An analysis of how the use of geoboards as visualisation tools can be utilised in the teaching of quadrilaterals
- Authors: Matengu, Given Kahale
- Date: 2019
- Subjects: Manipulatives (Education) , Information visualization , Visualization , Mathematics -- Study and teaching , Mathematics -- Study and teaching -- Activity programs , Geometry -- Study and teaching
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/96724 , vital:31312
- Description: The relationship between visualisation processes and using manipulatives in the teaching and learning of mathematics is apparent and yet not so vocal in the literature. This could be because of the common mistaken understanding that because manipulatives are visual in nature, then visualisation processes should be obvious. Literature warns that just because something is visual therefore it is transparent, is incorrect. This study argues that the effective use of manipulatives in the teaching of mathematics helps learners to effectively understand mathematical concepts. Research on the teaching and learning of mathematics suggests that physical manipulation experiences, especially of concrete materials concerning shapes, is an important process in learning at all ages. One such teaching tool, the Geoboard, a physical manipulative that employs visualisation processes when correctly used, is explored in this study. The aim of this interpretive case study was to investigate and analyse the use of Geoboards as a visualisation tool in the teaching of the properties of quadrilaterals. The study focused on visualisation processes and the use of Geoboards through a teaching framework that was informed by the Van Hiele phases of teaching geometry. The study was conducted in the Opuwo circuit of the Kunene region, Namibia, and it involved three selected Grade 7 mathematics teachers, each from a different primary school. It was underpinned by a constructivist theory using the Van Hiele phases of teaching geometry and framed within visualisation processes. The study employed the use of qualitative data collection techniques such as observations and interviews. The analysis of the findings of this study revealed that Geoboards were very useful in demonstrating the visual representations of the properties of quadrilaterals in a cheap and yet novel way in the selected teachers’ classes. Moreover, the use of Geoboards by the selected teachers effectively fostered visualisation processes such as concrete pictorial imagery, dynamic imagery, perceptual apprehension, sequential apprehension, discursive apprehension and operative apprehension. It was also revealed that Geoboards enabled the selected teachers to structure and teach their lessons in a well-planned manner according to the Van Hiele phases, although it was difficult for them to adhere strictly to the hierarchy of the phases.
- Full Text:
- Date Issued: 2019
- Authors: Matengu, Given Kahale
- Date: 2019
- Subjects: Manipulatives (Education) , Information visualization , Visualization , Mathematics -- Study and teaching , Mathematics -- Study and teaching -- Activity programs , Geometry -- Study and teaching
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/96724 , vital:31312
- Description: The relationship between visualisation processes and using manipulatives in the teaching and learning of mathematics is apparent and yet not so vocal in the literature. This could be because of the common mistaken understanding that because manipulatives are visual in nature, then visualisation processes should be obvious. Literature warns that just because something is visual therefore it is transparent, is incorrect. This study argues that the effective use of manipulatives in the teaching of mathematics helps learners to effectively understand mathematical concepts. Research on the teaching and learning of mathematics suggests that physical manipulation experiences, especially of concrete materials concerning shapes, is an important process in learning at all ages. One such teaching tool, the Geoboard, a physical manipulative that employs visualisation processes when correctly used, is explored in this study. The aim of this interpretive case study was to investigate and analyse the use of Geoboards as a visualisation tool in the teaching of the properties of quadrilaterals. The study focused on visualisation processes and the use of Geoboards through a teaching framework that was informed by the Van Hiele phases of teaching geometry. The study was conducted in the Opuwo circuit of the Kunene region, Namibia, and it involved three selected Grade 7 mathematics teachers, each from a different primary school. It was underpinned by a constructivist theory using the Van Hiele phases of teaching geometry and framed within visualisation processes. The study employed the use of qualitative data collection techniques such as observations and interviews. The analysis of the findings of this study revealed that Geoboards were very useful in demonstrating the visual representations of the properties of quadrilaterals in a cheap and yet novel way in the selected teachers’ classes. Moreover, the use of Geoboards by the selected teachers effectively fostered visualisation processes such as concrete pictorial imagery, dynamic imagery, perceptual apprehension, sequential apprehension, discursive apprehension and operative apprehension. It was also revealed that Geoboards enabled the selected teachers to structure and teach their lessons in a well-planned manner according to the Van Hiele phases, although it was difficult for them to adhere strictly to the hierarchy of the phases.
- Full Text:
- Date Issued: 2019
An analysis of how visualisation processes can be used by teachers participating in an intervention programme to teach for conceptual understanding of geometry
- Authors: Muhembo, Gottfried Mbundu
- Date: 2018
- Subjects: Geometry -- Study and teaching (Secondary) -- Namibia -- Kavango East , Visualization , Mathematics teachers -- Namibia -- Kavango East , Effective teaching -- Namibia -- Kavango East , Mathematics -- Study and teaching -- Activity programs
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/62439 , vital:28190
- Description: Visualisation in general and visualisation processes in particular have received much attention in the mathematics education research literature. Literature suggests that the appropriate use of visualisation helps learners to develop their conceptual understanding and skills of geometry as it allows them to visually interpret and understand fundamental mathematical and geometrical concepts. It is claimed that visual tools play an important role in communicating mathematical ideas through diagrams, gestures, images, sketches or drawings. Learning mathematics through visualisation can be a powerful tool to explore mathematical problems and give meaning to mathematical concepts and relationships between them. This interpretive case study focused on how selected teachers taught concepts in geometry through visualisation processes for conceptual understanding as a result of an intervention programme. The study was conducted at four high schools by four mathematics teachers in the Kavango East Region in Northern Namibia. The participants were involved in a three-week intervention programme and afterwards taught three lessons each on the topic of geometry. The data collection method of this research was: focus group and stimulus recall interviews, classroom observations and recorded videos. This research is located in constructivism. I used vertical and horizontal analysis strategies to analyse the data. My analytical instrument consisted of an observation schedule which I used in each lesson to identify how each of the visualisation processes was evident in each of the observed lessons. This study revealed that the participant teachers used visualisation processes in most of their lessons and these processes were used accurately in line with the requirements of the grade 8 mathematics syllabi. The visualisation processes were used through designed visual materials, posters and through the use of geometrical objects such as chalkboard ruler, protractor and compass. The results from this study also confirmed that visualisation processes can be a powerful instructional tool for enhancing learners’ conceptual understanding of geometry.
- Full Text:
- Date Issued: 2018
- Authors: Muhembo, Gottfried Mbundu
- Date: 2018
- Subjects: Geometry -- Study and teaching (Secondary) -- Namibia -- Kavango East , Visualization , Mathematics teachers -- Namibia -- Kavango East , Effective teaching -- Namibia -- Kavango East , Mathematics -- Study and teaching -- Activity programs
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/62439 , vital:28190
- Description: Visualisation in general and visualisation processes in particular have received much attention in the mathematics education research literature. Literature suggests that the appropriate use of visualisation helps learners to develop their conceptual understanding and skills of geometry as it allows them to visually interpret and understand fundamental mathematical and geometrical concepts. It is claimed that visual tools play an important role in communicating mathematical ideas through diagrams, gestures, images, sketches or drawings. Learning mathematics through visualisation can be a powerful tool to explore mathematical problems and give meaning to mathematical concepts and relationships between them. This interpretive case study focused on how selected teachers taught concepts in geometry through visualisation processes for conceptual understanding as a result of an intervention programme. The study was conducted at four high schools by four mathematics teachers in the Kavango East Region in Northern Namibia. The participants were involved in a three-week intervention programme and afterwards taught three lessons each on the topic of geometry. The data collection method of this research was: focus group and stimulus recall interviews, classroom observations and recorded videos. This research is located in constructivism. I used vertical and horizontal analysis strategies to analyse the data. My analytical instrument consisted of an observation schedule which I used in each lesson to identify how each of the visualisation processes was evident in each of the observed lessons. This study revealed that the participant teachers used visualisation processes in most of their lessons and these processes were used accurately in line with the requirements of the grade 8 mathematics syllabi. The visualisation processes were used through designed visual materials, posters and through the use of geometrical objects such as chalkboard ruler, protractor and compass. The results from this study also confirmed that visualisation processes can be a powerful instructional tool for enhancing learners’ conceptual understanding of geometry.
- Full Text:
- Date Issued: 2018
An analysis of selected grade 11 learners’ interactions with geometry tasks using visualization processes: a case study in Namibia
- Authors: Kabuku, Brian S
- Date: 2017
- Subjects: Mathematics -- Study and teaching -- Activity programs , Geometry -- Study and teaching (Secondary) -- Namibia , Geometry -- Study and teaching (Secondary) -- Namibia -- Cast studies , Visualization
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/5949 , vital:20997
- Description: This case study was conducted at a secondary school where I teach, situated in the semi-rural setting of Bukalo village in Namibia, and sought to gain insights into the nature and role of visualisation processes employed when selected grade 11 learners interacted with selected geometry problems. According to Mariotti and Pensci (1994), visualisation takes place when "thinking is spontaneously accompanied and supported by images”, and helps students to understand the problem at hand. Visualisation is regarded as "making the unseen visible and imagery as the power to imagine the possible and the impossible” (Mason 1992). The study is located within an interpretive research paradigm in order to obtain in-depth understanding of the participants’ visualisation processes. Within this paradigm, both quantitative and qualitative approaches were adopted. The eight Grade 11 participants engaged with 12 items of the Geometry Visualisation Tasks (GVT) worksheets. Data was collected using video-recorded learners’ interactions with the GVT, observations, stimulated recall interviews and post-GVT interviews with the learners. During the data analysis stage, I used inductive analysis to determine patterns evident in learners ‘thinking processes’. My analytical framework consisted of indicators that were used to identify and classify visualisation processes for each task of the GVT for each participant. I adapted this framework from Ho (2010) and Ho, Ramful and Lowrie’s (2015) clarification of the representations. The findings from this study revealed that the use of visualisations facilitated meaningful learning when learners made use of these to develop and scaffold their conceptual understanding. The findings revealed that most learners used visualisation processes fairly to very accurately when solving geometry problems. They used visualisation processes by using sketches and diagrams that transformed a mathematical problem pictorially, connected their thinking to previous knowledge and experience, clarified the algebraic task and assisted them to understand the spatial relationships within each task.
- Full Text:
- Date Issued: 2017
- Authors: Kabuku, Brian S
- Date: 2017
- Subjects: Mathematics -- Study and teaching -- Activity programs , Geometry -- Study and teaching (Secondary) -- Namibia , Geometry -- Study and teaching (Secondary) -- Namibia -- Cast studies , Visualization
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/5949 , vital:20997
- Description: This case study was conducted at a secondary school where I teach, situated in the semi-rural setting of Bukalo village in Namibia, and sought to gain insights into the nature and role of visualisation processes employed when selected grade 11 learners interacted with selected geometry problems. According to Mariotti and Pensci (1994), visualisation takes place when "thinking is spontaneously accompanied and supported by images”, and helps students to understand the problem at hand. Visualisation is regarded as "making the unseen visible and imagery as the power to imagine the possible and the impossible” (Mason 1992). The study is located within an interpretive research paradigm in order to obtain in-depth understanding of the participants’ visualisation processes. Within this paradigm, both quantitative and qualitative approaches were adopted. The eight Grade 11 participants engaged with 12 items of the Geometry Visualisation Tasks (GVT) worksheets. Data was collected using video-recorded learners’ interactions with the GVT, observations, stimulated recall interviews and post-GVT interviews with the learners. During the data analysis stage, I used inductive analysis to determine patterns evident in learners ‘thinking processes’. My analytical framework consisted of indicators that were used to identify and classify visualisation processes for each task of the GVT for each participant. I adapted this framework from Ho (2010) and Ho, Ramful and Lowrie’s (2015) clarification of the representations. The findings from this study revealed that the use of visualisations facilitated meaningful learning when learners made use of these to develop and scaffold their conceptual understanding. The findings revealed that most learners used visualisation processes fairly to very accurately when solving geometry problems. They used visualisation processes by using sketches and diagrams that transformed a mathematical problem pictorially, connected their thinking to previous knowledge and experience, clarified the algebraic task and assisted them to understand the spatial relationships within each task.
- Full Text:
- Date Issued: 2017
- «
- ‹
- 1
- ›
- »