Investigating the relationship between mathematical knowledge for teaching and self-efficacy of pre-service mathematical literacy teachers
- Van Zyl, Nicola Stephanie, Van Zyl, Marinda
- Authors: Van Zyl, Nicola Stephanie , Van Zyl, Marinda
- Date: 2016
- Subjects: Mathematics teachers -- South Africa Mathematics -- Study and teaching -- South Africa
- Language: English
- Type: Thesis , Doctoral , MEd
- Identifier: http://hdl.handle.net/10948/10849 , vital:26829
- Description: Although a good understanding of mathematical content knowledge is essential for effective mathematics teaching, this might not be enough. Mathematical knowledge for teaching (MKT) requires a kind of depth and detail special to teaching, and involves mathematical reasoning as well as thinking from a learners’ perspective. Educational outcomes are also influenced by teachers’ self-efficacy beliefs regarding their ability to teach effectively. This study was an investigation into the relationship between pre-service teachers’ mathematical knowledge for teaching (MKT) and their mathematical self-efficacy with regard to MKT. Participants in the study were 137 BEd (FET) students at Nelson Mandela Metropolitan University, specializing in Mathematical Literacy as teaching subject. The quantitative data used for the study were gathered using a questionnaire on MKT for the topics number concepts and operations. This questionnaire was designed by Deborah Ball’s Michigan research team, to which I added a question on self-efficacy for every item. An analysis of the data gathered from the questionnaire reveals interesting and disturbing trends. The results suggest that, in more than 80% of the cases, respondents were either completely sure their answer was correct, or tended to think their answer was correct, indicating high levels of self-efficacy. Since only about 40% of answers were in reality correct, this indicates that participants believed their answer to be correct, although their interpretation of the mathematical knowledge for teaching involved was incorrect. Hence: they don’t know that they don’t know! The results of this study suggest that there is a need for educators of teachers to help improve prospective mathematical literacy teachers’ mathematical knowledge for teaching. Pre-service teachers should be taught to use cognitive skills that will raise the likelihood of improved learner understanding. For this, robust understanding of the fundamental mathematics involved is needed, as well as high levels of self-efficacy with regard to the teaching of mathematics.
- Full Text:
- Date Issued: 2016
- Authors: Van Zyl, Nicola Stephanie , Van Zyl, Marinda
- Date: 2016
- Subjects: Mathematics teachers -- South Africa Mathematics -- Study and teaching -- South Africa
- Language: English
- Type: Thesis , Doctoral , MEd
- Identifier: http://hdl.handle.net/10948/10849 , vital:26829
- Description: Although a good understanding of mathematical content knowledge is essential for effective mathematics teaching, this might not be enough. Mathematical knowledge for teaching (MKT) requires a kind of depth and detail special to teaching, and involves mathematical reasoning as well as thinking from a learners’ perspective. Educational outcomes are also influenced by teachers’ self-efficacy beliefs regarding their ability to teach effectively. This study was an investigation into the relationship between pre-service teachers’ mathematical knowledge for teaching (MKT) and their mathematical self-efficacy with regard to MKT. Participants in the study were 137 BEd (FET) students at Nelson Mandela Metropolitan University, specializing in Mathematical Literacy as teaching subject. The quantitative data used for the study were gathered using a questionnaire on MKT for the topics number concepts and operations. This questionnaire was designed by Deborah Ball’s Michigan research team, to which I added a question on self-efficacy for every item. An analysis of the data gathered from the questionnaire reveals interesting and disturbing trends. The results suggest that, in more than 80% of the cases, respondents were either completely sure their answer was correct, or tended to think their answer was correct, indicating high levels of self-efficacy. Since only about 40% of answers were in reality correct, this indicates that participants believed their answer to be correct, although their interpretation of the mathematical knowledge for teaching involved was incorrect. Hence: they don’t know that they don’t know! The results of this study suggest that there is a need for educators of teachers to help improve prospective mathematical literacy teachers’ mathematical knowledge for teaching. Pre-service teachers should be taught to use cognitive skills that will raise the likelihood of improved learner understanding. For this, robust understanding of the fundamental mathematics involved is needed, as well as high levels of self-efficacy with regard to the teaching of mathematics.
- Full Text:
- Date Issued: 2016
The mining and visualisation of application services data
- Authors: Knoetze, Ronald Morgan
- Date: 2005
- Subjects: Data mining -- South Africa , Computer algorithms , Network performance (Telecommunication) -- Research -- South Africa
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:10480 , http://hdl.handle.net/10948/451 , Data mining -- South Africa , Computer algorithms , Network performance (Telecommunication) -- Research -- South Africa
- Description: Many network monitoring tools do not provide sufficiently in-depth and useful reports on network usage, particularly in the domain of application services data. The optimisation of network performance is only possible if the networks are monitored effectively. Techniques that identify patterns of network usage can assist in the successful monitoring of network performance. The main goal of this research was to propose a model to mine and visualise application services data in order to support effective network management. To demonstrate the effectiveness of the model, a prototype, called NetPatterns, was developed using data for the Integrated Tertiary Software (ITS) application service collected by a network monitoring tool on the NMMU South Campus network. Three data mining algorithms for application services data were identified for the proposed model. The data mining algorithms used are classification (decision tree), clustering (K-Means) and association (correlation). Classifying application services data serves to categorise combinations of network attributes to highlight areas of poor network performance. The clustering of network attributes serves to indicate sparse and dense regions within the application services data. Association indicates the existence of any interesting relationships between different network attributes. Three visualisation techniques were selected to visualise the results of the data mining algorithms. The visualisation techniques selected were the organisation chart, bubble chart and scatterplots. Colour and a variety of other visual cues are used to complement the selected visualisation techniques. The effectiveness and usefulness of NetPatterns was determined by means of user testing. The results of the evaluation clearly show that the participants were highly satisfied with the visualisation of network usage presented by NetPatterns. All participants successfully completed the prescribed tasks and indicated that NetPatterns is a useful tool for the analysis of network usage patterns.
- Full Text:
- Date Issued: 2005
- Authors: Knoetze, Ronald Morgan
- Date: 2005
- Subjects: Data mining -- South Africa , Computer algorithms , Network performance (Telecommunication) -- Research -- South Africa
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:10480 , http://hdl.handle.net/10948/451 , Data mining -- South Africa , Computer algorithms , Network performance (Telecommunication) -- Research -- South Africa
- Description: Many network monitoring tools do not provide sufficiently in-depth and useful reports on network usage, particularly in the domain of application services data. The optimisation of network performance is only possible if the networks are monitored effectively. Techniques that identify patterns of network usage can assist in the successful monitoring of network performance. The main goal of this research was to propose a model to mine and visualise application services data in order to support effective network management. To demonstrate the effectiveness of the model, a prototype, called NetPatterns, was developed using data for the Integrated Tertiary Software (ITS) application service collected by a network monitoring tool on the NMMU South Campus network. Three data mining algorithms for application services data were identified for the proposed model. The data mining algorithms used are classification (decision tree), clustering (K-Means) and association (correlation). Classifying application services data serves to categorise combinations of network attributes to highlight areas of poor network performance. The clustering of network attributes serves to indicate sparse and dense regions within the application services data. Association indicates the existence of any interesting relationships between different network attributes. Three visualisation techniques were selected to visualise the results of the data mining algorithms. The visualisation techniques selected were the organisation chart, bubble chart and scatterplots. Colour and a variety of other visual cues are used to complement the selected visualisation techniques. The effectiveness and usefulness of NetPatterns was determined by means of user testing. The results of the evaluation clearly show that the participants were highly satisfied with the visualisation of network usage presented by NetPatterns. All participants successfully completed the prescribed tasks and indicated that NetPatterns is a useful tool for the analysis of network usage patterns.
- Full Text:
- Date Issued: 2005
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