An analysis of mathematical connections in the presentations of fraction concepts in Namibian grade 7 mathematics textbooks
- Authors: Sibeso, Pumulo Priscah
- Date: 2024-04-05
- Subjects: Uncatalogued
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/436488 , vital:73276
- Description: This study investigated how selected grade 11 mathematics learners used smartphones with the MathCityMap application to learn trigonometry outdoors for conceptual understanding. The aim of this research project was to explore outdoor mathematics learning for conceptual understanding using smartphones. This case study of grade 11 mathematics learners in Lejweleputswa District in the Free State Province, was informed by the Realistic Mathematics Education theory. The study is grounded within an interpretive paradigm and used the explanatory sequential mixed-method design. Forty-two grade 11 mathematics learners participated in the survey and from these 12 were purposively selected to participate in walking the mathematics trails and interviews. The findings revealed that, while the grade 11 mathematics learners acknowledged the significance and value of using smartphones for learning mathematics, they were prohibited from carrying or using smartphones on the school premises, as part of the school code of conduct. The preferred use of smartphones for learning mathematics was understandable, as the survey was conducted at a time when the COVID-19 pandemic and associated restrictions were still in place. The survey unearthed that among applications for learning mathematics, the MathCityMap application was not known by the learners who participated in the survey. Mathematics trails observations indicated that outdoor tasks were a source of mathematical concepts or formal mathematical knowledge, and enabled learners to reinvent mathematical ideas and concepts with adult guidance. Learners were able to make use of appropriate mathematical models and connections. The mathematics trails ignited robust discussions among learners, and prompted learners to draw from prior knowledge, and recognise and identify suitable mathematical models and shapes from the real-world objects. Learners were able to use multiple representations, make necessary mathematical links, and use their prior knowledge to enhance their trigonometry conceptual understanding. This study concluded that using smartphones with the MathCityMap application could enhance conceptual understanding of trigonometry. The implications for teachers are that learners should be exposed to outdoor mathematics learning using smartphones with the MathCityMap application to improve their conceptual understanding. It is hoped that the results of this study can be used by various stakeholders, who include, inter alia, mathematics subject advisors and teacher training institutions, to enhance learners’ conceptual understanding of mathematics. , Thesis (MEd) -- Faculty of Education, Secondary and Post School Education, 2024
- Full Text:
- Date Issued: 2024-04-05
- Authors: Sibeso, Pumulo Priscah
- Date: 2024-04-05
- Subjects: Uncatalogued
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/436488 , vital:73276
- Description: This study investigated how selected grade 11 mathematics learners used smartphones with the MathCityMap application to learn trigonometry outdoors for conceptual understanding. The aim of this research project was to explore outdoor mathematics learning for conceptual understanding using smartphones. This case study of grade 11 mathematics learners in Lejweleputswa District in the Free State Province, was informed by the Realistic Mathematics Education theory. The study is grounded within an interpretive paradigm and used the explanatory sequential mixed-method design. Forty-two grade 11 mathematics learners participated in the survey and from these 12 were purposively selected to participate in walking the mathematics trails and interviews. The findings revealed that, while the grade 11 mathematics learners acknowledged the significance and value of using smartphones for learning mathematics, they were prohibited from carrying or using smartphones on the school premises, as part of the school code of conduct. The preferred use of smartphones for learning mathematics was understandable, as the survey was conducted at a time when the COVID-19 pandemic and associated restrictions were still in place. The survey unearthed that among applications for learning mathematics, the MathCityMap application was not known by the learners who participated in the survey. Mathematics trails observations indicated that outdoor tasks were a source of mathematical concepts or formal mathematical knowledge, and enabled learners to reinvent mathematical ideas and concepts with adult guidance. Learners were able to make use of appropriate mathematical models and connections. The mathematics trails ignited robust discussions among learners, and prompted learners to draw from prior knowledge, and recognise and identify suitable mathematical models and shapes from the real-world objects. Learners were able to use multiple representations, make necessary mathematical links, and use their prior knowledge to enhance their trigonometry conceptual understanding. This study concluded that using smartphones with the MathCityMap application could enhance conceptual understanding of trigonometry. The implications for teachers are that learners should be exposed to outdoor mathematics learning using smartphones with the MathCityMap application to improve their conceptual understanding. It is hoped that the results of this study can be used by various stakeholders, who include, inter alia, mathematics subject advisors and teacher training institutions, to enhance learners’ conceptual understanding of mathematics. , Thesis (MEd) -- Faculty of Education, Secondary and Post School Education, 2024
- Full Text:
- Date Issued: 2024-04-05
Exploring grade 11 learners’ mathematical problem-solving skills using Polka’s model during the learning of Euclidean geometry
- Authors: Hlupeni, Ratham
- Date: 2024-04-05
- Subjects: Uncatalogued
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/436465 , vital:73274
- Description: The skill of Problem-solving in Mathematics is very imperative. Poor performance by most South African learners in schools and international tests such as the Trends in International Mathematics and Science, calls for emphasis to be placed on problem-solving in the teaching and learning of Mathematics. Euclidean Geometry is perceived, especially by learners, to be one of the difficult components of Mathematics. Thus, the aim of this study was to explore and develop the mathematical problem-solving and geometric skills of Grade 11 learners in Euclidean Geometry. Polya’s model of problem-solving was employed in geometric skills development as a tool for intervention. The concepts Geometry and problem-solving formed the conceptual framework of the study, while the social cognitive theory constituted the theoretical framework. A case study was used as the main research method following a mixed method approach within an interpretivist paradigm. Purposive and convenience sampling methods were used in the selection of both the Mathematics class and the six learners whose work was further observed and analysed. Data about the geometric skills displayed by the learners was gathered using a moderated pre-intervention test; observations; document analysis; a moderated post-intervention test; and focus group interviews. Data was analysed quantitatively using descriptive statistics and qualitatively using thematic analysis. In the pre-intervention test, learners did not bring with them expected geometric skills to the classroom before they were introduced to grade11 Geometry content and when doing problem-solving during intervention, the four stages of model used were not necessarily following each other in a linear sequence with most of the learners not applying the fourth stage “look back”. In the post intervention test, the frequency of use and application of most geometric skills improved in comparison to the pre-intervention test; the frequency of correct and inappropriate application of the skills increased at the expense of incorrect application. Learners appreciated the four stages model and gave their views related to the challenged faced during the use of the four stages model and the challenges revealed include: practice related challenges, challenges specific to certain learners, concept related challenges, curriculum-related challenges, model application challenge, and context related challenges. The study concludes that the effective use of Polyas’ four stages model can yield great results in developing learners’ geometric and problem-solving skills. The study recommends that teachers give more attention to prior geometric knowledge, teaching of geometric theorems, teaching of geometric problem-solving, and the learning environment. , Thesis (MEd) -- Faculty of Education, Secondary and Post School Education, 2024
- Full Text:
- Date Issued: 2024-04-05
- Authors: Hlupeni, Ratham
- Date: 2024-04-05
- Subjects: Uncatalogued
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/436465 , vital:73274
- Description: The skill of Problem-solving in Mathematics is very imperative. Poor performance by most South African learners in schools and international tests such as the Trends in International Mathematics and Science, calls for emphasis to be placed on problem-solving in the teaching and learning of Mathematics. Euclidean Geometry is perceived, especially by learners, to be one of the difficult components of Mathematics. Thus, the aim of this study was to explore and develop the mathematical problem-solving and geometric skills of Grade 11 learners in Euclidean Geometry. Polya’s model of problem-solving was employed in geometric skills development as a tool for intervention. The concepts Geometry and problem-solving formed the conceptual framework of the study, while the social cognitive theory constituted the theoretical framework. A case study was used as the main research method following a mixed method approach within an interpretivist paradigm. Purposive and convenience sampling methods were used in the selection of both the Mathematics class and the six learners whose work was further observed and analysed. Data about the geometric skills displayed by the learners was gathered using a moderated pre-intervention test; observations; document analysis; a moderated post-intervention test; and focus group interviews. Data was analysed quantitatively using descriptive statistics and qualitatively using thematic analysis. In the pre-intervention test, learners did not bring with them expected geometric skills to the classroom before they were introduced to grade11 Geometry content and when doing problem-solving during intervention, the four stages of model used were not necessarily following each other in a linear sequence with most of the learners not applying the fourth stage “look back”. In the post intervention test, the frequency of use and application of most geometric skills improved in comparison to the pre-intervention test; the frequency of correct and inappropriate application of the skills increased at the expense of incorrect application. Learners appreciated the four stages model and gave their views related to the challenged faced during the use of the four stages model and the challenges revealed include: practice related challenges, challenges specific to certain learners, concept related challenges, curriculum-related challenges, model application challenge, and context related challenges. The study concludes that the effective use of Polyas’ four stages model can yield great results in developing learners’ geometric and problem-solving skills. The study recommends that teachers give more attention to prior geometric knowledge, teaching of geometric theorems, teaching of geometric problem-solving, and the learning environment. , Thesis (MEd) -- Faculty of Education, Secondary and Post School Education, 2024
- Full Text:
- Date Issued: 2024-04-05
Exploring outdoor mathematics learning for conceptual understanding through smartphones
- Authors: Pop, Vuyani Samuel
- Date: 2024-04-05
- Subjects: Uncatalogued
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/436477 , vital:73275
- Description: This study investigated how selected grade 11 mathematics learners used smartphones with the MathCityMap application to learn trigonometry outdoors for conceptual understanding. The aim of this research project was to explore outdoor mathematics learning for conceptual understanding using smartphones. This case study of grade 11 mathematics learners in Lejweleputswa District in the Free State Province, was informed by the Realistic Mathematics Education theory. The study is grounded within an interpretive paradigm and used the explanatory sequential mixed-method design. Forty-two grade 11 mathematics learners participated in the survey and from these 12 were purposively selected to participate in walking the mathematics trails and interviews. The findings revealed that, while the grade 11 mathematics learners acknowledged the significance and value of using smartphones for learning mathematics, they were prohibited from carrying or using smartphones on the school premises, as part of the school code of conduct. The preferred use of smartphones for learning mathematics was understandable, as the survey was conducted at a time when the COVID-19 pandemic and associated restrictions were still in place. The survey unearthed that among applications for learning mathematics, the MathCityMap application was not known by the learners who participated in the survey. Mathematics trails observations indicated that outdoor tasks were a source of mathematical concepts or formal mathematical knowledge, and enabled learners to reinvent mathematical ideas and concepts with adult guidance. Learners were able to make use of appropriate mathematical models and connections. The mathematics trails ignited robust discussions among learners, and prompted learners to draw from prior knowledge, and recognise and identify suitable mathematical models and shapes from the real-world objects. Learners were able to use multiple representations, make necessary mathematical links, and use their prior knowledge to enhance their trigonometry conceptual understanding. This study concluded that using smartphones with the MathCityMap application could enhance conceptual understanding of trigonometry. The implications for teachers are that learners should be exposed to outdoor mathematics learning using smartphones with the MathCityMap application to improve their conceptual understanding. It is hoped that the results of this study can be used by various stakeholders, who include, inter alia, mathematics subject advisors and teacher training institutions, to enhance learners’ conceptual understanding of mathematics. , Thesis (MEd) -- Faculty of Education, Secondary and Post School Education, 2024
- Full Text:
- Date Issued: 2024-04-05
- Authors: Pop, Vuyani Samuel
- Date: 2024-04-05
- Subjects: Uncatalogued
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/436477 , vital:73275
- Description: This study investigated how selected grade 11 mathematics learners used smartphones with the MathCityMap application to learn trigonometry outdoors for conceptual understanding. The aim of this research project was to explore outdoor mathematics learning for conceptual understanding using smartphones. This case study of grade 11 mathematics learners in Lejweleputswa District in the Free State Province, was informed by the Realistic Mathematics Education theory. The study is grounded within an interpretive paradigm and used the explanatory sequential mixed-method design. Forty-two grade 11 mathematics learners participated in the survey and from these 12 were purposively selected to participate in walking the mathematics trails and interviews. The findings revealed that, while the grade 11 mathematics learners acknowledged the significance and value of using smartphones for learning mathematics, they were prohibited from carrying or using smartphones on the school premises, as part of the school code of conduct. The preferred use of smartphones for learning mathematics was understandable, as the survey was conducted at a time when the COVID-19 pandemic and associated restrictions were still in place. The survey unearthed that among applications for learning mathematics, the MathCityMap application was not known by the learners who participated in the survey. Mathematics trails observations indicated that outdoor tasks were a source of mathematical concepts or formal mathematical knowledge, and enabled learners to reinvent mathematical ideas and concepts with adult guidance. Learners were able to make use of appropriate mathematical models and connections. The mathematics trails ignited robust discussions among learners, and prompted learners to draw from prior knowledge, and recognise and identify suitable mathematical models and shapes from the real-world objects. Learners were able to use multiple representations, make necessary mathematical links, and use their prior knowledge to enhance their trigonometry conceptual understanding. This study concluded that using smartphones with the MathCityMap application could enhance conceptual understanding of trigonometry. The implications for teachers are that learners should be exposed to outdoor mathematics learning using smartphones with the MathCityMap application to improve their conceptual understanding. It is hoped that the results of this study can be used by various stakeholders, who include, inter alia, mathematics subject advisors and teacher training institutions, to enhance learners’ conceptual understanding of mathematics. , Thesis (MEd) -- Faculty of Education, Secondary and Post School Education, 2024
- Full Text:
- Date Issued: 2024-04-05
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