An analysis of visualization processes used by selected Grade 11 and 12 learners when solving algebraic problems: a Namibian case study
- Authors: Josef, Joseane
- Date: 2017
- Subjects: Visualization , Mathematics -- Study and teaching -- Namibia -- Case studies , Mathematics -- Study and teaching (Secondary) -- Activity programs , Algebra -- Study and teaching (Secondary) -- Namibia -- Case studies
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/7843 , vital:21309
- Description: Visualisation is gaining visibility in mathematics education research. It is a powerful tool for solving different types of problems in many areas of mathematics, including Algebra - the mathematical domain of this study. The aim of this case study was to analyse the visualisation processes that selected senior secondary school learners used to solve a set of ten algebraic problems.The research was conducted at a secondary school in the Erongo region of Namibia. This is the school where the researcher is teaching. The sample consisted of six selected learners, three from Grade 11 and three from Grade 12. The learners were purposefully selected to participate in this study based on their mathematics performance in class and their willingness to participate. The participants were video recorded as they worked through the ten items of an Algebraic Visualisation Tasks (AVT) worksheet. They were also interviewed about the visualisation processes they employed when solving each of the tasks. The AVT, the videos and the interviews were analysed with the aid of an adapted visualisation template. The findings of the study show that learners used visualisations in all their problem-solving processes. These visualisations were used for different purposes such as starting points, for illustrative purposes, as organizational tools and as simplification tools. Visualisations as starting points were used when the problem was wordy and had lengthy descriptions and explanations. Illustrative visualisations enabled learners to articulate in their own way mathematical notations, mathematical equations and expressions that they then used to solve the problem. Organizational pictures provided a useful structural framework for solving the problems.This research suggests that the selected participants indeed used visualisation processes to solve algebraic problems. It is thus important for teachers to harness this aid and make the most use of these visualisation processes when teaching Algebra.
- Full Text:
- Date Issued: 2017
- Authors: Josef, Joseane
- Date: 2017
- Subjects: Visualization , Mathematics -- Study and teaching -- Namibia -- Case studies , Mathematics -- Study and teaching (Secondary) -- Activity programs , Algebra -- Study and teaching (Secondary) -- Namibia -- Case studies
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/7843 , vital:21309
- Description: Visualisation is gaining visibility in mathematics education research. It is a powerful tool for solving different types of problems in many areas of mathematics, including Algebra - the mathematical domain of this study. The aim of this case study was to analyse the visualisation processes that selected senior secondary school learners used to solve a set of ten algebraic problems.The research was conducted at a secondary school in the Erongo region of Namibia. This is the school where the researcher is teaching. The sample consisted of six selected learners, three from Grade 11 and three from Grade 12. The learners were purposefully selected to participate in this study based on their mathematics performance in class and their willingness to participate. The participants were video recorded as they worked through the ten items of an Algebraic Visualisation Tasks (AVT) worksheet. They were also interviewed about the visualisation processes they employed when solving each of the tasks. The AVT, the videos and the interviews were analysed with the aid of an adapted visualisation template. The findings of the study show that learners used visualisations in all their problem-solving processes. These visualisations were used for different purposes such as starting points, for illustrative purposes, as organizational tools and as simplification tools. Visualisations as starting points were used when the problem was wordy and had lengthy descriptions and explanations. Illustrative visualisations enabled learners to articulate in their own way mathematical notations, mathematical equations and expressions that they then used to solve the problem. Organizational pictures provided a useful structural framework for solving the problems.This research suggests that the selected participants indeed used visualisation processes to solve algebraic problems. It is thus important for teachers to harness this aid and make the most use of these visualisation processes when teaching Algebra.
- Full Text:
- Date Issued: 2017
Understanding the differences in marking performance of JSC mathematics markers in Namibia : a case study
- Authors: Mutuku, Elizabeth
- Date: 2009
- Subjects: Educational change -- Namibia , Mathematics -- Namibia -- Examinations -- Case studies , Mathematics -- Study and teaching -- Namibia -- Case studies , Grading and marking (Students) -- Namibia -- Case studies
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1999 , http://hdl.handle.net/10962/d1015223
- Description: Education reform in Namibia brought about changes to mathematics education since independence. This has put pressure on the government to provide both resources and qualified mathematics teachers to help drive the reform process in all teaching and learning activities. This included availing reliable and valid national examination results which is a measure of whether the newly introduced programmes are working or not. For the Ministry of Education this meant training more mathematics teachers and ensuring that competent and reliable teachers are appointed for marking national examination every year. The teachers' training process however, has not been going as fast as it was expected and year after year the Directorate of National Examinations and Assessment experienced problems in obtaining competent teachers for the marking of national examination. The purpose of the study was to understand the differences in marking performances of the JSC mathematics national examination markers. Particularly the study was to create a clear and detailed understanding of different factors that could possibly affect the marking performance of different markers. In addition, the study was to investigate the effect the mathematical content knowledge of the markers has on their marking performance. It was evident from the findings that their mathematical content knowledge had influenced their marking performance. Moreover the research findings also gave a strong indication that there are other factors that were influencing the markers marking performance. These were the markers' knowledge of the assessment and marking process, the markers' marking experience, the markers' socioeconomic background. The difference in their moderators' input has emerged as the other factors that have influenced their performance in marking and consequently contributed to the differences in their marking performances.
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- Date Issued: 2009
- Authors: Mutuku, Elizabeth
- Date: 2009
- Subjects: Educational change -- Namibia , Mathematics -- Namibia -- Examinations -- Case studies , Mathematics -- Study and teaching -- Namibia -- Case studies , Grading and marking (Students) -- Namibia -- Case studies
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1999 , http://hdl.handle.net/10962/d1015223
- Description: Education reform in Namibia brought about changes to mathematics education since independence. This has put pressure on the government to provide both resources and qualified mathematics teachers to help drive the reform process in all teaching and learning activities. This included availing reliable and valid national examination results which is a measure of whether the newly introduced programmes are working or not. For the Ministry of Education this meant training more mathematics teachers and ensuring that competent and reliable teachers are appointed for marking national examination every year. The teachers' training process however, has not been going as fast as it was expected and year after year the Directorate of National Examinations and Assessment experienced problems in obtaining competent teachers for the marking of national examination. The purpose of the study was to understand the differences in marking performances of the JSC mathematics national examination markers. Particularly the study was to create a clear and detailed understanding of different factors that could possibly affect the marking performance of different markers. In addition, the study was to investigate the effect the mathematical content knowledge of the markers has on their marking performance. It was evident from the findings that their mathematical content knowledge had influenced their marking performance. Moreover the research findings also gave a strong indication that there are other factors that were influencing the markers marking performance. These were the markers' knowledge of the assessment and marking process, the markers' marking experience, the markers' socioeconomic background. The difference in their moderators' input has emerged as the other factors that have influenced their performance in marking and consequently contributed to the differences in their marking performances.
- Full Text:
- Date Issued: 2009
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