Thesis (doctoral)--Universität Bremen, 2004. / Includes bibliographical references (p. 121-136). Also available online in PDF format.

Thesis (doctoral)--University of Hamburg.

Thesis (doctoral)--Université de Genève, 1980. / Includes bibliographical references (p. [443]-449).

Thesis (doctoral)--University of Hamburg. / Description based on print version record.

Thesis (doctoral)--Universiteit van Amsterdam, 1998. / Includes bibliographical references (p. 233-249).

"The present study has been accepted as a doctoral thesis by the Department of Economics of the Johann Wolfgang Goethe-University in Frankfurt am Main"--Pref. / Includes bibliographical references (p. 177-188).

Please read the abstract in the section 00front of this document / Dissertation (M Eng (Metallurgical Engineering))--University of Pretoria, 2006. / Materials Science and Metallurgical Engineering / unrestricted

Metacognition is commonly understood in the context of the learners and not their teachers. Extant literature focusing on how Mathematics teachers apply their metacognitive skills in the classroom, clearly distinguishes between teaching with metacognition (TwM) referring to teachers thinking about their own thinking and teaching for metacognition (TfM) which refers to teachers creating opportunities for learners to reflect on their thinking. However, in both of these cases, thinking requires a language, in particular appropriate mathematical language to communicate the thinking by both teacher and learners in the Mathematics classroom. In this qualitative study, which forms part of a bigger project within SANPAD (South Africa Netherlands Research Programme on Alternatives in Development), the metacognitive skills and mathematical language used by Mathematics teachers who teach at two township schools were interrogated using the design-based research approach with lesson study. Data collection instruments included individual interviews and a trigonometric assessment task. Lessons were also observed and video-taped to be viewed and discussed during focus group discussions in which the teachers, together with five Mathematics lecturers, participated. The merging of the design-based research approach with lesson study brought about teacher-lecturer collaboration, referred to in this study as the Mathematics Educators’ Reflective Inquiry (ME’RI) group, and enabled the design of a hypothetical teaching and learning trajectory (HTLT) for the teaching of trigonometric functions. A metacognitive performance profile for the two grade 10 teachers was also developed. The Framework for Analysing Mathematics Teaching for the Advancement of Metacognition (FAMTAM) from Ader (2013) and the Teacher Metacognitive Framework (TMF) from Artzt and Armour-Thomas (2002) were adjusted and merged to develop a new framework, the Metacognitive Teaching for Metacognition Framework (MTMF) to analyse the metacognitive skills used by mathematics teachers TwM as well as TfM. Without oversimplifying the magnitude of these concepts, the findings suggest a simple mathematical equation: metacognitive skills + enhanced mathematical language = conceptualization skills. The findings also suggest that both TwM and TfM are required for effective mathematics instruction. Lastly the findings suggest that the ME’RI group holds promise to enhance the use of the metacognitive skills and mathematical language of Mathematics teachers in Mathematics classrooms. / PhD (Mathematics Education), North-West University, Potchefstroom Campus, 2014

Metacognition is commonly understood in the context of the learners and not their teachers. Extant literature focusing on how Mathematics teachers apply their metacognitive skills in the classroom, clearly distinguishes between teaching with metacognition (TwM) referring to teachers thinking about their own thinking and teaching for metacognition (TfM) which refers to teachers creating opportunities for learners to reflect on their thinking. However, in both of these cases, thinking requires a language, in particular appropriate mathematical language to communicate the thinking by both teacher and learners in the Mathematics classroom. In this qualitative study, which forms part of a bigger project within SANPAD (South Africa Netherlands Research Programme on Alternatives in Development), the metacognitive skills and mathematical language used by Mathematics teachers who teach at two township schools were interrogated using the design-based research approach with lesson study. Data collection instruments included individual interviews and a trigonometric assessment task. Lessons were also observed and video-taped to be viewed and discussed during focus group discussions in which the teachers, together with five Mathematics lecturers, participated. The merging of the design-based research approach with lesson study brought about teacher-lecturer collaboration, referred to in this study as the Mathematics Educators’ Reflective Inquiry (ME’RI) group, and enabled the design of a hypothetical teaching and learning trajectory (HTLT) for the teaching of trigonometric functions. A metacognitive performance profile for the two grade 10 teachers was also developed. The Framework for Analysing Mathematics Teaching for the Advancement of Metacognition (FAMTAM) from Ader (2013) and the Teacher Metacognitive Framework (TMF) from Artzt and Armour-Thomas (2002) were adjusted and merged to develop a new framework, the Metacognitive Teaching for Metacognition Framework (MTMF) to analyse the metacognitive skills used by mathematics teachers TwM as well as TfM. Without oversimplifying the magnitude of these concepts, the findings suggest a simple mathematical equation: metacognitive skills + enhanced mathematical language = conceptualization skills. The findings also suggest that both TwM and TfM are required for effective mathematics instruction. Lastly the findings suggest that the ME’RI group holds promise to enhance the use of the metacognitive skills and mathematical language of Mathematics teachers in Mathematics classrooms. / PhD (Mathematics Education), North-West University, Potchefstroom Campus, 2014

Basic mathematical competency seems to be lacking for engineering students starting their studies in this field. Students generally find the cognitive transition from secondary to tertiary mathematics challenging which in turn negatively influences their academic achievement in mathematics. The cognitive challenge is the transition from the application of mathematics to familiar questions to applying mathematical principles to varying practical application and problem solving. Mathematics provides the foundation for the cognitive toolset required for the development of skills required for analysing engineering systems and processes. It is therefore important to assess mathematical and cognitive competency and ability at the time of admission to a tertiary institution in order to identify and address gaps. This research demonstrates that first-year engineering students need to have a specific level of mathematical competency and cognitive ability to use mathematics within the context of engineering studies. This research attempts to connect the mathematic competency of first year engineering students to their academic results for subjects in the first year curriculum that rely heavily on mathematical competency. To satisfy the research question, the study firstly looks at relevant literature to identify the mathematical competency levels as well as the operational specification. Secondly, development theories and taxonomies were analysed to gain insight into the development processes associated with learning, cognitive development and the gap between cognitive competencies in transition from secondary to tertiary education. Further, cognitive competencies were identified that are essential for successful completion of first year engineering modules. Through synthesis of the different theories and taxonomies a framework was identified. This framework was used to analyse secondary data in order to measure mathematical and cognitive levels. Thirdly, the theoretical investigation was followed by a three-phase empirical study. A mixed quantative-qualitative (QUAN-qual) approached was followed. Phase 1 uses the assessment framework to measure first year students‟ mathematical competency at the inception of their studies as well as at the completion of their first semester. The mathematical competency at inception was measured with their Grade 12 mathematics marks and with relevant analysis of their initial bridging assessments, on a question by question basis. In addition, their first semester exams questions were analysed using the same approach as above. Phase 2 comprises the measurement of the relationship between the mathematical competency of first year enigineering students at admission and their achievement levels in selected first year subjects that required mathematical competency. Phase 3 includes the guidelines derived from the gaps and shortcomings identified. These gaps were identified in order to inform appropriate study support to first year students and to assists academic personnel with setting appropriate and dependable admission standards. The analysis of mathematical competency creates quality data that gives a clearer picture than a simple comparison of admission scores and first semester marks. The empirical study contributes to a better understanding of the problems associated with the transition from secondary to tertiary learning environments. From the study it was derived that study inception information of the students correlated only with their academic results on questions that tested mathematical and programming application. The inception information was not a predictor of mathematical achievement and results for both the lowest and highest mathematical competency levels. Futher study in this field is required to create frameworks for the measurements of both low and high levels of mathematical competency. / MEd (Mathematics Education), North-West University, Potchefstroom Campus, 2014