The use of dynamic software to potentially enhance conceptual understanding and a productive disposition in the visual learning of algebra: an interventionist case study
- Authors: Junius, Daniel Franscius
- Date: 2023-10-13
- Subjects: Mathematics education , Algebra Study and teaching (Secondary) Namibia , Educational technology , Visual learning , GeoGebra , High school students Attitudes
- Language: English
- Type: Academic theses , Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/431542 , vital:72784 , DOI 10.21504/10962/431542
- Description: Over the decades, the didactics and practice of teaching mathematics has offered many unique challenges and opportunities for exploration and understanding. The introduction and development of technology into mathematics is one of the occurrences which has also contributed to a new discourse in teaching mathematics – in this case the teaching of algebra. Algebra is still seen as a gatekeeper and remains as one of the key reasons for a negative disposition amongst learners towards learning the subject. Across the globe psychologists, philosophers and educators continue to engage in debates and research projects in search of answers and solutions for the improvement of algebra teaching and an improvement in dispositions towards learning algebra. This thesis reports on a research project that focused on the use of dynamic software to enhance the conceptual understanding and productive dispositions of selected learners through the visual learning of abstract algebraic concepts. The research was executed as an interventionist case study. A case study methodological strategy was adopted with two groups of 30 Grade 9 learners. One group was a Grade 9 mathematics class of a school in Windhoek who scored above average in algebra but showed a very low disposition score, while the other group was made up of learners from a community project who scored high on the disposition scale but achieved below average results in algebra. The analytical framework of the case study is structured around a combination of complementary algebraic topics presented through visual learning, with GeoGebra as a medium of instruction. With the focus on visualisation and the use of technology the study investigated and attempted to understand how participants processed and internalised algebraic concepts to make sense of abstract algebraic concepts and eventually gain sustained conceptual understanding. The study was framed by the theoretical theories of constructivism and the Dual Coding Theory. For the collection of data, a mixed methods approach was adopted following three cycles. Three algebraic topics were taught with GeoGebra applets yielding both qualitative and quantitative data, through the observation of participants, screen captures and reflective interviews, using instruments designed specifically for the study and collecting quantitative achievement test results. The study, a journey that both the participants and the researcher embarked upon, revealed that the use of technology enhanced conceptual understanding for both groups and both groups showed a positive change in disposition towards learning algebra. The intervention with GeoGebra consistently and progressively improved in terms of conceptual understanding and dispositions towards learning algebra significant improvements in results were achieved. The findings showed that this approach to teaching algebra yielded positive results and gave new insights into visual teaching with technology. New opportunities for further research were created. , Thesis (PhD) -- Faculty of Education, Secondary and Post-School Education, 2023
- Full Text:
- Authors: Junius, Daniel Franscius
- Date: 2023-10-13
- Subjects: Mathematics education , Algebra Study and teaching (Secondary) Namibia , Educational technology , Visual learning , GeoGebra , High school students Attitudes
- Language: English
- Type: Academic theses , Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/431542 , vital:72784 , DOI 10.21504/10962/431542
- Description: Over the decades, the didactics and practice of teaching mathematics has offered many unique challenges and opportunities for exploration and understanding. The introduction and development of technology into mathematics is one of the occurrences which has also contributed to a new discourse in teaching mathematics – in this case the teaching of algebra. Algebra is still seen as a gatekeeper and remains as one of the key reasons for a negative disposition amongst learners towards learning the subject. Across the globe psychologists, philosophers and educators continue to engage in debates and research projects in search of answers and solutions for the improvement of algebra teaching and an improvement in dispositions towards learning algebra. This thesis reports on a research project that focused on the use of dynamic software to enhance the conceptual understanding and productive dispositions of selected learners through the visual learning of abstract algebraic concepts. The research was executed as an interventionist case study. A case study methodological strategy was adopted with two groups of 30 Grade 9 learners. One group was a Grade 9 mathematics class of a school in Windhoek who scored above average in algebra but showed a very low disposition score, while the other group was made up of learners from a community project who scored high on the disposition scale but achieved below average results in algebra. The analytical framework of the case study is structured around a combination of complementary algebraic topics presented through visual learning, with GeoGebra as a medium of instruction. With the focus on visualisation and the use of technology the study investigated and attempted to understand how participants processed and internalised algebraic concepts to make sense of abstract algebraic concepts and eventually gain sustained conceptual understanding. The study was framed by the theoretical theories of constructivism and the Dual Coding Theory. For the collection of data, a mixed methods approach was adopted following three cycles. Three algebraic topics were taught with GeoGebra applets yielding both qualitative and quantitative data, through the observation of participants, screen captures and reflective interviews, using instruments designed specifically for the study and collecting quantitative achievement test results. The study, a journey that both the participants and the researcher embarked upon, revealed that the use of technology enhanced conceptual understanding for both groups and both groups showed a positive change in disposition towards learning algebra. The intervention with GeoGebra consistently and progressively improved in terms of conceptual understanding and dispositions towards learning algebra significant improvements in results were achieved. The findings showed that this approach to teaching algebra yielded positive results and gave new insights into visual teaching with technology. New opportunities for further research were created. , Thesis (PhD) -- Faculty of Education, Secondary and Post-School Education, 2023
- Full Text:
Visual representations of linear algebraic expressions: a case study in a Grade 9 after-school mathematics club
- Authors: Herbert, Sindisiwe
- Date: 2023-10-13
- Subjects: Visual learning , Algebra Study and teaching (Secondary) South Africa , Algebras, Linear , After-school programs , Kinaesthetic learning
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/424019 , vital:72116
- Description: Visualisation is commonly used as a tool in introducing algebra through visual or kinaesthetic sequences designed to prompt learners' development of a general rule for moving from a term's position to its output value. Fluency in both the concepts and the conventions of elementary algebra are essential to learners, as algebra forms the language in which many advanced mathematical ideas are encoded. Moreover, algebraic fluency is often associated with an ability to think abstractly about arithmetic processes. In many classrooms, however, research has shown that learners often focus on fluency in algebraic conventions rather than concepts, learning how to manipulate expressions without understanding the algorithms they are taught to follow. This trend can be linked to several causes, including teacher-centred mathematics classrooms in which learners are – whether implicitly or explicitly – encouraged to copy formulae and methods in order to ‘get it right in a test’ without necessarily grasping the underlying logical relationships. This case study, therefore, aimed to determine whether there was value in using visual, kinaesthetic models to broaden and deepen learners' use of algebra. To that end, in the context of an extra-curricular mathematics club that aimed to decentre the teachers and demand innovative ideas of the participants, six pairs of Grade 9 learners were tasked with creating visual representations of a linear algebraic expression using coloured building cubes. The responses to this task over the course of five assignments were many and varied and almost universally displayed a sustained internal logic that the learners were able to explain and develop. Most pairs began with a visual list of terms arranged in sets of towers, pyramids or, in one case, a spiral. At the end of the study, all but one of the pairs had settled on a Visual Expression, in which various colours were used to represent elements of the algebra such as the values of the coefficient, the variable and the constant term. The participants' representations grew in complexity over the course of the study and the conformity of the final responses showed that the club was a collaborative space in which learners shared ideas. However, the structure of the Visual Expressions and their own confessions of nerves about ‘getting it wrong’ in the interviews suggest that the participants were stuck in a mindset that led them to seek out and idealise the representation closest to the original algebra, even though that representation revealed little about the structural relationship underlying the expression. , Thesis (MEd) -- Faculty of Education, Secondary and Post-School Education, 2023
- Full Text:
- Authors: Herbert, Sindisiwe
- Date: 2023-10-13
- Subjects: Visual learning , Algebra Study and teaching (Secondary) South Africa , Algebras, Linear , After-school programs , Kinaesthetic learning
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/424019 , vital:72116
- Description: Visualisation is commonly used as a tool in introducing algebra through visual or kinaesthetic sequences designed to prompt learners' development of a general rule for moving from a term's position to its output value. Fluency in both the concepts and the conventions of elementary algebra are essential to learners, as algebra forms the language in which many advanced mathematical ideas are encoded. Moreover, algebraic fluency is often associated with an ability to think abstractly about arithmetic processes. In many classrooms, however, research has shown that learners often focus on fluency in algebraic conventions rather than concepts, learning how to manipulate expressions without understanding the algorithms they are taught to follow. This trend can be linked to several causes, including teacher-centred mathematics classrooms in which learners are – whether implicitly or explicitly – encouraged to copy formulae and methods in order to ‘get it right in a test’ without necessarily grasping the underlying logical relationships. This case study, therefore, aimed to determine whether there was value in using visual, kinaesthetic models to broaden and deepen learners' use of algebra. To that end, in the context of an extra-curricular mathematics club that aimed to decentre the teachers and demand innovative ideas of the participants, six pairs of Grade 9 learners were tasked with creating visual representations of a linear algebraic expression using coloured building cubes. The responses to this task over the course of five assignments were many and varied and almost universally displayed a sustained internal logic that the learners were able to explain and develop. Most pairs began with a visual list of terms arranged in sets of towers, pyramids or, in one case, a spiral. At the end of the study, all but one of the pairs had settled on a Visual Expression, in which various colours were used to represent elements of the algebra such as the values of the coefficient, the variable and the constant term. The participants' representations grew in complexity over the course of the study and the conformity of the final responses showed that the club was a collaborative space in which learners shared ideas. However, the structure of the Visual Expressions and their own confessions of nerves about ‘getting it wrong’ in the interviews suggest that the participants were stuck in a mindset that led them to seek out and idealise the representation closest to the original algebra, even though that representation revealed little about the structural relationship underlying the expression. , Thesis (MEd) -- Faculty of Education, Secondary and Post-School Education, 2023
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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:
- 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
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An analysis of selected Grade 8 mathematics teachers’ use of gestures as visualisation tools to support mathematical meaning-making
- Authors: Haipinge, David Tuhafeni
- Date: 2021-10-29
- Subjects: Gesture , Gesture in mathematics education , Visual learning , Visualization , Mathematics Study and teaching (Secondary) Namibia
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/191969 , vital:45184
- Description: The purpose of this Namibian case study was to investigate how different types of gestures are used to support the construction of mathematical meaning making in teaching and learning. Gestures of three selected Grade 8 mathematics teachers were observed and analysed. This study was intended to answer the following research question: how do selected Grade 8 mathematics teachers use gestures as visualisation tools to support mathematical meaning making? The study was framed by an enactivist perspective and the research was oriented in the interpretive paradigm. Data were collected through video-recorded observations of three selected teachers and through stimulus recall interviews. In order to generate rich data and support validity, five lessons per selected teacher were video recorded. The study found that the participating teachers incorporated a variety of mathematical gestures into their lessons in order to support and provide mathematical meaning. Further, this study found that gestures facilitated meaning making in mathematics. The findings in the study suggest a need for mathematics teachers to be trained in using gestures appropriately to communicate mathematically in their lessons. In addition, this study discovered a new type of gesture – the overlapping gesture in addition to McNeill's (1992) types, namely: pointing gestures, metaphor gestures, beating gestures and iconic gestures. This case study also showed that the more experienced the teachers are, the more mathematical gestures they produce during their mathematics lessons. , Thesis (MEd) -- Faculty of Education, Education, 2021
- Full Text:
- Authors: Haipinge, David Tuhafeni
- Date: 2021-10-29
- Subjects: Gesture , Gesture in mathematics education , Visual learning , Visualization , Mathematics Study and teaching (Secondary) Namibia
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/191969 , vital:45184
- Description: The purpose of this Namibian case study was to investigate how different types of gestures are used to support the construction of mathematical meaning making in teaching and learning. Gestures of three selected Grade 8 mathematics teachers were observed and analysed. This study was intended to answer the following research question: how do selected Grade 8 mathematics teachers use gestures as visualisation tools to support mathematical meaning making? The study was framed by an enactivist perspective and the research was oriented in the interpretive paradigm. Data were collected through video-recorded observations of three selected teachers and through stimulus recall interviews. In order to generate rich data and support validity, five lessons per selected teacher were video recorded. The study found that the participating teachers incorporated a variety of mathematical gestures into their lessons in order to support and provide mathematical meaning. Further, this study found that gestures facilitated meaning making in mathematics. The findings in the study suggest a need for mathematics teachers to be trained in using gestures appropriately to communicate mathematically in their lessons. In addition, this study discovered a new type of gesture – the overlapping gesture in addition to McNeill's (1992) types, namely: pointing gestures, metaphor gestures, beating gestures and iconic gestures. This case study also showed that the more experienced the teachers are, the more mathematical gestures they produce during their mathematics lessons. , Thesis (MEd) -- Faculty of Education, Education, 2021
- Full Text:
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:
- 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
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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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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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