Despite the fact that the facilitation of inquiry learning is a core methodology in the General Education and Training (GET) band of the South African National Curriculum Statement, rote learning and memorization of algorithms remains common practice in many mathematics classrooms. The inquiry-based Family Maths professional development programme, offered by the Nelson Mandela Metropolitan University, attempts not only to support the transformative education practices targeted by the South African National Department of Education, but also to extend them beyond the school walls to the community at large. This study investigates the extent to which the Family Maths professional development programme develops facilitators’ ability to implement inquiry-based learning. It also seeks to explore which aspects of the programme are effective in developing an inquiry-based approach. The research undertaken is an empirical study of 39 facilitators and uses both qualitative and quantitative methods. The facilitators’ inquiry beliefs and ability to implement inquiry learning was measured by means of questionnaires, observation schedules and interviews. As the ‘teacher as facilitator of inquiry-based teaching and learning’ is a requirement of all South African teachers, the findings of this research should make a meaningful contribution to the field of mathematics teacher education in the South African context.

This research study has emerged as a result of my concern regarding the apparent low self-efficacy amongst initial teacher education students in my mathematics education classes. It also reflects a reported renewed interest in values, and the promotion of excellence in education. The effects of a values-based approach to mathematics education towards improving students’ self-efficacy and promoting excellence have been investigated, grounded within my ontology of excellence in mathematics education, which incorporates the values of respect, fairness, accountability, honesty and compassion. An inquiry-based teaching and learning approach formed the framework within which the study took place. Notions of ‘new scholarship’, premised on the view that teaching is about engagement in participatory learning, and the development of communities of creative students, provided the theoretical framework. Both quantitative and qualitative data gathering methods were used. Data-collection tools included affective-disposition statements, interviews, journal entries, as well as a video recording of a mathematics education lesson. The quantitative and qualitative data generated suggest improved levels of self-efficacy amongst the students who participated in the study. The data also suggest that a valuesbased approach to teaching can be used as an effective approach by mathematics teachers – and mathematics teacher educators – for the purpose of promoting the pursuit of excellence. As teacher education worldwide is currently characterised by a lack of vitality in teacher preparation (Grossman, 2008), the findings of this study should provide insights for teacher educators, teachers and policy makers who wish to promote mathematics self-efficacy, excellence and facilitate enhanced vitality within the teaching profession.

The creation of an instructional genius hour framework for classroom implementation is an objective of this study. Currently, genius hour educators use a wide variety of frameworks. Some genius hour educators do not follow a set framework, yet others continually modify their genius hour frameworks. This study draws attention to the need to create an instructional framework for classroom implementation. This study was conducted through semi-structured interviews with five of the most respected genius hour educators. For the purposes of this study, each individual educator was treated as a separate case study. During the semi-structured interviews, genius hour educators shared their personal experience with implementing genius hour, their personal philosophies and ideas related to genius hour, their recommendations regarding genius hour implementation, and their recommendations regarding genius hour frameworks for classroom implementation. Moreover, this study also conducted two observations of genius hour classrooms in action. These classroom observations offered data related to genius hour educational philosophy and the need for a genius hour framework. This study recommends that educators use an instructional framework when implementing genius hour. A framework will have a positive effect on the performance of genius hour because of the added structure and clarity it provides for students and educators. It is recommended that educators choose a framework, and modify it in order to best serve the academic needs of their particular genius hour programme. This study moves beyond the genius hour framework by identifying major themes that genius hour educators should consider when implementing genius hour in the classrooms. Alongside the importance of the framework model, the common themes of front-loading, learning from failure, developing passion, and mentoring emerged from the interviews and observations. In essence, this study developed a framework model, game time, based around the importance of incorporating the aforementioned themes. The findings within this study offer an understanding of the importance of using a genius hour framework for classroom implementation. This study envisions that educators can use the research gathered in order to create an optimal genius hour framework for classroom implementation. This offers a framework for classroom implementation, which should be individualized in order to best suit the classroom specific needs. / Hierdie studie het die skepping van ʼn genie-uur-onderrigraamwerk vir klaskamer-implementering ten doel. Tans gebruik genie-uuropvoeders ’n wye verskeidenheid raamwerke. Sommige genie-uuropvoeders volg nie ’n vasgestelde raamwerk nie, terwyl andere voortdurend hul genie-uurraamwerke verander. Hierdie studie vestig aandag op die behoefte om ʼn onderrigraamwerk vir klaskamerimplementering te skep. Hierdie studie is uitgevoer deur middel van halfgestruktureerde onderhoude met vyf van die mees gerespekteerde genie-uuropvoeders. Vir die doeleindes van hierdie studie is elke individuele opvoeder as ’n afsonderlike gevallestudie behandel. Gedurende die halfgestruktureerde onderhoude het genie-uuropvoeders hul persoonlike ervarings van die inwerkingstelling van genie-uur, hul persoonlike filosofieë en idees oor genie-uur, hul aanbevelings vir genie-uurimplementering, en hul aanbevelings vir genie-uurraamwerke vir klaskamerimplementering gedeel. Verder het hierdie stude ook twee waarnemings van genie-uurklaskamers-in-aksie uitgevoer. Hierdie klaskamerwaarnemings het data in verband met genie-uuronderwysfilosofie en die behoefte aan ’n genie-uurraamwerk opgelewer. Hierdie studie beveel aan dat opvoeders ʼn onderrigraamwerk gebruik wanneer hulle genie-uur in werking stel. ’n Raamwerk sal ’n positiewe uitwerking op die uitvoering van genie-uur hê as gevolg van die bykomende struktuur en duidelikheid wat dit aan studente en opvoeders bied. Daar word aanbeveel dat opvoeders ’n raamwerk kies en dit aanpas ten einde die beste in die akademiese behoeftes van hul betrokke genie-uurprogram te voorsien. Hierdie studie beweeg verder as die genie-uurraamwerk deur belangrike temas te identifiseer wat genie-uuropvoeders kan oorweeg wanneer hulle genie-uur in die klaskamers in werking stel. Afgesien van die belangrikheid van die raamwerkmodel het die algemene temas van voorkantlading, leer uit mislukking, ontwikkeling van passie en leidinggewing uit die onderhoude en waarnemings na vore gekom. Hierdie studie het wesenlik ’n raamwerkmodel ontwikkel, genaamd speeltyd, wat gebaseer is op die belangrikheid daarvan om die voorgenoemde temas te inkorporeer. Die bevindings van hierdie studie bied ʼn begrip van die belangrikheid daarvan om ’n genie-uurraamwerk vir klaskamerimplementering te gebruik. Hierdie studie stel in die vooruitsig dat opvoeders die navorsing sal gebruik wat ingesamel is om ʼn optimale genie-uurraamwerk vir klaskamerimplementering te skep. Dit bied ’n raamwerk vir klaskamerimplementering, wat geïndividualiseer behoort te word om die beste in die spesifieke behoeftes van elke klaskamer te voorsien. / Ukwakhiwa kohlaka lokufundisa ngendlela ye-genius hour oluzosetshenziswa ekilasini yiyona njongo yalolu cwaningo. Njengamanje, othisha abalandela indlela yegenius hour basebenzisa izinhlobonhlobo zezinhlaka. Abanye othisha abalandela indlela yegenius hour abasebenzisi izinhlaka ezibekiwe, kodwa abanye bayaqhubeka nokulungisa izinhlaka zabo zegenius hour. Lolu cwaningo luveza isidingo sokwakhiwa kohlaka lokufundisa oluzosetshenziswa ekilasini. Lolu cwaningo lwaluqhutshwa ngokuxoxisana okuhleliwe nothisha abahlanu abahlonishwa kakhulu begenius hour. Ngokwenjongo yalolu cwaningo, uthisha ngamunye wayethathwa njengowahlukile kwabanye abasetshenziswe ocwaningweni. Ngenkathi kuqhubeka izingxoxo ezihleliwe, othisha begenius hour baxoxa ngabahlangabezana nakho uma beqalisa ukusebenzisa igenius hour, imigomo abayilandelayo kanye namasu ahambisana negenius hour, izincomo zabo mayelana negenius hour kanye nezincomo zabo ngezinhlaka zegenius hour ezizosetshenziswa ekilasini. Phezu kwalokho, lolu cwaningo luphinde lwabuka kusetshenziswa igenius hour kabili emakilasini ngenkathi eqhubeka. Lokhu kubhekwa kwamakilasi kwaveza imininingwane eqondene nemigomo yezemfundo yegenius hour kanye nesidingo sohlaka lwegenius hour. Lolu cwaningo luncoma ukuba othisha basebenzise uhlaka lokufundisa uma beqala ukusebenzisa igenius hour. Uhlaka luzoba nomphumela omuhle ekusebenzeni kwegenius hour, ngenxa yokwakheka okwengeziwe kanye nokucacisa, ihlinzekela abafundi nothisha. Kunconywa ukuba othisha bakhethe uhlaka, balulungise kahle ukuze luhambisane nezidingo zezemfundo zohlelo lwabo oluthile lwegenius hour. Lolu cwaningo luhamba ludlulele ngale kohlaka lwegenius hour ngokuhlonza izingqikithi okufanele othisha begenius hour bacabange ngazo uma beqala ukusebenzisa igenius hour emakilasini. Ngaphandle kokubaluleka kwesimo sohlaka, izingqikithi ezejwayelekile zokufundisa ngokuhlahla indlela, ukufunda ngokwehluleka kuqala, ukukhula kothando kanye nokwalusa kwavela ezingxoxweni nasekubukeni. Empeleni. lolu cwaningo selwakhe isimo sohlaka, isikhathi semidlalo, okuncike ekubalulekeni kokuhlanganisa lezi zingqikithi ezibaliwe. Okutholakele kulolu cwaningo kunikeza ukuqonda kokubaluleka kokusebenzisa uhlaka lwegenius hour ekilasini. Lolu cwaningo lubona ukuthi othisha bangasebenzisa imininingwane etholakale ocwaningweni ukwakha uhlaka lwegenius hour olusebenza kahle oluzosetshenziswa ekilasini. Lokhu kuhlinzeka uhlaka oluzosetshenziswa ekilasini, okumele lwenziwe lusebenzele umuntu ngamunye ukuze luhambisane kahle nezidingo zekilasi ngalinye. / Curriculum and Instructional Studies / D. Ed. (Curriculum and Instructional Studies)

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)

Abstracts in English, Afrikaans and Zulu / This qualitative, single high school case-study conveniently sampled eight natural sciences teachers and, after conducting lesson observations and document analysis, interviewed all participants to obtain their perceptions about the effectiveness of inquirybased teaching in motivating learners to specialise in sciences. The major finding was that most participants were sceptical about inquiry-based teaching. Participants from a behaviourist epistemology did not believe that learner motivation resulted from inquirybased teaching while those from an eclectic epistemology preferred a complementary use of both approaches. The few participants oriented towards inquiry acknowledged the link between learner motivation and inquiry-based teaching but faced the challenge of limited time to prepare all the apparatus and procedures required for inquiry-based teaching. This researcher recommends employing laboratory assistants to assist teachers with setting up apparatus for inquiry-based lessons, trimming some content to reduce overload in the Annual Teaching Plans (ATP), and in-service training on inquirybased teaching to develop learner interest in sciences. / Hierdie kwalitatiewe gevallestudie het agt natuurwetenskap onderwysers betrek en na leswaarnemings en dokumentanalise, is onderhoude met die deelnemers gevoer om hul sienings te bekom oor die bydrae van die ondersoek-gebaseerde konstruktivistiese benadering as ’n strategie om leerders te motiveer om in wetenskap-verwante vakke te spesialiseer. Die belangrikste bevindings was dat die deelnemers logiese positivistiese en eklektiese benaderings verkies; dat hulle skepties is oor ondersoek-gebaseerde onderrig en dat hulle nie leerder motivering aan onderwysbenaderings koppel nie. Daar was egter enkele deelnemers wat wel ondersoekend onderrig het en wat leerder belangstelling in wetenskap aan ondersoek-gebaseerde onderrig gekoppel het. Op grond van die data wat verkry is, beveel hierdie navorser aan dat laboratoriumassistente aangestel moet word om onderwysers by te staan met die opstel van apparaat vir ondersoek-gebaseerde lesse; dat spesifieke modelle van ondersoek in die “CAPS”- dokument ingesluit word; dat inhoud afgeskaal moet word om oorlading in die jaarlikse onderrigplanne (ATP) te verminder, en dat voor- en indiensopleiding aan onderwysers oor ondersoek-gebaseerde onderrig verskaf word as ‘n manier om die belangstelling van die leerders in die wetenskappe te prikkel. / Lesisifundo socwaningo esenziwe esikoleni esisodwa samabanga aphakeme lwakhetha othisha beSayensi Yemvelo (NS) abayisishiyagalombili ukuze kwazakale ukuthi bayibona kanjani indlela yokufundisa iSayensi ngophenyo (inquiry-based teaching) ehlose ukukhuphula intshisekelo yabafundi kwiSayensi. Ngemuva kokubona othisha beSayensi befundisa, lomcwaningi wahlaziya incwadi eziphathelene nokufundiswa kohlelo lwe CAPS, waphinde wenza izingxoxo nabothisha. Okumqoka okutholakale kuloluphenyo kube ukuthi iningi lababambe iqhaza, abakhuthalela ukufundisa ngendlela egxile kuthisha (logical positivism) bangabaza ukuthi abafundi bafunde bephenya njalo abakubonanga ukuxhumana kwenzindlela zokufundisa nokunyuka kwentshiseko yabafundi ezifundweni ze Sayensi. Ababambiqhaza abahlanganisa indlela yokufundisa egxile kuthisha ne ndlela yokufundisa ngophenyo (eclectic) bakholelwa ukuthi indlela yokufundisa egxile kuthisa nendlela yokuthi abafundi bafunde bephenya, kuyomela zisetshenziswe zombili. Kwatholakala ingcosana yabothisha eyenelisa ukufundisa isayensi ngendlela yophenyo eyayisezingeni eliphansi njalo yaqinisekisa ukuthi bukhona ubudlelwano phakathi kwendlela zokufundisa nokunyusa intshiseko yabafundi kwi Sayensi. Ngokolwazi olutholakele, lolucwaningo luncome ukusebenzisa abasizi basemagunjini okusebenzela ososayensi ukusiza ukuhlela amalungiselelo okwenza uphenyo lwezifundo, nokuhlinzekwa kwezindlela eziqondile zokuphenya izincwadi zikaCAPS, kanye nokunciphisa okunye okuqukethwe, kwehliswe umthwalo kuhlelo lokufundisa lonyaka (i-ATP), ukuqeqeshwa kothisha kwi ndlela yokufundisa iSayensi ngokuphenya ukuze kuthuthukiswe intshiseko yabafundi. / Curriculum and Instructional Studies / M. Ed. (Curriculum Studies)

Problem-based learning (PBL) is an active teaching strategy that could be implemented in the South African educational system to assist in developing problem-solving skills, critical thinking skills, collaborative skills, self-directed learning and intrinsic motivation in students. Even though it is not easy to drift from a teacher-centred strategy to a student-centred strategy, but this drift is supposed to be a paradigm drift for the nation. ‘Physics is difficult’ has been the anthem of students in South African high schools. This has led to lower pass rates in physics and as a result low physics career person in society. Physics students in high schools need to be exposed to the PBL strategy since the PBL strategy focuses on real-life problems to develop problem-solving skills, critical thinking skills and self-directed learning in students which are the skills needed for concept formation in Physical Science. Basically, the education of Physical Science students focused on the ability to acquire skills to solve real-life problems. This study focuses on exploring the experiences of high school physics teachers at Entsikeni cluster, South African, when implementing problem-based learning (PBL) in their physics classrooms. The study uses the mixed-method approach where three different research instruments were used to collect quantitative and qualitative data sequentially. Questionnaires, RTOP and interview protocol were employed. The findings of the study indicate that teachers project positive attitudes toward the PBL strategy but may probably not continue to use it because it requires more time than that which is allocated in the Curriculum Assessment and Policy Statement (CAPS) Physical Science document and as a result may not be able to finish their ATP on time. Teachers are teaching physics with no specialization in physics, which probably could lead to poor, pass rates in Physical Science. Teachers were inexperienced in teaching physics in the FET and could probably affect students’ academic performance. It is recommended they apply the PBL strategy to correct the negative effect of their inexperience on students’ performance. It is evident that if inexperienced trained teachers apply an instructional strategy based on research, they tend to develop students' performance as compared to applying the traditional instructional strategy. / Science and Technology Education / M. Sc. (Physics Education)