools in Namibia. It also addresses and explores the teaching strategies teachers employ in their classrooms. Kilpatrick et al.’s model for proficient teaching and the van Hiele model of geometric thinking were used to explore the type of teaching strategies employed by selected mathematics teachers. These two models served as guidelines from which interview and classroom observation protocols were developed. Given the continuing debate across the world about the learning and teaching of geometry, my thesis aims to contribute to a wider understanding of the teaching of geometry with regard to the van Hiele levels 1 and 2. There are no similar studies on the teaching of geometry in Namibia. My study concentrates on selected Grade 10 mathematics teachers and how they teach geometry using the van Hiele theory and the five Kilpatrick components of proficient teaching. As my research looks at teaching practice it was important to deconstruct teaching proficiency with a view to understanding what makes good teachers effective. The results from this study indicated that the selected Grade 10 mathematics teachers have a good conceptual understanding of geometry as all of them involved in this study were able to facilitate the learning and teaching of geometry that is consistent with the van Hiele levels 1 and 2.
- Full Text:
- Authors: Muyeghu, Augustinus
- Date: 2009
- Subjects: Hiele, Pierre M. van Kilpatrick, Jeremy Geometry -- Study and teaching (Secondary) -- Namibia Mathematics -- Study and teaching (Secondary) -- Namibia Mathematics teachers -- Training of -- Namibia
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1817 , http://hdl.handle.net/10962/d1003703
- Description: This study reports on the extent to which selected mathematics teachers facilitate the teaching and learning of geometry at the van Hiele levels 1 and 2 at a Grade 10 level in selected schools in Namibia. It also addresses and explores the teaching strategies teachers employ in their classrooms. Kilpatrick et al.’s model for proficient teaching and the van Hiele model of geometric thinking were used to explore the type of teaching strategies employed by selected mathematics teachers. These two models served as guidelines from which interview and classroom observation protocols were developed. Given the continuing debate across the world about the learning and teaching of geometry, my thesis aims to contribute to a wider understanding of the teaching of geometry with regard to the van Hiele levels 1 and 2. There are no similar studies on the teaching of geometry in Namibia. My study concentrates on selected Grade 10 mathematics teachers and how they teach geometry using the van Hiele theory and the five Kilpatrick components of proficient teaching. As my research looks at teaching practice it was important to deconstruct teaching proficiency with a view to understanding what makes good teachers effective. The results from this study indicated that the selected Grade 10 mathematics teachers have a good conceptual understanding of geometry as all of them involved in this study were able to facilitate the learning and teaching of geometry that is consistent with the van Hiele levels 1 and 2.
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Understanding the differences in marking performance of JSC mathematics markers in Namibia : a case study
- Authors: Mutuku, Elizabeth
- Date: 2009
- Subjects: Educational change -- Namibia , Mathematics -- Namibia -- Examinations -- Case studies , Mathematics -- Study and teaching -- Namibia -- Case studies , Grading and marking (Students) -- Namibia -- Case studies
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1999 , http://hdl.handle.net/10962/d1015223
- Description: Education reform in Namibia brought about changes to mathematics education since independence. This has put pressure on the government to provide both resources and qualified mathematics teachers to help drive the reform process in all teaching and learning activities. This included availing reliable and valid national examination results which is a measure of whether the newly introduced programmes are working or not. For the Ministry of Education this meant training more mathematics teachers and ensuring that competent and reliable teachers are appointed for marking national examination every year. The teachers' training process however, has not been going as fast as it was expected and year after year the Directorate of National Examinations and Assessment experienced problems in obtaining competent teachers for the marking of national examination. The purpose of the study was to understand the differences in marking performances of the JSC mathematics national examination markers. Particularly the study was to create a clear and detailed understanding of different factors that could possibly affect the marking performance of different markers. In addition, the study was to investigate the effect the mathematical content knowledge of the markers has on their marking performance. It was evident from the findings that their mathematical content knowledge had influenced their marking performance. Moreover the research findings also gave a strong indication that there are other factors that were influencing the markers marking performance. These were the markers' knowledge of the assessment and marking process, the markers' marking experience, the markers' socioeconomic background. The difference in their moderators' input has emerged as the other factors that have influenced their performance in marking and consequently contributed to the differences in their marking performances.
- Full Text:
- Authors: Mutuku, Elizabeth
- Date: 2009
- Subjects: Educational change -- Namibia , Mathematics -- Namibia -- Examinations -- Case studies , Mathematics -- Study and teaching -- Namibia -- Case studies , Grading and marking (Students) -- Namibia -- Case studies
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1999 , http://hdl.handle.net/10962/d1015223
- Description: Education reform in Namibia brought about changes to mathematics education since independence. This has put pressure on the government to provide both resources and qualified mathematics teachers to help drive the reform process in all teaching and learning activities. This included availing reliable and valid national examination results which is a measure of whether the newly introduced programmes are working or not. For the Ministry of Education this meant training more mathematics teachers and ensuring that competent and reliable teachers are appointed for marking national examination every year. The teachers' training process however, has not been going as fast as it was expected and year after year the Directorate of National Examinations and Assessment experienced problems in obtaining competent teachers for the marking of national examination. The purpose of the study was to understand the differences in marking performances of the JSC mathematics national examination markers. Particularly the study was to create a clear and detailed understanding of different factors that could possibly affect the marking performance of different markers. In addition, the study was to investigate the effect the mathematical content knowledge of the markers has on their marking performance. It was evident from the findings that their mathematical content knowledge had influenced their marking performance. Moreover the research findings also gave a strong indication that there are other factors that were influencing the markers marking performance. These were the markers' knowledge of the assessment and marking process, the markers' marking experience, the markers' socioeconomic background. The difference in their moderators' input has emerged as the other factors that have influenced their performance in marking and consequently contributed to the differences in their marking performances.
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The initial grounding of rational numbers : an investigation
- Authors: Brown, Bruce John Lindsay
- Date: 2007
- Subjects: Number theory Numbers, Rational -- Study and teaching (Elementary) Numeracy -- Study and teaching (Elementary) Mathematics -- Study and teaching (Elementary)
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1904 , http://hdl.handle.net/10962/d1006351
- Description: This small scale exploratory research project investigated the grounding of rational number concepts in informal, everyday life situations. A qualitative approach was taken to allow for the identification and then in depth investigation, of issues of importance for such a grounding of rational number understanding. The methodology followed could be seen as a combination of grounded theory and developmental research. And the data was generated through in-depth and clinical interviews structured around a number of grounded tasks related to rational numbers. The research comprised three cycles of interviews that were transcribed and then analysed in detail, interspersed with periods of reading and reflection. The pilot cycle involved a single grade three teacher, the second cycle involved 2 grade three teachers and the third cycle involved 2 grade three children. The research identified a number of different perspectives that were all important for the development of a fundamental intuitive understanding that could be considered personally meaningful to the individual concerned and relevant to the development of rational number concepts. Firstly in order to motivate and engage the child on a personal level the grounding situation needed to be seen as personally significant by the child. Secondly, coordinating operations provided a means of developing a fundamental intuitive understanding, through coordination with affording structures of the situation that are relevant to rational numbers. Finally, goal directed actions that are deliberately structured to achieve explicit goals in a situation are important for the development of more explicit concepts and skills fundamental for rational number understanding. Different explicit structures give rise to different interpretations of rational numbers in grounding situations. In addition to these perspectives, it became evident that building and learning representations was important for developing a more particularly mathematical understanding, based on the fundamental understanding derived from the child's grounded experience. The conclusion drawn in this research as a result of this complexity, is that to achieve a comprehensive and meaningful grounding, children's learning of rational numbers will not follow a simple linear trajectory. Rather this process forms a web of learning, threading coordinating operations for intuitive development, interpretations for explicit grounding and representations to develop more formal mathematical conceptions.
- Full Text:
- Authors: Brown, Bruce John Lindsay
- Date: 2007
- Subjects: Number theory Numbers, Rational -- Study and teaching (Elementary) Numeracy -- Study and teaching (Elementary) Mathematics -- Study and teaching (Elementary)
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1904 , http://hdl.handle.net/10962/d1006351
- Description: This small scale exploratory research project investigated the grounding of rational number concepts in informal, everyday life situations. A qualitative approach was taken to allow for the identification and then in depth investigation, of issues of importance for such a grounding of rational number understanding. The methodology followed could be seen as a combination of grounded theory and developmental research. And the data was generated through in-depth and clinical interviews structured around a number of grounded tasks related to rational numbers. The research comprised three cycles of interviews that were transcribed and then analysed in detail, interspersed with periods of reading and reflection. The pilot cycle involved a single grade three teacher, the second cycle involved 2 grade three teachers and the third cycle involved 2 grade three children. The research identified a number of different perspectives that were all important for the development of a fundamental intuitive understanding that could be considered personally meaningful to the individual concerned and relevant to the development of rational number concepts. Firstly in order to motivate and engage the child on a personal level the grounding situation needed to be seen as personally significant by the child. Secondly, coordinating operations provided a means of developing a fundamental intuitive understanding, through coordination with affording structures of the situation that are relevant to rational numbers. Finally, goal directed actions that are deliberately structured to achieve explicit goals in a situation are important for the development of more explicit concepts and skills fundamental for rational number understanding. Different explicit structures give rise to different interpretations of rational numbers in grounding situations. In addition to these perspectives, it became evident that building and learning representations was important for developing a more particularly mathematical understanding, based on the fundamental understanding derived from the child's grounded experience. The conclusion drawn in this research as a result of this complexity, is that to achieve a comprehensive and meaningful grounding, children's learning of rational numbers will not follow a simple linear trajectory. Rather this process forms a web of learning, threading coordinating operations for intuitive development, interpretations for explicit grounding and representations to develop more formal mathematical conceptions.
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The use of Van Hiele's theory to explore problems encountered in circle geometry: a grade 11 case study
- Authors: Siyepu, Sibawu Witness
- Date: 2005
- Subjects: Geometry -- Study and teaching (Secondary) -- South Africa Mathematics -- Study and teaching (Secondary) -- South Africa Mathematics teachers -- Training of -- South Africa Mathematical ability -- Testing
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1871 , http://hdl.handle.net/10962/d1004777
- Description: The research presented in this thesis is a case study located in the interpretive paradigm of qualitative research. The focus is on the use of van Hiele's theory to explore problems encountered in circle geometry by grade 11 learners and making some policy recommendations concerning the curriculum structure and teaching of the geometry at all grades. The interpretation is based to the learners' background in geometry i.e. their prior knowledge and experience of learning geometry. The study was carried out over a period of three years. The data collection process took a period of two months (April and May 2003) with a group of 21 grade 11 mathematics learners in a rural senior secondary school in the Eastern Cape. The researcher used document analysis, worksheets, participants' observation, van Hiele tests, a questionnaire and semi-structured interviews to collect data. The study showed that the structure of the South African geometry syllabus consists of a some what disorganized mixture of concepts. It is not sequential and hierarchical and it sequences concepts in a seemingly unrelated manner. The study revealed that the South African high school geometry curriculum is presented at a higher van Hiele level than what the learners can attain. The findings of the study showed that many of the grade 11 learners were under-prepared for the study of more sophisticated geometry concepts and proofs. Three categories of reasons could be ascribed to this: Firstly, there was insufficient preparation of learners during the primary and senior phases. Secondly the study indicated that there is overload of geometry at the high school level in the South African mathematics curriculum. Thirdly, the over-reliance on the traditional approach to teaching geometry, poor presentation of mathematical technical concepts and language problems, were identified as possible additional reasons for the poor learner understanding of geometry in general and circle geometry in particular. The study recommends that the structure of the South African geometry curriculum should be revisited and redesigned. Teachers should be empowered and developed to be more effective in teaching geometry through further studies in mathematics and in-service workshops. They should also be engaged in the process of implementing the van Hiele's theory in the teaching of geometry in their classrooms.
- Full Text:
- Authors: Siyepu, Sibawu Witness
- Date: 2005
- Subjects: Geometry -- Study and teaching (Secondary) -- South Africa Mathematics -- Study and teaching (Secondary) -- South Africa Mathematics teachers -- Training of -- South Africa Mathematical ability -- Testing
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1871 , http://hdl.handle.net/10962/d1004777
- Description: The research presented in this thesis is a case study located in the interpretive paradigm of qualitative research. The focus is on the use of van Hiele's theory to explore problems encountered in circle geometry by grade 11 learners and making some policy recommendations concerning the curriculum structure and teaching of the geometry at all grades. The interpretation is based to the learners' background in geometry i.e. their prior knowledge and experience of learning geometry. The study was carried out over a period of three years. The data collection process took a period of two months (April and May 2003) with a group of 21 grade 11 mathematics learners in a rural senior secondary school in the Eastern Cape. The researcher used document analysis, worksheets, participants' observation, van Hiele tests, a questionnaire and semi-structured interviews to collect data. The study showed that the structure of the South African geometry syllabus consists of a some what disorganized mixture of concepts. It is not sequential and hierarchical and it sequences concepts in a seemingly unrelated manner. The study revealed that the South African high school geometry curriculum is presented at a higher van Hiele level than what the learners can attain. The findings of the study showed that many of the grade 11 learners were under-prepared for the study of more sophisticated geometry concepts and proofs. Three categories of reasons could be ascribed to this: Firstly, there was insufficient preparation of learners during the primary and senior phases. Secondly the study indicated that there is overload of geometry at the high school level in the South African mathematics curriculum. Thirdly, the over-reliance on the traditional approach to teaching geometry, poor presentation of mathematical technical concepts and language problems, were identified as possible additional reasons for the poor learner understanding of geometry in general and circle geometry in particular. The study recommends that the structure of the South African geometry curriculum should be revisited and redesigned. Teachers should be empowered and developed to be more effective in teaching geometry through further studies in mathematics and in-service workshops. They should also be engaged in the process of implementing the van Hiele's theory in the teaching of geometry in their classrooms.
- Full Text:
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