published_or_final_version / Mathematics / Master / Master of Philosophy

Thesis (M. Phil.)--University of Hong Kong, 1973. / Mimeographed.

A research report submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg in partial fulfilment of the requirements for the degree of Master of Science, 2017 / This research explores the importance of Self- Directed Metacognitive questioning in the solving of Euclidean Geometry problems by grade 11 learners. A quasi-experiment was carried out at an urban school with fifty eleventh grade learners. Most researches in Mathematics Education aimed at unveiling socio-economic factors that hamper mathematics learning. In this research, I suggested that strategies that target the learners' metacognitive development can assist in addressing poor mathematics achievement. Metacognition (thinking about thinking) makes learners drivers of their own cognitive processes so that they can become better doers of the subject The research answered the question: Does teaching of metacognition to Further Education and Training (FET) learners help them to become better learners of Euclidian Geometry? This question was broken down into the following sub-questions: What is the effect of the use of Self -Directed Metacognitive (SDM) questions on the confidence level and preparedness of learners in the learning of Euclidean Geometry? To what extent does purposeful teaching and learning of metacognitive skills yield positive results in answering Euclidean Geometry questions? Metacognitive skills helped learners to perform better in problem-solving. This result agrees with previous researchers and is also consistent with the results of earlier investigations showing that achievement in mathematics can be raised through instruction enriched with metacognitive activity. Where previous research dealt with metacognitive training in an implicit manner this research on metacognitive training was done explicitly and it resulted in improved mathematics performance by learners. / XL2017

Thesis (Ph. D.)--University of Missouri-Columbia, 2008. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on June 8, 2009) Vita. Includes bibliographical references.

Το θέμα στην ουσία αφορά την Αξιωματική θεμελίωση του Ευκλείδη (καθ'ύλη αξιωματική) που έχει ως αντικείμενο την μελέτη της γεωμετρίας του φυσικού χώρου, και επομένως διατηρεί τον εμπειρικό της χαρακτήρα. Επομένως ο φυσικός αυτός χώρος εφοδιάζει τον μελετητή και με μια ισχυρή γεωμετρική διαίσθηση. Από την άλλη μεριά η αφηρημένη αξιωματική του Hilbert, και η σχετική θεμελίωση της Γεωμετρίας, καταφέρνει να εξοβελίσει την γεωμετρική διαίσθηση. Από κει και πέρα η αλγεβροποίηση των μαθηματικών, εξοβελίζει και αυτή την γεωμετρική άποψη. / We present the axiomatic method of Euclid's elements in geometry (~300 B.C.) and the axiomatization of Euclid's geometry later (first quarter of the twentieth century) by Hilbert and Tarski (formalization).

No description available.

The focus of this thesis is on the investigation of the geodesics of ruled surfaces.

Researchers conceptually recommend inquiry-based learning as a necessary means to alleviate the problems of learning but this study has embarked on practical implementation of inquiry-based facilitation and learning in Euclidean Geometry. Inquiry-based learning is student-centred. Therefore, the teaching or monitoring of inquiry-based learning in this study is referred to as inquiry-based facilitation. The null hypothesis discarded in this study explains that there is no difference between inquiry-based facilitation and traditional axiomatic approach in teaching Euclidean Geometry, that is, H0: μinquiry-based facilitation = μtraditional axiomatic approach. This study emphasises a pragmatist view that constructivism is fundamental to realism, that is, inductive inquiry supplements deductive inquiry in teaching and learning. Participants in this study comprise schools in Tshwane North district that served as experimental group and Tshwane West district schools classified as comparison group. The two districts are in the Gauteng Province of South Africa. The total number of students who participated is 166, that is, 97 students in the experimental group and 69 students in the comparison group. Convenient sampling applied and three experimental and three comparison group schools were sampled. Embedded mixed-method methodology was employed. Quantitative and qualitative methodologies are integrated in collecting data; analysis and interpretation of data. Inquiry-based-facilitation occurred in experimental group when the facilitator probed asking students to research, weigh evidence, explore, share discoveries, allow students to display authentic knowledge and skills and guiding students to apply knowledge and skills to solve problems for the classroom and for the world out of the classroom. In response to inquiry-based facilitation, students engaged in cooperative learning, exploration, self-centred and self-regulated learning in order to acquire knowledge and skills. In the comparison group, teaching progressed as usual. Quantitative data revealed that on average, participant that received intervention through inquiry-based facilitation acquired inquiry-based learning skills and improved (M= -7.773, SE= 0.7146) than those who did not receive intervention (M= -0.221, SE = 0.4429). This difference (-7.547), 95% CI (-8.08, 5.69), was significant at t (10.88), p = 0.0001, p<0.05 and represented a large effect size of 0.55. The large effect size emphasises that inquiry-based facilitation contributed significantly towards improvement in inquiry-based learning and that the framework contributed by this study can be considered as a framework of inquiry-based facilitation in Euclidean Geometry. This study has shown that the traditional axiomatic approach promotes rote learning; passive, deductive and algorithmic learning that obstructs application of knowledge in problem-solving. Therefore, this study asserts that the application of Inquiry-based facilitation to implement inquiry-based learning promotes deeper, authentic, non-algorithmic, self-regulated learning that enhances problem-solving skills in Euclidean Geometry. / Mathematics Education / Ph. D. (Mathematics, Science and Technology Education)