The role of visualisation in redefining the pedagogy of fractions in mathematics classrooms among senior primary school teachers
- Authors: Ausiku, Charity Makwiliro
- Date: 2022-10-14
- Subjects: Mathematics Study and teaching (Elementary) Namibia , Fractions Study and teaching (Elementary) Namibia , Visualization , Visual learning , Dual-coding hypothesis , Constructivism (Education) Namibia
- Language: English
- Type: Academic theses , Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/405456 , vital:70173 , DOI 10.21504/10962/405456
- Description: This mixed methods study explored the impact of the use of a visualisation approach on the pedagogy of eight teacher participants who were involved in the Rundu Campus Fraction Project (RCFP). The aim of this study was to determine the extent to which participants incorporated visualisation processes in the pedagogy of fractions, in view of their exposure to visualisation activities in the RCFP. Since fractions are difficult to teach and learn, visualisation was considered as an alternative approach to the pedagogy of fractions because it presents learners with opportunities to improve their proportional and spatial reasoning. This study was founded on the premise that the incorporation of both verbal and nonverbal cues can enhance the teaching and learning of fractions rather than the use of a single cue. Hence, the two theories underpinning this study are the Dual Coding Theory and the Constructivist Theory. While the Dual Coding Theory advocates for the use of verbal and nonverbal codes, the Constructivist theory states that meaningful learning occurs when learners are presented with opportunities to construct their own knowledge. Thus, the two codes are intertwined. In other words, the active construction of knowledge among learners is aided by using constructivist teaching approaches through the incorporation of both verbal and nonverbal codes. Although this study was predominantly qualitative, quantitative methods were also used in the data collection process. A questionnaire was administered to identify teacher participants for this study, based on their teaching orientations. Their views on best practices in mathematics classrooms in general and the incorporation of visualisation processes in particular, were instrumental in the selection of participants for this study. In addition, observations and semi-structured interviews were also used as research methods. Twenty-five lesson samples were video recorded, transcribed and analysed using both qualitative and quantitative methods. Moreover, each of the eight participants was exposed to a set of pre- and post-observation interviews during which they were expected to express their views on the selection, incorporation and impact of visualisation processes on the teaching of fractions. Data sets from all three instruments were analysed using both quantitative and qualitative methods. The findings indicate that the RCFP had an impact on the teaching strategies employed by the participants as they all incorporated visualisation processes into their teaching to some extent. In some lessons, the visual code was effectively blended into the verbal code while in others, the purpose of and connection between the two codes was not evident. Hence, although all the participants embraced the incorporation of visualisation in the pedagogy of mathematics, some of them struggled to find its rightful position in the teaching of fractions. The findings suggest that despite the participants’ eagerness to use visualisation in their fraction lessons, some of them did not have adequate knowledge to successfully merge it with the conventional verbal code. Thus, for the integration of visuals to be impactful, it should be carefully merged in the teaching of fractions by taking into account various factors. , Thesis (PhD) -- Faculty of Education, Education, 2022
- Full Text:
- Authors: Ausiku, Charity Makwiliro
- Date: 2022-10-14
- Subjects: Mathematics Study and teaching (Elementary) Namibia , Fractions Study and teaching (Elementary) Namibia , Visualization , Visual learning , Dual-coding hypothesis , Constructivism (Education) Namibia
- Language: English
- Type: Academic theses , Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/405456 , vital:70173 , DOI 10.21504/10962/405456
- Description: This mixed methods study explored the impact of the use of a visualisation approach on the pedagogy of eight teacher participants who were involved in the Rundu Campus Fraction Project (RCFP). The aim of this study was to determine the extent to which participants incorporated visualisation processes in the pedagogy of fractions, in view of their exposure to visualisation activities in the RCFP. Since fractions are difficult to teach and learn, visualisation was considered as an alternative approach to the pedagogy of fractions because it presents learners with opportunities to improve their proportional and spatial reasoning. This study was founded on the premise that the incorporation of both verbal and nonverbal cues can enhance the teaching and learning of fractions rather than the use of a single cue. Hence, the two theories underpinning this study are the Dual Coding Theory and the Constructivist Theory. While the Dual Coding Theory advocates for the use of verbal and nonverbal codes, the Constructivist theory states that meaningful learning occurs when learners are presented with opportunities to construct their own knowledge. Thus, the two codes are intertwined. In other words, the active construction of knowledge among learners is aided by using constructivist teaching approaches through the incorporation of both verbal and nonverbal codes. Although this study was predominantly qualitative, quantitative methods were also used in the data collection process. A questionnaire was administered to identify teacher participants for this study, based on their teaching orientations. Their views on best practices in mathematics classrooms in general and the incorporation of visualisation processes in particular, were instrumental in the selection of participants for this study. In addition, observations and semi-structured interviews were also used as research methods. Twenty-five lesson samples were video recorded, transcribed and analysed using both qualitative and quantitative methods. Moreover, each of the eight participants was exposed to a set of pre- and post-observation interviews during which they were expected to express their views on the selection, incorporation and impact of visualisation processes on the teaching of fractions. Data sets from all three instruments were analysed using both quantitative and qualitative methods. The findings indicate that the RCFP had an impact on the teaching strategies employed by the participants as they all incorporated visualisation processes into their teaching to some extent. In some lessons, the visual code was effectively blended into the verbal code while in others, the purpose of and connection between the two codes was not evident. Hence, although all the participants embraced the incorporation of visualisation in the pedagogy of mathematics, some of them struggled to find its rightful position in the teaching of fractions. The findings suggest that despite the participants’ eagerness to use visualisation in their fraction lessons, some of them did not have adequate knowledge to successfully merge it with the conventional verbal code. Thus, for the integration of visuals to be impactful, it should be carefully merged in the teaching of fractions by taking into account various factors. , Thesis (PhD) -- 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
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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.
- Full Text:
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.
- Full Text:
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