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:
- 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.
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An investigation of teachers’ experiences of a Geoboard intervention programme in area and perimeter in selected Grade 9 classes: a case study
- Authors: Mkhwane, Fezeka Felicia
- Date: 2018
- Subjects: Mathematics -- Study and teaching (Secondary) -- South Africa , Teachers -- Training of -- South Africa , Manipulatives (Education) , Effective teaching , Area measurement , Perimeters (Geometry) , Problem solving -- Study and teaching , Geoboard Intervention Programme , RUMEP
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/61646 , vital:28045
- Description: The study was undertaken with three Grade 9 teachers at three selected schools which are part of RUMEP’s Collegial Cluster Schools’ programme that I coordinate. Collegial clusters are communities of teachers who aim at improving their practice by working on their own professional development. The purpose of this study was to investigate the selected Grade 9 teachers’ experiences of a Geoboard intervention programme. It also wanted to investigate the role that a Geoboard can play in the teaching and learning of area and perimeter of two-dimensional shapes. The research was a case-study within the interpretive paradigm. A variety of data collection techniques was used. These included baseline assessment tasks, observations during the intervention programme, post intervention assessment tasks and semistructured interviews with the participating teachers and a few learners from each participating school. The collected data was analysed using both the quantitative and qualitative methods. My research findings reveal that a Geoboard, as a manipulative, developed confidence in the participating teachers. In the interviews with teachers, it transpired that teachers’ skills in teaching area and perimeter of two-dimensional shapes had been sharpened. According to the interviews with learners, the use of a Geoboard led to better conceptual understanding of the area and perimeter, as learners no longer had to rely on formulae. Kilpatrick et al. (2001) refer to conceptual understanding as an integrated functional grasp of mathematical ideas. The post intervention assessment task showed a positive shift in learners’ performance. The average learner performance improved from 29% in the baseline assessment task to 61% in the post intervention assessment task. This shows that the use of a Geoboard led to meaningful learning of area and perimeter of two-dimensional shapes. The overall research findings reveal that the use of manipulatives has a positive impact in the teaching and learning of area and perimeter. Learners’ responses to the interview questions showed that there was better understanding of the two concepts, which enabled them to construct their own knowledge. They further said the Geoboard allowed them to be hands-on, which contributed to their active involvement in the lesson.
- Full Text:
- Authors: Mkhwane, Fezeka Felicia
- Date: 2018
- Subjects: Mathematics -- Study and teaching (Secondary) -- South Africa , Teachers -- Training of -- South Africa , Manipulatives (Education) , Effective teaching , Area measurement , Perimeters (Geometry) , Problem solving -- Study and teaching , Geoboard Intervention Programme , RUMEP
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/61646 , vital:28045
- Description: The study was undertaken with three Grade 9 teachers at three selected schools which are part of RUMEP’s Collegial Cluster Schools’ programme that I coordinate. Collegial clusters are communities of teachers who aim at improving their practice by working on their own professional development. The purpose of this study was to investigate the selected Grade 9 teachers’ experiences of a Geoboard intervention programme. It also wanted to investigate the role that a Geoboard can play in the teaching and learning of area and perimeter of two-dimensional shapes. The research was a case-study within the interpretive paradigm. A variety of data collection techniques was used. These included baseline assessment tasks, observations during the intervention programme, post intervention assessment tasks and semistructured interviews with the participating teachers and a few learners from each participating school. The collected data was analysed using both the quantitative and qualitative methods. My research findings reveal that a Geoboard, as a manipulative, developed confidence in the participating teachers. In the interviews with teachers, it transpired that teachers’ skills in teaching area and perimeter of two-dimensional shapes had been sharpened. According to the interviews with learners, the use of a Geoboard led to better conceptual understanding of the area and perimeter, as learners no longer had to rely on formulae. Kilpatrick et al. (2001) refer to conceptual understanding as an integrated functional grasp of mathematical ideas. The post intervention assessment task showed a positive shift in learners’ performance. The average learner performance improved from 29% in the baseline assessment task to 61% in the post intervention assessment task. This shows that the use of a Geoboard led to meaningful learning of area and perimeter of two-dimensional shapes. The overall research findings reveal that the use of manipulatives has a positive impact in the teaching and learning of area and perimeter. Learners’ responses to the interview questions showed that there was better understanding of the two concepts, which enabled them to construct their own knowledge. They further said the Geoboard allowed them to be hands-on, which contributed to their active involvement in the lesson.
- Full Text:
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