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
An investigation of how Visual Technology for the Autonomous Learning of Mathematics (VITALmaths) video clips on mobile phones can be used by student teachers as a visualisation tool in the teaching of Number Sense: a case study
- Authors: Kangwa, Lemmy
- Date: 2017
- Subjects: Mathematics -- Study and teaching -- Zambia -- Case studies , Visualization , Number concept , Mobile communication systems in education , Mathematics -- Study and teaching -- Software , Telecommunications in education , Educational innovations , VITALmaths
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/6930 , vital:21201
- Description: Visualisation is increasingly being recognised as having a significant role in the learning of mathematics especially when students are solving mathematical problems (Thornton, 2001). It is argued that visualisation is a powerful tool for learners to construct mental and physical representations that correctly mirror mathematical relationships and concepts. To gain a thorough understanding of the scope of visualisation, three Visual Technology for Autonomous Learning of Mathematics (VITALmaths) (www.vitalmaths.com) video clips were uploaded on mobile phones of each of the eleven participating student teachers who used them in their teaching practice. This is in cognisance of the educational potential offered by mobile phones and their current pervasiveness in the daily lives of both teachers and learners in Zambia (Zambia. Ministry of Education [M.O.E], 2013]). This study sought to investigate how VITALmaths video clips on mobile phones could be used by student teachers as a visualisation tool in the teaching of Number Sense. The videos of the lessons formed the core of my analysis. The study was conducted at four primary schools by eleven student teachers of a public university in Zambia. The study is framed as a case study and is grounded within the interpretive paradigm. The findings revealed that the student teachers’ use of the video clips in the classrooms for teaching was generally approached from two perspectives: at the beginning of the lesson or at the end. The videos were used at the beginning of the lesson as a means to introduce a topic or an idea, and at the end of the lesson to consolidate what was taught. The videos were also used to enhance the conceptual understanding of Number Sense. The findings also revealed that students encountered both enabling and constraining factors in their use of mobile phones to teach number sense. The overall findings revealed that, if well utilised, mobile phones as visualisation tools had the potential to enhance the teaching of Mathematics in general and Number Sense in particular, and therefore teachers should be encouraged to use them in their teaching.
- Full Text:
- Date Issued: 2017
- Authors: Kangwa, Lemmy
- Date: 2017
- Subjects: Mathematics -- Study and teaching -- Zambia -- Case studies , Visualization , Number concept , Mobile communication systems in education , Mathematics -- Study and teaching -- Software , Telecommunications in education , Educational innovations , VITALmaths
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/6930 , vital:21201
- Description: Visualisation is increasingly being recognised as having a significant role in the learning of mathematics especially when students are solving mathematical problems (Thornton, 2001). It is argued that visualisation is a powerful tool for learners to construct mental and physical representations that correctly mirror mathematical relationships and concepts. To gain a thorough understanding of the scope of visualisation, three Visual Technology for Autonomous Learning of Mathematics (VITALmaths) (www.vitalmaths.com) video clips were uploaded on mobile phones of each of the eleven participating student teachers who used them in their teaching practice. This is in cognisance of the educational potential offered by mobile phones and their current pervasiveness in the daily lives of both teachers and learners in Zambia (Zambia. Ministry of Education [M.O.E], 2013]). This study sought to investigate how VITALmaths video clips on mobile phones could be used by student teachers as a visualisation tool in the teaching of Number Sense. The videos of the lessons formed the core of my analysis. The study was conducted at four primary schools by eleven student teachers of a public university in Zambia. The study is framed as a case study and is grounded within the interpretive paradigm. The findings revealed that the student teachers’ use of the video clips in the classrooms for teaching was generally approached from two perspectives: at the beginning of the lesson or at the end. The videos were used at the beginning of the lesson as a means to introduce a topic or an idea, and at the end of the lesson to consolidate what was taught. The videos were also used to enhance the conceptual understanding of Number Sense. The findings also revealed that students encountered both enabling and constraining factors in their use of mobile phones to teach number sense. The overall findings revealed that, if well utilised, mobile phones as visualisation tools had the potential to enhance the teaching of Mathematics in general and Number Sense in particular, and therefore teachers should be encouraged to use them in their teaching.
- Full Text:
- Date Issued: 2017
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