Design of an LMS-mediated tutorial to support deep and effective engagement in the process of learning mathematics
- Authors: Kigundu, Stephen
- Date: 2023-10-13
- Subjects: Learning Management Systems (LMS) , e-learning , Educational technology , Mathematics Study and teaching (Secondary) , Constructivism (Education) , Mixed methods research
- Language: English
- Type: Academic theses , Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/431565 , vital:72786 , DOI 10.21504/10962/431565
- Description: Many institutions of Higher Learning have adopted a variety of Learning Management Systems (LMS) as platforms for e-learning implementation. However, the design and nature of LMS technologies present challenges to the design of LMS-based activities that engage students in learning to do mathematics. There are no clear guidelines or strategies for designing LMS-based activities that engage students in complex mathematical processes. Hence, using technologies in mathematics education often replicates instructivist positions and practices. Conversely, using constructivist principles, modes of mathematical engagement, and e-learning tools to mediate learning provides an integrated framework to transform the use of an LMS as a platform for e-learning implementation and promote deep engagement in mathematical learning. The objective of this study was to explore mechanisms that could be useful for conceiving activities to support the learning of Mathematics using an LMS-mediated tutorial. The design, redesign and evaluation of the e-tutorial are reported upon. In preparation for the study, an LMS-based tutorial was designed and developed to be used as a test-bed to investigate how these e-learning tools could support learning to do mathematics. A Trigonometry module, consisting of course content in the form of resources and tasks to help the students to explore, practice and apply right triangle concepts, was used to investigate and derive design strategies. A mixed method research approach with a reflexive self-study research design was used. A group of first-year university student volunteers studying mathematics in the mechanical engineering department were used to test the tutorial. The students were asked to do a series of tasks using the e-learning environment during the Mathematics tutorial period. Data was collected using in-class observations, interviews, screen capture videos, student-written responses, and system-generated data. All students were encouraged to complete a learning journal detailing their experiences during the tutorial using an LMS-based tool. The students were given no training, but a tutor (researcher) was available to answer any questions they may have had. Contradiction analysis was used to evaluate the data, compare purpose and practice and judge whether the activity or tool was fitted for the intended purpose. Findings were in the form of transformations of the e-tutorial system as it was developed. Among the most noteworthy contributory modifications were changing from 1) “read first, then do” to “do first, read when necessary”, 2) “work on the computer” to “work on paper then capture on the computer”, 3) “physically separated work with computer-enabled social contact”, to "individual computer work in face-to-face social settings.” 4) “single-level of resource provision” to “multi-level, demand-driven resource provision” and 5) “self-regulated” learning process regulation to “computer-assisted” learning process regulation. The discussion of these findings indicated that to enable students’ deep and effective engagement in the process of learning fundamental trigonometry within an LMS-mediated tutorial, one needs to design the system with some activities that can create a demand for knowledge, encourage rough work and face-to-face social interaction, supported by multi-level, demand-driven resources, and computer-assisted learning-process regulation. Contributions to research by this study were in the form of 1) Design Principles for LMS-mediated tutorials, 2) Principles for an e-tutorial development methodology, and 3) The LMS-mediated tutorial system. , Thesis (PhD) -- Faculty of Education, Primary and Early Childhood Education, 2023
- Full Text:
- Date Issued: 2023-10-13
- Authors: Kigundu, Stephen
- Date: 2023-10-13
- Subjects: Learning Management Systems (LMS) , e-learning , Educational technology , Mathematics Study and teaching (Secondary) , Constructivism (Education) , Mixed methods research
- Language: English
- Type: Academic theses , Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/431565 , vital:72786 , DOI 10.21504/10962/431565
- Description: Many institutions of Higher Learning have adopted a variety of Learning Management Systems (LMS) as platforms for e-learning implementation. However, the design and nature of LMS technologies present challenges to the design of LMS-based activities that engage students in learning to do mathematics. There are no clear guidelines or strategies for designing LMS-based activities that engage students in complex mathematical processes. Hence, using technologies in mathematics education often replicates instructivist positions and practices. Conversely, using constructivist principles, modes of mathematical engagement, and e-learning tools to mediate learning provides an integrated framework to transform the use of an LMS as a platform for e-learning implementation and promote deep engagement in mathematical learning. The objective of this study was to explore mechanisms that could be useful for conceiving activities to support the learning of Mathematics using an LMS-mediated tutorial. The design, redesign and evaluation of the e-tutorial are reported upon. In preparation for the study, an LMS-based tutorial was designed and developed to be used as a test-bed to investigate how these e-learning tools could support learning to do mathematics. A Trigonometry module, consisting of course content in the form of resources and tasks to help the students to explore, practice and apply right triangle concepts, was used to investigate and derive design strategies. A mixed method research approach with a reflexive self-study research design was used. A group of first-year university student volunteers studying mathematics in the mechanical engineering department were used to test the tutorial. The students were asked to do a series of tasks using the e-learning environment during the Mathematics tutorial period. Data was collected using in-class observations, interviews, screen capture videos, student-written responses, and system-generated data. All students were encouraged to complete a learning journal detailing their experiences during the tutorial using an LMS-based tool. The students were given no training, but a tutor (researcher) was available to answer any questions they may have had. Contradiction analysis was used to evaluate the data, compare purpose and practice and judge whether the activity or tool was fitted for the intended purpose. Findings were in the form of transformations of the e-tutorial system as it was developed. Among the most noteworthy contributory modifications were changing from 1) “read first, then do” to “do first, read when necessary”, 2) “work on the computer” to “work on paper then capture on the computer”, 3) “physically separated work with computer-enabled social contact”, to "individual computer work in face-to-face social settings.” 4) “single-level of resource provision” to “multi-level, demand-driven resource provision” and 5) “self-regulated” learning process regulation to “computer-assisted” learning process regulation. The discussion of these findings indicated that to enable students’ deep and effective engagement in the process of learning fundamental trigonometry within an LMS-mediated tutorial, one needs to design the system with some activities that can create a demand for knowledge, encourage rough work and face-to-face social interaction, supported by multi-level, demand-driven resources, and computer-assisted learning-process regulation. Contributions to research by this study were in the form of 1) Design Principles for LMS-mediated tutorials, 2) Principles for an e-tutorial development methodology, and 3) The LMS-mediated tutorial system. , Thesis (PhD) -- Faculty of Education, Primary and Early Childhood Education, 2023
- Full Text:
- Date Issued: 2023-10-13
The nature of Visual Representations of multiplication and division exercises in nine Grades 1 to 3 South African textbooks
- Authors: Booysen, Tammy Irene
- Date: 2023-03-29
- Subjects: Mathematics Textbooks , Mathematics Study and teaching (Elementary) South Africa , Visual learning , Multiplication Study and teaching (Elementary) South Africa , Division Study and teaching (Elementary) South Africa , Constructivism (Education)
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/422579 , vital:71959
- Description: Mathematics is a language that is rich in visual representations (Mudaly & Rampersad, 2010). Visual Representations assist us in developing our reasoning skills when solving a problem and our understanding of the relationships between concepts (Ozkan et al., 2018). This thesis focuses on the different visual representations (VR) in South African Foundation Phase mathematics textbooks and workbooks. Textbooks and workbooks play an important role in developing an understanding of mathematical concepts for both teachers and learners (Harries & Spooner, 2000). While teachers generally rely heavily on textbooks, they were a key resource while schools were closed due to COVID-19 lockdown regulations. The theory of Constructivism forms part of the theoretical framework for this study. Constructivism advocates that learners actively construct knowledge through experiences rather than passively receiving knowledge from the outside (Von Glaserfeld, 2001). Vygotsky believed that social interactions create experiences that facilitate the learning and meaning-making process (Vygotsky, 1978). This case study is underpinned by an interpretivist paradigm as it sought to examine the nature of VRs in three Grades 1 - 3 textbooks/workbooks. My research approach is primarily qualitative with descriptive statistics to assist in developing a more comprehensive understanding of the research questions. The study was guided by the analytic tool designed by Fotakopoulou and Spiliotopoulou (2008) which I adapted for Foundation Phase mathematics use. The framework provides insight on the type of VR, VRs relation to content, VRs relation to reality, the function of the VR and dimensionality of a VR. While the workbooks had many more VRs than textbooks, the dominant type of VR in textbooks and workbooks are images. The VRs mostly have a strong relation to content with a realistic relation to reality as they were predominantly 2D representation of a 3D object that had an exemplifying function (type b). , Thesis (MEd) -- Faculty of Education, Education, 2023
- Full Text:
- Date Issued: 2023-03-29
- Authors: Booysen, Tammy Irene
- Date: 2023-03-29
- Subjects: Mathematics Textbooks , Mathematics Study and teaching (Elementary) South Africa , Visual learning , Multiplication Study and teaching (Elementary) South Africa , Division Study and teaching (Elementary) South Africa , Constructivism (Education)
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/422579 , vital:71959
- Description: Mathematics is a language that is rich in visual representations (Mudaly & Rampersad, 2010). Visual Representations assist us in developing our reasoning skills when solving a problem and our understanding of the relationships between concepts (Ozkan et al., 2018). This thesis focuses on the different visual representations (VR) in South African Foundation Phase mathematics textbooks and workbooks. Textbooks and workbooks play an important role in developing an understanding of mathematical concepts for both teachers and learners (Harries & Spooner, 2000). While teachers generally rely heavily on textbooks, they were a key resource while schools were closed due to COVID-19 lockdown regulations. The theory of Constructivism forms part of the theoretical framework for this study. Constructivism advocates that learners actively construct knowledge through experiences rather than passively receiving knowledge from the outside (Von Glaserfeld, 2001). Vygotsky believed that social interactions create experiences that facilitate the learning and meaning-making process (Vygotsky, 1978). This case study is underpinned by an interpretivist paradigm as it sought to examine the nature of VRs in three Grades 1 - 3 textbooks/workbooks. My research approach is primarily qualitative with descriptive statistics to assist in developing a more comprehensive understanding of the research questions. The study was guided by the analytic tool designed by Fotakopoulou and Spiliotopoulou (2008) which I adapted for Foundation Phase mathematics use. The framework provides insight on the type of VR, VRs relation to content, VRs relation to reality, the function of the VR and dimensionality of a VR. While the workbooks had many more VRs than textbooks, the dominant type of VR in textbooks and workbooks are images. The VRs mostly have a strong relation to content with a realistic relation to reality as they were predominantly 2D representation of a 3D object that had an exemplifying function (type b). , Thesis (MEd) -- Faculty of Education, Education, 2023
- Full Text:
- Date Issued: 2023-03-29
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:
- Date Issued: 2021-10-29
- 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:
- Date Issued: 2021-10-29
Research projects
- Authors: Adusei-Owusu, James
- Date: 2001
- Subjects: Constructivism (Education) , Review literature , College students -- Study and teaching , Teaching -- Methods , Competency based education -- Eastern Cape (South Africa)
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:1740 , http://hdl.handle.net/10962/d1003624 , Constructivism (Education) , Review literature , College students -- Study and teaching , Teaching -- Methods , Competency based education -- Eastern Cape (South Africa)
- Description: RESEARCH PROJECTS: 1 RESEARCH PROJECT ONE: A literature review: Constructivism: An alternate approach to teaching and learning. Abstract The constructivist perspectives on learning have helped enhance science educators' understanding of how students make sense of their lived experiences. Constructivism purports to be a transformation of the traditional curriculum. As such this article starts with a brief overview of behaviorism: the scientific approach to education. The main tenets underlying constructivism, how constructivism guides educators to change their classroom practice, and the implications to science teaching have been reviewed. 2 RESEARCH PROJECT TWO (Empirical study): Being Constructive: College students' learning of work and heat as aspects of the energy concept based a constructivist approach. Abstract This study is an extension of a literature review on constructivism as an alternate teaching and learning approach discussed in research project one. It is an empirical study concerning the use of a learning module based on a constructivist approach to develop pre-service student teachers' understanding of work and heat as aspects of the energy concept. The data consisted mainly of transcripts of students' interviews, written responses to questionnaires designed in the form of a worksheet, and comments from non-participant observers and students. The results seem to suggest that a carefully designed learning module based on a constructivist teaching and learning approach may be a valuable tool in developing pre-service student teachers' understanding of work and heat. 3 RESEARCH PROJECT THREE (Empirical study): A College in transition: A case study of the readiness of a college in the Eastern Cape province to implement Outcomes-Based Education in an Education Development centre. Abstract Curriculum 2005 premised on Outcomes-Based Education is the new curriculum framework for South Africa. It signifies a paradigm shift in education from the traditional 'telling-listening' relationship between the teacher and the learner to one that emphasises leamer-centred approach to the teaching process. Teachers, though recognized as crucial to the educational transformation process in the country have also being identified as ill-equipped to meet the challenges posed by Outcomes-Based Education. This study starts with a brief overview of the South African curriculum and the main tenets underlying Outcomes-Based Education. The institutional conditions and whether the lecturers at a college in the Eastern Cape province perceive the need for a change in their classroom practice were also investigated. Bearing in mind the need for further research to validate the findings of this study, positive indicators that emerged from the study suggest the readiness of the college to implement Outcomes-Based Education at the proposed Education Development Centre.
- Full Text:
- Date Issued: 2001
- Authors: Adusei-Owusu, James
- Date: 2001
- Subjects: Constructivism (Education) , Review literature , College students -- Study and teaching , Teaching -- Methods , Competency based education -- Eastern Cape (South Africa)
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:1740 , http://hdl.handle.net/10962/d1003624 , Constructivism (Education) , Review literature , College students -- Study and teaching , Teaching -- Methods , Competency based education -- Eastern Cape (South Africa)
- Description: RESEARCH PROJECTS: 1 RESEARCH PROJECT ONE: A literature review: Constructivism: An alternate approach to teaching and learning. Abstract The constructivist perspectives on learning have helped enhance science educators' understanding of how students make sense of their lived experiences. Constructivism purports to be a transformation of the traditional curriculum. As such this article starts with a brief overview of behaviorism: the scientific approach to education. The main tenets underlying constructivism, how constructivism guides educators to change their classroom practice, and the implications to science teaching have been reviewed. 2 RESEARCH PROJECT TWO (Empirical study): Being Constructive: College students' learning of work and heat as aspects of the energy concept based a constructivist approach. Abstract This study is an extension of a literature review on constructivism as an alternate teaching and learning approach discussed in research project one. It is an empirical study concerning the use of a learning module based on a constructivist approach to develop pre-service student teachers' understanding of work and heat as aspects of the energy concept. The data consisted mainly of transcripts of students' interviews, written responses to questionnaires designed in the form of a worksheet, and comments from non-participant observers and students. The results seem to suggest that a carefully designed learning module based on a constructivist teaching and learning approach may be a valuable tool in developing pre-service student teachers' understanding of work and heat. 3 RESEARCH PROJECT THREE (Empirical study): A College in transition: A case study of the readiness of a college in the Eastern Cape province to implement Outcomes-Based Education in an Education Development centre. Abstract Curriculum 2005 premised on Outcomes-Based Education is the new curriculum framework for South Africa. It signifies a paradigm shift in education from the traditional 'telling-listening' relationship between the teacher and the learner to one that emphasises leamer-centred approach to the teaching process. Teachers, though recognized as crucial to the educational transformation process in the country have also being identified as ill-equipped to meet the challenges posed by Outcomes-Based Education. This study starts with a brief overview of the South African curriculum and the main tenets underlying Outcomes-Based Education. The institutional conditions and whether the lecturers at a college in the Eastern Cape province perceive the need for a change in their classroom practice were also investigated. Bearing in mind the need for further research to validate the findings of this study, positive indicators that emerged from the study suggest the readiness of the college to implement Outcomes-Based Education at the proposed Education Development Centre.
- Full Text:
- Date Issued: 2001
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