This study employed a qualitative approach to investigate the use of cooperative learning to enhance conceptual understanding of trigonometry in a Grade 11 mathematics classroom, conducted at a high school in Moletlane Circuit, Capricorn District in Limpopo Province, South Africa. A single case study was used as a research design to get an in-depth analysis and collect detailed data using semi-interviews and lesson observation of the cooperative learning of trigonometry in Grade 11 from the learners and the teacher. Participants were purposely chosen and consisted of (n=30) Grade 11 mathematics learners and their mathematics teacher. Data from the participants were collected through semi-structured interviews and observation, with the aid of observation guide (Appendix C) for three weeks. The salient findings from the study showed how cooperative learning was used, research questions, the approaches, the teacher did not adequately highlight the importance of trigonometry to students without integrating the topic to real-life situations. Some students said that the teacher did not teach trigonometry in a manner that they understood, which made trigonometry challenging for them. Concerning cooperative learning, the study found that many learners were passively engaged, listened to or watched the teacher. Mainly, the study recommends teacher-training institutions to host practical workshops to help teachers integrate theoretical training and practical cooperative learning experience. While this study was qualitative in nature, future researchers could conduct quantitative data collection. This would allow for the collection of numerical findings through survey questionnaires. / Mathematics Education / M. Ed. (Mathematics Education)

Summaries in English and Afrikaans / The second fully democratic election in South Africa is scheduled to take place in May 1999. In the five years since the first election, it appears that very little attention has been paid to the political literacy of the electorate in general, and the youth in particular. The purpose of this study was to establish adolescents' level of political knowledge and whether they are able to think critically about political issues or not. The first part of the literature study which was concerned with critical thinking revealed that the major aspects of critical thinking are: deductive reasoning, inductive inference, recognition of assumptions, credibility, and problem solving. The second part of the literature study was an analysis of which factors may play a role in the development of critical thinking of an adolescent. with particular reference to a political context. The third part was an examination of important current political and social issues. These were: the new Constitution. Truth and Reconciliation Commission, housing, land redistribution, education, labour, health, crime, political violence, environment, and the next election. A reliable measuring instrument was developed in order to measure adolescents' knowledge of political issues, and their ability to think critically about these issues. The results of the empirical study revealed that intellectual potential and academic achievement were significantly related to critical thinking ability, while gender, environment, and personality appeared not to play a role. There was a significant correlation between political knowledge and critical thinking in a political context, implying that critical thinking is subject-specific. Cultural background also played a significant role in critical thinking in a political context. In terms of political knowledge, boys were found to be at a significantly higher level than girls. The subjects from urban areas were also at a significantly higher level than those from rural areas. There was also a positive correlation between intellectual potential, academic achievement, and political knowledge. Finally, some recommendations for improving the levels of political knowledge and critical thinking abilities with regard to political issues of South African adolescents were given. / Die tweede ten valle demokratiese verkiesing in Suid-Afrika is geskeduleer om in Mei 1999 plaas te vind. In die vyf jaar sedert die vorige verkiesing is baie min aandag gegee aan die politieke geletterdheid van die verkiesingspubliek in die algemeen en die jeug in besonder. Die doel van hierdie studie was om adolessente se vlak van politieke kennis te bepaal en om vas te stel of hulle in staat is om krities oar politieke kwessies na te dink. Die eerste deel van die literatuurstudie wat verband hou met kritiese denke het uitgewys dat die hoofaspekte van kritiese denke die volgende is: deduktiewe redenering, induktiewe inferensies, herkenning van aannames, geloofwaardigheid en probleemoplossing. Die tweede deel van die literatuurstudie behels 'n analise van die faktore wat 'n rol kan speel in die ontwikkeling van die kritiese denke van die adolessent, met spesifieke verwysing na 'n politieke konteks. Die derde deel is 'n ondersoek na belangrike teenswoordige politieke en sosiale kwessies. Hierdie kwessies sluit in: die nuwe Grondwet, die Waarheids- en Versoeningskommissie, behuising, herverdeling van grand, opvoeding, arbeid, gesondheid, misdaad, politieke geweld, die omgewing en die volgende verkiesing. 'n Betroubare meetinstrument om adolessente se kennis van politieke kwessies asook hul vermoe om krities daaroor na te dink, is ontwikkel. Die resultate van die empiriese ondersoek het aangetoon dat intellektuele potensiaal en akademiese prestasie betekenisvol verband hou met kritiese denkvermoe, terwyl geslag, omgewing en persoonlikheid klaarblyklik nie 'n rol speel nie. Daar is ook 'n betekenisvolle korrelasie tussen politieke kennis en kritiese denke in 'n politieke konteks wat impliseer dat kritiese denke vakspesifiek is. Kulturele agtergrond speel ook 'n betekenisvolle rol in kritiese denke in 'n politieke konteks. Ten opsigte van politieke kennis is daar bevind dat seuns op 'n betekenisvolle hoer vlak is as dogters. Respondente uit stedelike gebiede is oak op 'n betekenisvolle hoer vlak as diegene uit plattelandse gebiede. Oaar is oak 'n betekenisvolle korrelasie tussen intellektuele potensiaal, akademiese prestasie en politieke kennis. Ten slotte is aanbevelings gemaak om die vlakke van politieke kennis en kritiese denkvermoens met betrekking tot politieke aangeleenthede by Suid-Afrikaanse adolessente te verbeter. / Psychology of Education / D. Ed. (Psychology of Education)

Summaries in English and Afrikaans / The second fully democratic election in South Africa is scheduled to take place in May 1999. In the five years since the first election, it appears that very little attention has been paid to the political literacy of the electorate in general, and the youth in particular. The purpose of this study was to establish adolescents' level of political knowledge and whether they are able to think critically about political issues or not. The first part of the literature study which was concerned with critical thinking revealed that the major aspects of critical thinking are: deductive reasoning, inductive inference, recognition of assumptions, credibility, and problem solving. The second part of the literature study was an analysis of which factors may play a role in the development of critical thinking of an adolescent. with particular reference to a political context. The third part was an examination of important current political and social issues. These were: the new Constitution. Truth and Reconciliation Commission, housing, land redistribution, education, labour, health, crime, political violence, environment, and the next election. A reliable measuring instrument was developed in order to measure adolescents' knowledge of political issues, and their ability to think critically about these issues. The results of the empirical study revealed that intellectual potential and academic achievement were significantly related to critical thinking ability, while gender, environment, and personality appeared not to play a role. There was a significant correlation between political knowledge and critical thinking in a political context, implying that critical thinking is subject-specific. Cultural background also played a significant role in critical thinking in a political context. In terms of political knowledge, boys were found to be at a significantly higher level than girls. The subjects from urban areas were also at a significantly higher level than those from rural areas. There was also a positive correlation between intellectual potential, academic achievement, and political knowledge. Finally, some recommendations for improving the levels of political knowledge and critical thinking abilities with regard to political issues of South African adolescents were given. / Die tweede ten valle demokratiese verkiesing in Suid-Afrika is geskeduleer om in Mei 1999 plaas te vind. In die vyf jaar sedert die vorige verkiesing is baie min aandag gegee aan die politieke geletterdheid van die verkiesingspubliek in die algemeen en die jeug in besonder. Die doel van hierdie studie was om adolessente se vlak van politieke kennis te bepaal en om vas te stel of hulle in staat is om krities oar politieke kwessies na te dink. Die eerste deel van die literatuurstudie wat verband hou met kritiese denke het uitgewys dat die hoofaspekte van kritiese denke die volgende is: deduktiewe redenering, induktiewe inferensies, herkenning van aannames, geloofwaardigheid en probleemoplossing. Die tweede deel van die literatuurstudie behels 'n analise van die faktore wat 'n rol kan speel in die ontwikkeling van die kritiese denke van die adolessent, met spesifieke verwysing na 'n politieke konteks. Die derde deel is 'n ondersoek na belangrike teenswoordige politieke en sosiale kwessies. Hierdie kwessies sluit in: die nuwe Grondwet, die Waarheids- en Versoeningskommissie, behuising, herverdeling van grand, opvoeding, arbeid, gesondheid, misdaad, politieke geweld, die omgewing en die volgende verkiesing. 'n Betroubare meetinstrument om adolessente se kennis van politieke kwessies asook hul vermoe om krities daaroor na te dink, is ontwikkel. Die resultate van die empiriese ondersoek het aangetoon dat intellektuele potensiaal en akademiese prestasie betekenisvol verband hou met kritiese denkvermoe, terwyl geslag, omgewing en persoonlikheid klaarblyklik nie 'n rol speel nie. Daar is ook 'n betekenisvolle korrelasie tussen politieke kennis en kritiese denke in 'n politieke konteks wat impliseer dat kritiese denke vakspesifiek is. Kulturele agtergrond speel ook 'n betekenisvolle rol in kritiese denke in 'n politieke konteks. Ten opsigte van politieke kennis is daar bevind dat seuns op 'n betekenisvolle hoer vlak is as dogters. Respondente uit stedelike gebiede is oak op 'n betekenisvolle hoer vlak as diegene uit plattelandse gebiede. Oaar is oak 'n betekenisvolle korrelasie tussen intellektuele potensiaal, akademiese prestasie en politieke kennis. Ten slotte is aanbevelings gemaak om die vlakke van politieke kennis en kritiese denkvermoens met betrekking tot politieke aangeleenthede by Suid-Afrikaanse adolessente te verbeter. / Psychology of Education / D. Ed. (Psychology of Education)

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)