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
Factors influencing the implementation of mathematical word problems in foundation phase classrooms: theory and practice
- Authors: Van Zyl, Marinda
- Date: 2012
- Subjects: Education -- Curriculum planning -- Foundation phase
- Language: English
- Type: Thesis , Masters , MA
- Identifier: vital:9564 , http://hdl.handle.net/10948/d1015954
- Description: This treatise investigated mathematical word problems (MWPs) and their implementation in Foundation Phase classrooms. Factors influencing the implementation of MWPs, with specific reference to the teachers and learners involved, emerged. Direct and indirect factors influencing the implementation of MWPs were acknowledged. Student teachers‟ reflections on classroom practices experienced during their teaching practice training period for their initial teaching qualification inspired me as lecturer to embark on my own journey of inquiry and study the phenomenon above. As this study was undertaken in South Africa, the need arose to take into consideration the changes that have occurred since 1994. Observations of how democratic values and desires feature, or do not feature, when engaging with the phenomenon had to be considered. This study also aimed to emphasise inequalities in everyday practice. The discovery of “good practice” (Cooper 2010:170) contributed towards addressing the factors that emerged as influencing the implementation of MWPs. Jansens (2009:170) book Knowledge in the blood presents compelling reasons for disclosing the state of current practice and seeks alternatives to promote the required change in mathematics teaching, with one of the perspectives on mathematics education being the emphasis on implementing MWPs in the Foundation Phase. Teachers often extend their own preferences into practice and emphasise their “knowledge in the blood” as their view of good practice. Learners‟ needs and learner diversity are often overlooked. Learners‟ assessment scores, both nationally and internationally, have revealed more negative facts. These low scores have often been, and often still are, news flashes, contributing to a negative view of teachers and education. In order to address the widespread sentiment that there is “no hope for teachers” (Jansen 2011:19), and to avoid a recycling of negativity, “good practice” (Cooper 2010:170) is key to success. This study aimed to discover hope for teachers and learners.
- Full Text:
- Date Issued: 2012
- Authors: Van Zyl, Marinda
- Date: 2012
- Subjects: Education -- Curriculum planning -- Foundation phase
- Language: English
- Type: Thesis , Masters , MA
- Identifier: vital:9564 , http://hdl.handle.net/10948/d1015954
- Description: This treatise investigated mathematical word problems (MWPs) and their implementation in Foundation Phase classrooms. Factors influencing the implementation of MWPs, with specific reference to the teachers and learners involved, emerged. Direct and indirect factors influencing the implementation of MWPs were acknowledged. Student teachers‟ reflections on classroom practices experienced during their teaching practice training period for their initial teaching qualification inspired me as lecturer to embark on my own journey of inquiry and study the phenomenon above. As this study was undertaken in South Africa, the need arose to take into consideration the changes that have occurred since 1994. Observations of how democratic values and desires feature, or do not feature, when engaging with the phenomenon had to be considered. This study also aimed to emphasise inequalities in everyday practice. The discovery of “good practice” (Cooper 2010:170) contributed towards addressing the factors that emerged as influencing the implementation of MWPs. Jansens (2009:170) book Knowledge in the blood presents compelling reasons for disclosing the state of current practice and seeks alternatives to promote the required change in mathematics teaching, with one of the perspectives on mathematics education being the emphasis on implementing MWPs in the Foundation Phase. Teachers often extend their own preferences into practice and emphasise their “knowledge in the blood” as their view of good practice. Learners‟ needs and learner diversity are often overlooked. Learners‟ assessment scores, both nationally and internationally, have revealed more negative facts. These low scores have often been, and often still are, news flashes, contributing to a negative view of teachers and education. In order to address the widespread sentiment that there is “no hope for teachers” (Jansen 2011:19), and to avoid a recycling of negativity, “good practice” (Cooper 2010:170) is key to success. This study aimed to discover hope for teachers and learners.
- Full Text:
- Date Issued: 2012
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