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
- 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
- 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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