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
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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
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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
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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.
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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.
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