Teachers’ use of authentic tasks through mathematics trails in a mobile learning environment to facilitate conceptual teaching
- Authors: Matengu, Given Kahale
- Date: 2024-10-11
- Subjects: Uncatalogued
- Language: English
- Type: Academic theses , Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/466429 , vital:76727 , DOI https://doi.org/10.21504/10962/466429
- Description: The teaching and learning of mathematics in Namibia is confronted by various forms of challenges that require continuous search for effective pedagogical strategies and approaches to enhance mathematical understanding. Some of the ways include using real and authentic outdoor activities and technological tools, such as smartphones, for teaching and learning purposes. The need to use authentic and realistic tasks in outdoor settings in the teaching of mathematics has strong support from the literature. Moreover, many recent reforms in education challenge teachers across all subjects to use modern and up-to-date technologies to complement and support existing approaches to teaching. Smartphones, in particular, offer new opportunities in the evolution of technology-enhanced learning by allowing teaching and learning to occur in authentic and realistic contexts that extend to real-life environments. This qualitative case study proposes a practical framework that can facilitate mathematical understanding in teaching through the implementation of authentic and realistic outdoor tasks by using the Math City Map (MCM) project on a smartphone. The study aims to analyse and understand how mathematics teachers can create and implement authentic and realistic tasks in an outdoor mathematics trail to facilitate the conceptual teaching of area, volume, ratio and proportion topics, within the context of the Realistic Mathematics Education theory (RME). The study is framed within the RME theory and the iPAC (personalisation, authenticity, collaboration) mobile pedagogical framework. The research process is underpinned by an interpretivist paradigm. Data was collected from eight selected teachers through observations and interviews and analysed using frameworks derived from the RME and iPAC mobile pedagogical theories and the emergence of common themes. The findings suggest that the integration of smartphones and mathematics trails have pedagogical benefits in mathematics teaching and can facilitate the use of outdoor tasks that are connected to learners’ realities. The study argues that while MCM mathematics trail tasks can be difficult to create, it was worthwhile for teachers using them to conceptually teach the selected topics. It is therefore hoped that the findings of this study contribute towards the use of outdoor mathematics trails and smartphones in the teaching of mathematics. , Thesis (PhD) -- Faculty of Education, Secondary and Post-School Education, 2024
- Full Text:
- Date Issued: 2024-10-11
- Authors: Matengu, Given Kahale
- Date: 2024-10-11
- Subjects: Uncatalogued
- Language: English
- Type: Academic theses , Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/466429 , vital:76727 , DOI https://doi.org/10.21504/10962/466429
- Description: The teaching and learning of mathematics in Namibia is confronted by various forms of challenges that require continuous search for effective pedagogical strategies and approaches to enhance mathematical understanding. Some of the ways include using real and authentic outdoor activities and technological tools, such as smartphones, for teaching and learning purposes. The need to use authentic and realistic tasks in outdoor settings in the teaching of mathematics has strong support from the literature. Moreover, many recent reforms in education challenge teachers across all subjects to use modern and up-to-date technologies to complement and support existing approaches to teaching. Smartphones, in particular, offer new opportunities in the evolution of technology-enhanced learning by allowing teaching and learning to occur in authentic and realistic contexts that extend to real-life environments. This qualitative case study proposes a practical framework that can facilitate mathematical understanding in teaching through the implementation of authentic and realistic outdoor tasks by using the Math City Map (MCM) project on a smartphone. The study aims to analyse and understand how mathematics teachers can create and implement authentic and realistic tasks in an outdoor mathematics trail to facilitate the conceptual teaching of area, volume, ratio and proportion topics, within the context of the Realistic Mathematics Education theory (RME). The study is framed within the RME theory and the iPAC (personalisation, authenticity, collaboration) mobile pedagogical framework. The research process is underpinned by an interpretivist paradigm. Data was collected from eight selected teachers through observations and interviews and analysed using frameworks derived from the RME and iPAC mobile pedagogical theories and the emergence of common themes. The findings suggest that the integration of smartphones and mathematics trails have pedagogical benefits in mathematics teaching and can facilitate the use of outdoor tasks that are connected to learners’ realities. The study argues that while MCM mathematics trail tasks can be difficult to create, it was worthwhile for teachers using them to conceptually teach the selected topics. It is therefore hoped that the findings of this study contribute towards the use of outdoor mathematics trails and smartphones in the teaching of mathematics. , Thesis (PhD) -- Faculty of Education, Secondary and Post-School Education, 2024
- Full Text:
- Date Issued: 2024-10-11
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
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