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:
- Date Issued: 2023-10-13
- 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:
- Date Issued: 2023-10-13
The incorporation of GeoGebra as a visualisation tool to teach calculus in teacher education institutions: the Zambian case
- Authors: Kangwa, Lemmy
- Date: 2022-10-14
- Subjects: GeoGebra , Calculus Study and teaching (Secondary) Zambia , Visual learning
- Language: English
- Type: Academic theses , Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/405470 , vital:70174 , DOI
- Description: This qualitative case study investigated teacher educators’ (lecturers) use of the dynamic mathematics software, GeoGebra, to teach calculus in three teacher education institutions (TEIs) in Zambia. Visualisation, a key characteristic of GeoGebra, is increasingly gaining recognition of playing a critical role in mathematics teaching and learning, especially in problem solving tasks. It is considered a powerful didactical tool for students to construct mental and physical representations that can enhance conceptual understanding of mathematics. GeoGebra is a visualisation tool that can be used for problem-oriented teaching and foster mathematical experiments and discoveries. GeoGebra’s inherent visualisation characteristics align well with the teaching of calculus, the mathematical domain of this study. The study (whose research methodology was underpinned by the interpretive paradigm) was undertaken with a broader goal of designing and implementing GeoGebra applets and instructional materials on various calculus topics. The study is located within the “Teaching and Learning Mathematics with GeoGebra (TLMG) project” – a project that involves mathematics teachers and lecturers in Zambia. The case in this study is the six mathematics lecturers who co-designed and used GeoGebra applets to teach derivatives and integrals to pre-service mathematics teachers in TEIs. The unit of analysis therefore is the six lecturers’ use of GeoGebra as a visualisation tool to teach calculus to enhance conceptual understanding, their perceptions and experiences of using GeoGebra and the enabling and constraining factors of using GeoGebra to teach and learn mathematics. The data for the study were video recordings of observations and interviews of lecturers. The data was analysed thematically and was guided and informed by an analytical framework adopted from the theory of constructivism – the umbrella theoretical framework of this study – and the models of Technological Pedagogical Content Knowledge (TPACK), and the Technology Acceptance Model (TAM). A detailed analysis of the lecturers’ interactions with the applets enabled me to gain insights into the participants’ experiences and perceptions of GeoGebra applets in the teaching and learning process. The findings of the study revealed that the visualisation characteristics of GeoGebra generally enhanced the conceptual understanding of calculus. It also revealed that adequate training, coupled with sufficient knowledge of the subject matter in calculus, were necessary for lecturers to use GeoGebra effectively, and that the lack of resources and expertise were major hindrances in the use of GeoGebra to teach mathematics in TEIs. It also revealed that there is a need to equip GeoGebra with other features that would make it more versatile, and suggested a teaching approach that would complement the use of conventional methods and GeoGebra to provide a link between abstract and concrete concepts of calculus. , Thesis (PhD) -- Faculty of Education, Education, 2022
- Full Text:
- Date Issued: 2022-10-14
- Authors: Kangwa, Lemmy
- Date: 2022-10-14
- Subjects: GeoGebra , Calculus Study and teaching (Secondary) Zambia , Visual learning
- Language: English
- Type: Academic theses , Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/405470 , vital:70174 , DOI
- Description: This qualitative case study investigated teacher educators’ (lecturers) use of the dynamic mathematics software, GeoGebra, to teach calculus in three teacher education institutions (TEIs) in Zambia. Visualisation, a key characteristic of GeoGebra, is increasingly gaining recognition of playing a critical role in mathematics teaching and learning, especially in problem solving tasks. It is considered a powerful didactical tool for students to construct mental and physical representations that can enhance conceptual understanding of mathematics. GeoGebra is a visualisation tool that can be used for problem-oriented teaching and foster mathematical experiments and discoveries. GeoGebra’s inherent visualisation characteristics align well with the teaching of calculus, the mathematical domain of this study. The study (whose research methodology was underpinned by the interpretive paradigm) was undertaken with a broader goal of designing and implementing GeoGebra applets and instructional materials on various calculus topics. The study is located within the “Teaching and Learning Mathematics with GeoGebra (TLMG) project” – a project that involves mathematics teachers and lecturers in Zambia. The case in this study is the six mathematics lecturers who co-designed and used GeoGebra applets to teach derivatives and integrals to pre-service mathematics teachers in TEIs. The unit of analysis therefore is the six lecturers’ use of GeoGebra as a visualisation tool to teach calculus to enhance conceptual understanding, their perceptions and experiences of using GeoGebra and the enabling and constraining factors of using GeoGebra to teach and learn mathematics. The data for the study were video recordings of observations and interviews of lecturers. The data was analysed thematically and was guided and informed by an analytical framework adopted from the theory of constructivism – the umbrella theoretical framework of this study – and the models of Technological Pedagogical Content Knowledge (TPACK), and the Technology Acceptance Model (TAM). A detailed analysis of the lecturers’ interactions with the applets enabled me to gain insights into the participants’ experiences and perceptions of GeoGebra applets in the teaching and learning process. The findings of the study revealed that the visualisation characteristics of GeoGebra generally enhanced the conceptual understanding of calculus. It also revealed that adequate training, coupled with sufficient knowledge of the subject matter in calculus, were necessary for lecturers to use GeoGebra effectively, and that the lack of resources and expertise were major hindrances in the use of GeoGebra to teach mathematics in TEIs. It also revealed that there is a need to equip GeoGebra with other features that would make it more versatile, and suggested a teaching approach that would complement the use of conventional methods and GeoGebra to provide a link between abstract and concrete concepts of calculus. , Thesis (PhD) -- Faculty of Education, Education, 2022
- Full Text:
- Date Issued: 2022-10-14
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