The aim of this study was to investigate the comparative effects of Constructivist-Based Teaching Method (CBTM) and the Traditional Teaching Method (TTM) on Grade 11 Mathematics learners’ errors in algebra. The constructivist learning theory (CLT) was used to frame this study. Mainly, CLT was used to influence the design of CBTI to hone participants’ errors in algebra that militate against their performance in Mathematics. The study was conducted in the Mpumalanga Province of South Africa with a four-week intervention programme in each of the two participating secondary schools. Participants consisted of n=78 Grade 11 Mathematics learners and one Grade 11 Mathematics teacher. A non-equivalent control group design consisting of a pre-test and post-test measure was employed. The Grade 11 teacher in the control school employed the TTM while the researcher implemented CBTM in the experimental school. The main aspects of CBTM entailed participants’ construction of their own knowledge from the base of prior knowledge and through group learning approach and exploratory talk in which discussions included argumentation, verbalising explanations, justifications and reflections. Participants in experimental school became familiar with the basic principles of CBTI such as group work, which enhanced the construction of conceptual understanding of algebraic concepts. This reduced most of the errors they commit in algebra and elevated their performance in Mathematics. The principal instruments for data collection consisted of a standardised Algebra Concept Achievement Test and lesson observations. The pre-test was used to determine participants’ initial errors in algebra before the intervention. A post-test was given at the end of intervention to ascertain change in participants’ errors in algebra over a four-week intervention period. Using descriptive and inferential statistical techniques, the study found that participants in experimental school significantly reduced their errors in algebra than those in control school. The study showed that CBTM was a more effective pedagogy that improved the errors Grade 11 learners commit in algebra than the TTM. / College of Education / M. Ed. (Mathematics Education)

Cette recherche se caractérise, premièrement, par une discussion théorique sur le concept d'agent autonome, basée sur des éléments issus des paradigmes de l'Intelligence Artificielle Située et de l'Intelligence Artificielle Affective. Ensuite, cette thèse présente le problème de l'apprentissage de modèles du monde, en passant en revue la littérature concernant les travaux qui s'y rapportent. À partir de ces discussions, l'architecture CAES et le mécanisme CALM sont présentés. CAES (Coupled Agent-Environment System) constitue une architecture pour décrire des systèmes basés sur la dichotomie agent-environnement. Il définit l'agent et l'environnement comme deux systèmes partiellement ouverts, en couplage dynamique. L'agent, à son tour, est composé de deux sous-systèmes, l'esprit et le corps, suivant les principes de la situativité et de la motivation intrinsèque. CALM (Constructivist Anticipatory Learning Mechanism) est un mécanisme d'apprentissage fondé sur l'approche constructiviste de l'Intelligence Artificielle. Il permet à un agent situé de construire un modèle du monde dans des environnements partiellement observables et partiellement déterministes, sous la forme d'un processus de décision markovien partiellement observable et factorisé (FPOMDP). Le modèle du monde construit est ensuite utilisé pour que l'agent puisse définir une politique d'action visant à améliorer sa propre performance. / Esta pesquisa caracteriza-se, primeiramente, pela condução de uma discussão teórica sobre o conceito de agente autônomo, baseada em elementos provenientes dos paradigmas da Inteligência Artificial Situada e da Inteligência Artificial Afetiva. A seguir, a tese apresenta o problema da aprendizagem de modelos de mundo, fazendo uma revisão bibliográfica a respeito de trabalhos relacionados. A partir dessas discussões, a arquitetura CAES e o mecanismo CALM são apresentados. O CAES (Coupled Agent-Environment System) é uma arquitetura para a descrição de sistemas baseados na dicotomia agente-ambiente. Ele define agente e ambiente como dois sistemas parcialmente abertos, em acoplamento dinâmico. O agente, por sua vez, é composto por dois subsistemas, mente e corpo, seguindo os princípios de situatividade e motivação intrínseca. O CALM (Constructivist Anticipatory Learning Mechanism) é um mecanismo de aprendizagem fundamentado na abordagem construtivista da Inteligência Artificial. Ele permite que um agente situado possa construir um modelo de mundo em ambientes parcialmente observáveis e parcialmente determinísticos, na forma de um Processo de Decisão de Markov Parcialmente Observável e Fatorado (FPOMDP). O modelo de mundo construído é então utilizado para que o agente defina uma política de ações a fim de melhorar seu próprio desempenho. / This research is characterized, first, by a theoretical discussion on the concept of autonomous agent, based on elements taken from the Situated AI and the Affective AI paradigms. Secondly, this thesis presents the problem of learning world models, providing a bibliographic review regarding some related works. From these discussions, the CAES architecture and the CALM mechanism are presented. The CAES (Coupled Agent-Environment System) is an architecture for describing systems based on the agent-environment dichotomy. It defines the agent and the environment as two partially open systems, in dynamic coupling. The agent is composed of two sub-systems, mind and body, following the principles of situativity and intrinsic motivation. CALM (Constructivist Learning Anticipatory Mechanism) is based on the constructivist approach to Artificial Intelligence. It allows a situated agent to build a model of the world in environments partially deterministic and partially observable in the form of Partially Observable and Factored Markov Decision Process (FPOMDP). The model of the world is constructed and used for the agent to define a policy for action in order to improve its own performance.

Cette recherche se caractérise, premièrement, par une discussion théorique sur le concept d'agent autonome, basée sur des éléments issus des paradigmes de l'Intelligence Artificielle Située et de l'Intelligence Artificielle Affective. Ensuite, cette thèse présente le problème de l'apprentissage de modèles du monde, en passant en revue la littérature concernant les travaux qui s'y rapportent. À partir de ces discussions, l'architecture CAES et le mécanisme CALM sont présentés. CAES (Coupled Agent-Environment System) constitue une architecture pour décrire des systèmes basés sur la dichotomie agent-environnement. Il définit l'agent et l'environnement comme deux systèmes partiellement ouverts, en couplage dynamique. L'agent, à son tour, est composé de deux sous-systèmes, l'esprit et le corps, suivant les principes de la situativité et de la motivation intrinsèque. CALM (Constructivist Anticipatory Learning Mechanism) est un mécanisme d'apprentissage fondé sur l'approche constructiviste de l'Intelligence Artificielle. Il permet à un agent situé de construire un modèle du monde dans des environnements partiellement observables et partiellement déterministes, sous la forme d'un processus de décision markovien partiellement observable et factorisé (FPOMDP). Le modèle du monde construit est ensuite utilisé pour que l'agent puisse définir une politique d'action visant à améliorer sa propre performance. / Esta pesquisa caracteriza-se, primeiramente, pela condução de uma discussão teórica sobre o conceito de agente autônomo, baseada em elementos provenientes dos paradigmas da Inteligência Artificial Situada e da Inteligência Artificial Afetiva. A seguir, a tese apresenta o problema da aprendizagem de modelos de mundo, fazendo uma revisão bibliográfica a respeito de trabalhos relacionados. A partir dessas discussões, a arquitetura CAES e o mecanismo CALM são apresentados. O CAES (Coupled Agent-Environment System) é uma arquitetura para a descrição de sistemas baseados na dicotomia agente-ambiente. Ele define agente e ambiente como dois sistemas parcialmente abertos, em acoplamento dinâmico. O agente, por sua vez, é composto por dois subsistemas, mente e corpo, seguindo os princípios de situatividade e motivação intrínseca. O CALM (Constructivist Anticipatory Learning Mechanism) é um mecanismo de aprendizagem fundamentado na abordagem construtivista da Inteligência Artificial. Ele permite que um agente situado possa construir um modelo de mundo em ambientes parcialmente observáveis e parcialmente determinísticos, na forma de um Processo de Decisão de Markov Parcialmente Observável e Fatorado (FPOMDP). O modelo de mundo construído é então utilizado para que o agente defina uma política de ações a fim de melhorar seu próprio desempenho. / This research is characterized, first, by a theoretical discussion on the concept of autonomous agent, based on elements taken from the Situated AI and the Affective AI paradigms. Secondly, this thesis presents the problem of learning world models, providing a bibliographic review regarding some related works. From these discussions, the CAES architecture and the CALM mechanism are presented. The CAES (Coupled Agent-Environment System) is an architecture for describing systems based on the agent-environment dichotomy. It defines the agent and the environment as two partially open systems, in dynamic coupling. The agent is composed of two sub-systems, mind and body, following the principles of situativity and intrinsic motivation. CALM (Constructivist Learning Anticipatory Mechanism) is based on the constructivist approach to Artificial Intelligence. It allows a situated agent to build a model of the world in environments partially deterministic and partially observable in the form of Partially Observable and Factored Markov Decision Process (FPOMDP). The model of the world is constructed and used for the agent to define a policy for action in order to improve its own performance.

The objective of this qualitative study was to explore the extent to which body maps could be implemented by educators as part of the fulfilment of their pastoral role. I approached the study from a constructivistinterpretivist perspective underpinned by action research principles. I implemented an instrumental case study as research design and selected a primary school located in an informal settlement community in the Nelson Mandela Metropole. Ten female educators at this school, three other members of a research team and I took part in the process of data generation. Having acquired baseline information during the first field visit, a fellow researcher and I implemented an intervention during which the techniques of body mapping and making memory boxes (the study focus of my fellow researcher) were introduced to the participants. We then requested them to apply the two techniques (as part of a research assignment) before we undertook a second field visit. At the second visit, we attempted to explore the participants' experiences during the application of the techniques. Throughout the study I relied on focus group discussions, observation, critical self-reflection, auditive methods, visual methods, photos, a reflective research journal and field notes as data collection and capture methods. I analysed and interpreted raw data thematically. Baseline information indicated that educators were quite clear about the theoretical nature of the pastoral role, yet the practical application of this role presented a challenge. Data generated after the intervention indicates how educators understood and used the body mapping technique. This theme was refined into subthemes dealing with implementation modes, application contexts and application outcomes of the body mapping technique. The second main theme indicated the applicability of body maps in the classroom context as part of the pastoral role. This theme comprises subthemes relating to general curricula, practical considerations, alternative uses and application modes, pastoral responsibilities that were facilitated (and not) by participants' use of the body mapping technique. Research findings therefore seem to indicate that the body mapping technique could be used by educators in fulfilling their pastoral role. / Dissertation (MEd (Educational Psychology))--University of Pretoria, 2007. / Educational Psychology / MEd / unrestricted

Alors que les principales activités d’un chef de projet s’effectuent à travers le processus de communication, on observe que de nombreux projets font l'objet de retards, dérives ou défauts de spécifications. Excès de mesures pour prévenir le risque ou gestion déficiente de la communication laissant trop de place à l’incertitude ? La Théorie de la Réduction de l’Incertitude développée par Berger et Calabrese (1975) dans le champ de la communication ne permet pas de totalement saisir comment un chef de projet dissipe l’incertitude existante entre les acteurs. En revisitant un projet opérationnel dans le cadre d’une recherche-action, nous nous employons à identifier comment incertitude et communication s’influencent et se structurent mutuellement. Nous avons convoqué l’approche constructiviste et la théorie de l’acteur-réseau de Callon et Latour pour accéder au sens de cette relation circulaire. Nous avançons les hypothèses selon lesquelles : - L’incertitude est un actant qui intervient dans la construction du réseau (au sens de Bruno Latour (2007) « ce qui est tracé par les traductions »).- Le processus de communication diffère suivant la nature de l’incertitude rencontrée ou ressentie. - Le processus de communication performe et scelle les relations en les rendant si coûteuses à défaire et si économiques à maintenir, qu’elles deviennent irréversibles. L’approche communicationnelle de l’incertitude mettra en évidence plusieurs caractéristiques de cet actant, comme sa capacité à peupler un « réseau de manques », la façon dont le réseau se hiérarchise pour faire sens, la description du processus d’estimation continue dont il fait l’objet (l’Incertus). Si nous concevons l’incertitude comme l’attribut d’un phénomène alors la « communication-incertitude » fabrique le sens en même temps qu’elle détermine la valeur de cet attribut. En positionnant l’incertitude comme un phénomène socialement construit, nous présentons un modèle constructiviste de « communication-incertitude » où l’observateur est un acteur intentionnel limité par des contraintes (Boudon, 2009) et proposons de distinguer la nature de l’incertitude suivant une typologie : l’incertitude de variabilité (inhérente à la variabilité des choses), l’incertitude épistémique ambiguë ou non (due à l’imperfection de nos connaissances) et l’incertitude d'échelle (en rapport avec l’imperfection de nos modèles de représentations). Dans ce mouvement vers l’irréversibilité, les processus de communication participent au remplacement des médiateurs (qui transforment, redonnent du sens, font faire des choses inattendues) par des intermédiaires (qui transmettent, transfèrent sans modifier) et les actants les plus réversibles sont évacués vers la périphérie du réseau. / While the main activities of a project manager are done through the communication process, it is observed that many projects are subject to delays, excesses or defects specifications. Excess of measurements to prevent the risk ? Defective management of the communication which leaves too much place to uncertainty ? The Theory of Uncertainty Reduction developed by Berger and Calabrese (1975) in the field of communication does not fully understand how a project dissipates the existing uncertainty between actors. By revisiting an operational project within the framework of action research, we strive to identify how uncertainty and communication influence and form themselves mutually. We used the constructivist approach and the actor-network theory of Callon and Latour to reach the meaning of this circular relationship. We advance the following hypotheses: - Uncertainty is a nonhuman actor involved in the construction of the network (as defined by Bruno Latour (2007) "which is drawn by translations"). - The communication process differs according to the nature of the uncertainty encountered or felt. - The communication process performs and seals relationships by making them so expensive to undo and so economic to maintain, that they become irreversible. The communicational approach of the uncertainty will highlight several features of this nonhuman actor, as its ability to populate a "network of gaps", the way the network ranks into a hierarchy to make sense, the description of the continuous process of estimation (the Incertus). If we conceive uncertainty as an attribute of a phenomenon, then "communication-uncertainty" makes sense at the same time it determines the value of this attribute. By positioning uncertainty as a socially constructed phenomenon, we present a constructivist model of "communication-uncertainty" where the observer is an intentional actor limited by constraints (Boudon, 2009). We propose to distinguish the nature of uncertainty following a typology: the variability uncertainty (inherent variability of things), the epistemic uncertainty ambiguous or not (due to the imperfection of our knowledge) and the scale uncertainty (in touch with the imperfection of our models of representations). In this movement towards irreversibility, the communication processes involved in replacing mediators (which transform, give meaning, make unexpected things do) by intermediaries (which transmit, transfer without changing) and the most reversible nonhumans actors are evacuated to the network edge.

Abstract is in English, Zulu and Xhosa / In Ghanaian primary schools, music is a compulsory study area which is taught by generalist teachers. However, information is deficient on the strategies teachers use to implement the music curriculum. The aim of this study was to determine how teachers organise musical learning experiences in terms of developmentally appropriate practice (DAP) for lower primary school pupils. DAP is an educational concept which refers to teaching strategies that consider children’s age, abilities, interests and experiences, to help them achieve challenging and achievable goals. The study was underpinned by the concept of teaching within the context of constructivist theory. Qualitative Interpretative Phenomenological Analysis and ethnographic research methods were used to find answers to the research questions. Data were collected by means of observations, interviews and document analysis. Singing, movements and the playing of improvised instruments (although they constitute only a part of the planned music curriculum in the Creative Arts syllabus) dominate the music activities provided in the schools. In fact, unplanned music activities dominate planned music lessons due to teachers’ perceived lack of adequate training to teach music, the non-application of ICT in teaching, a lack of teaching and learning materials, unsuitable physical conditions for teaching, lack of motivation and support to teach, and lack of time to teach music because of the emphasis on meeting the targets of teaching and assessment in core subjects. Strategies the teachers adopt to overcome the challenges they encounter in teaching music include collaboration with their colleagues in planning, teaching and integrating music into most classroom activities and drawing on pupils’ expertise in teaching and learning. It is recommended that teachers be given in-service training, that specialist teachers be used, and that adequate teaching and learning materials be provided, as well as support for teachers to integrate ICT in teaching music. Limitations associated with the study make generalisation of the findings impossible. A larger sample from various primary schools within the Ashanti region of Ghana should be considered for further research. Functional integration of music in the other subject areas within the Ghanaian context should also be explored and further studies should be conducted about the application of developmentally appropriate practice in teaching music in the lower-primary classroom. / Ezikoleni zamabanga aphansi zaseGhana, umculo uyindawo eyimpoqo yokufunda efundiswa ngothisha abajwayelekile. Kodwa-ke, ulwazi alwanele ngamasu othisha abawasebenzisayo ukwenza izifundo zomculo. Inhloso yalolu cwaningo kwakuwukuthola ukuthi othisha bahlela kanjani amava okufunda omculo ngokwendlela efanelekile yokuthuthuka (NET) yabafundi bezikole zamabanga aphansi. NET ingumqondo wezemfundo obhekisa kumasu okufundisa abheka iminyaka yezingane, amakhono, izintshisekelo kanye nezipiliyoni ezithile, ukuzisiza ukuthi zifeze izinhloso eziyinselele futhi ezingafinyeleleka.Ucwaningo lwalusekelwa ngumqondo wokufundisa ngokwengqikithi yethiyori yokwakha. Ukuhlaziywa Okufanelekile Kokuhunyushelwa Kokubukeka Kwabantu nezindlela zokucwaninga ngobuzwe zisetshenzisiwe ukuthola izimpendulo zemibuzo yocwaningo. Kuye kwaqoqwa imininingwane yolwazi ngokubheka okwenzekayo, izinhlolokhono kanye nokuhlaziywa kwemibhalo. Ukucula, ukunyakaza nokudlalwa kwezinsimbi ezithuthukisiwe (yize ziyingxenye nje kuphela zekharikhulamu yomculo ehleliwe kusilabhasi Yezobuciko Bokuzenzela) kulawula imisebenzi yomculo enikezwe ezikoleni. Empeleni, imisebenzi yomculo engahlelwanga ilawula izifundo zomculo ezihleliwe ngenxa yokungabi bikho kothisha abaqeqeshwe ngokwanele ukufundisa umculo, ukungasetshenziswa kwe- ICT/Ezobuchwepheshe ekufundiseni, ukuntuleka kwezinto zokufundisa nokufunda, izimo ezzibambekayo ezingafanelekile zokufundisa, ukungabi nogqozi nokusekelwa ekufundiseni, nokungabi nesikhathi sokufundisa umculo ngenxa yokugcizelelwa ekuhlangabezaneni nezinhloso zokufundisa nokuhlola ezifundweni ezibalulekile. Amasu othisha abawasebenzisayo ukunqoba izinselelo abahlangabezana nazo ekufundiseni umculo kufaka phakathi ukusebenzisana nozakwabo ekuhleleni, ukufundisa nokuhlanganisa umculo emisebenzini eminingi yasekilasini nokudweba ubuchwepheshe babafundi ekufundiseni nasekufundeni. Kunconywa ukuthi othisha banikezwe ukuqeqeshwa emsebenzini, ukuthi kusetshenziswe othisha abangochwepheshe, nokuthi kuhlinzekwe ngezinto ezanele zokufundisa nokufunda, kanye nokuxhaswa kothisha ukuze bahlanganise i-ICT/Ezobuchwepheshe ekufundiseni umculo. Ukulinganiselwa okuhambisana nesifundo kwenza ukuthi okwenziwa jikelele kokutholakale kungenzeki. Isampula elikhudlwana elivela ezikoleni ezahlukahlukene zamabanga aphansi esifundeni sase-Ashanti eGhana kufanele licatshangwe ukuqhubeka nocwaningo. Ukuhlanganiswa kokusebenza komculo kwezinye izindawo ezingaphansi komongo waseGhana nakho kufanele kuhlolwe futhi kufanele kuqhutshekwe nezifundo ezimayelana nokusetshenziswa kwenqubo efanelekile yentuthuko ekufundiseni umculo ekilasini lamabanga aphansi. / Kwizikolo zaseGhana zamabanga asezantsi, kusisinyanzelo ukufundisa umculo, kwaye oku kwenziwa ngabafundisi ntsapho okanye ootitshala abafundisa yonke into. Noxa kunjalo, akukho lwazi lwaneleyo ngamacebo asetyenziswa ziititshala ekufundiseni ikharityhulam yomculo. Injongo yesi sifundo kukuqwalasela ukuba iititshala zikulungiselela njani ukufundisa ngendlela yophuhliso olufanelekileyo (iDAP) kumabanga asezantsi. Le DAP nesisishunqulelo sesiNgesi sebinza elithi developmentally appropriate practice, yingcinga yezemfundo emalunga namacebo okufundisa athathela ingqalelo ubudala bomntwana, izinto akwaziyo ukuzenza, umdla namava akhe, ukuze ancedwe ekufezekiseni iinjongo ezicela umngeni nezinokufikeleleka. Esi sifundo sisekelwe yingcinga yokufundisa ephuma kwimeko yengcingane yokuzakhela ulwazi. Iimpendulo zophando zifunyenwe ngokusebenzisa iindlela zophando ngokuxoxa nokutolika iimeko ezahlukeneyo (Qualitative Interpretative Phenomenological Analysis) kunye nokuqwalasela inkcubeko. Iinkcukacha zolwazi okanye idatha, ziqokelelwe ngokujonga okuqhubekayo, udliwano ndlebe nokuphengulula imibhalo ekhoyo. Ukucula, ukushukuma nokudlala izixhobo zomculo ezingoozenzele (nangona ziyinxalenye yekharityhulam ecetywayo yobuGcisa Bokuzenzela) kudlala indima eyongameleyo kwimisebenzi yomculo eyenziwa ezikolweni. Xa sithetha inyaniso, into eyenzekayo ekufundiseni umculo yimisebenzi engacetywanga ezifundweni ngenxa yokuba ootitshala abaqeqeshekanga kakuhle ekufundiseni umculo, abusetyenziswa ubuchwepheshe ekufundiseni umculo, azikho izixhobo zokufundisa nokufunda umculo, iindawo ekufundiselwa kuzo azifanelekanga, inkxaso nenkuthazo yokufundisa umculo iyasilela kwaye lincinci ixesha lokufundisa umculo ngenxa yokuleqa ukufezekisa imiqathango yokufundisa nokuhlola kwizifundo ezingoondoqo. Ekulweni nemingeni yokufundisa umculo, ootitshala babhenela ekusebenzisaneni nabanye ekwenzeni amacebo okufundisa nokubandakanya umculo kwimisebenzi yeklasi nasekusebenziseni ulwazi lwabafundi. Kucetyiswa ukuba ootitshala bafumane uqeqesho lo gama besebenza, kusetyenziswe ootitshala abaziingcali zomculo kwaye kufumaneke izixhobo ezifanelekileyo zokufundisa nokufunda, kuxhaswe ootitshala ekusebenziseni ubuchwepheshe xa befundisa umculo. Ukunqaba kolwazi okungqonge esi sifundo kwenza kube nzima ukugqiba jikelele ngokufunyanisiweyo. Mhlawumbi kunokuthathwa isampulu yophando enkulu kwingingqi yaseAshanti eGhana ukuze kwandiswe olu phando. Okunye okunokwenziwa kukuhlanganisa umculo nezinye izifundo ngokwemeko yaseGhana, kwaye kufuneka kuqhutywe izifundo ezithe chatha malunga nokusebenzisa iindlela zokufundisa ezinophuhliso olufanelekileyo ekufundiseni umculo kwiklasi yamabanga asezantsi. / Art History, Visual Arts and Musicology / Ph D. (Music)

Abstracts in English, Afrikaans and Zulu / The purpose of this study was to explore the learners’ understanding of trigonometric functions using GeoGebra software. A qualitative case study approach was used with six Grade 11 learners at a school in Tshwane South District. The data were collected during a seven-day period using multiple methods: a diagnostic test, worksheets, a smart recorder, a trigonometric functions test, one-on-one interviews and focus-group discussions. The findings showed clearly that the use of GeoGebra enhanced Grade 11 learners’ understanding of trigonometric functions. The findings also showed that the use of GeoGebra helped the learners to understand the basic trigonometric functions graphs. This enabled them to sketch freely without using the point-by-point method. Based on this study, it is recommended that GeoGebra should be made available to all Grade 11 learners. This will encourage them use the software out of regular school hours. / Die doel van hierdie studiegids was om die leerder se kennis van die gebruik van GeoGebra sagteware, ten opsigte van trigonometriese funksies te ondersoek. ‘n Kwalitatiewe benadering is gevolg met ses Graad 11 leerders by ‘n skool in die Tshwane Suid Distrik. Die data is ingewin oor ‘n periode van sewe dae, deur gebruik te maak van verskeie metodes: ‘n diagnostiese toets, werkkaarte, ‘n “smart” opname, ‘n trigonometriese funksies toets, een-tot-een onderhoude en fokusgroepe waar besprekings plaasgevind het. Die data-analise wys duidelik dat die gebruik van GeoGebra, die Graad 11 leerders gehelp het om trigonometriese funksies beter te verstaan. Die uitkomste wys ook duidelik dat GeoGebra die leerders gehelp het met ‘n beter begrip van die basiese trigonometriese funksies. Dit het hulle gehelp om vryhand sketse te doen en nie noodwendig die punt-tot-punt metode nie. Gebaseer op hierdie studie beveel ons aan dat GeoGebra beskikbaar gemaak moet word aan aale Graad 11 leerders. Dit sal leerders motiveer om ook die sagteware op hulle eie buite skoolure te gebruik. / Injongo yocwaningo lolu bekuyikuhlola ukuzwisisa kwabantwana amagrafu e-trigonometry ma bewafunda nge softhiwe ye GeoGebra. Abantwana abayisithupha abakubanga letshumi lanye abaphuma kusigodi se Tshwane South babambiqhaza kulolucwaningo lwendlela ye ‘qualitative case study’. Imininingo iqoqwe kumalanga ayisikhombisa kusetshenziswa indlela ezilandelayo: ukuhlolwa kwe-diagnostic, amaphepha okusebenzela, isingxoxo zamunye ngamunye lezingxoxo leqembu. Iziphumo ezinkulu zikhombe ngokucacile ukuthi ukusetshenziswa kwesofthiwe yeGeoGebra kukhulise ukuzwisisa kwamagrafu e-trigonometry ngabafundi bebanga letshumi lanye.Iziphumo njalo zibonise ukuthi abafundi bazwisisa izinto eziyisiseko ngala magrafu ma bewafunda ngesofthiwe ye GeoGebra. Lokhu kunike abafundi amandla okudwebadweba lamagrafu ngokushesha ngokukhululeka. Kusekelwa ngalezi ziphumo, kunconyiwe ukuthi abafundi bafumane isofthiwe yeGeoGebra ngaso sonke isikhathi. Lokhu kuzabakhuthaza ukuthi basebenzise lesofthiwe noma bengaphandle kwesikolo. / Mathematics Education / M. Ed. (Mathematics Education)

With the realization that traditional instructional approach has not yielded satisfactory results, quasi-experimental and descriptive research designs were employed to investigate whether the application of constructivist instructional approach in the learning of stationary points in differential calculus by Grade 12 learners in South Africa would improve conceptual learning. Three Gauteng high schools of 204 Grade 12 learners constituted the research fields – one served as the control group while the other two represented the experimental group. Being a mixed-method research, quantitative data were gathered through pre-test and post-test while qualitative data were collected from classroom observations. Both inferential and descriptive statistical methods of data collection and analysis were used. The results obtained indicate that the experimental group demonstrated a better understanding of the concept of stationary points than the control group. / Mathematics Education / M. Sc. (Mathematics Education)

<p>In this dissertation, I investigate the authentic learning experiences of students participating in the Engineering Projects in Community Service (EPICS) program at Purdue University within the framework of authentic education. Utilizing a quantitative approach, the study assesses the performance of new and returning students across five key outcomes that measure authentic learning during a single semester. The analysis of variance (ANOVA) revealed significant main effects for time of assessment and type of student on performance, with an overall improvement in all outcomes observed from mid-term to final evaluations and returning students typically outperforming new students. Interaction effects between time and type were also examined, revealing subtle yet complex dynamics in students’ learning trajectories. The findings hold implications for enhancing authentic learning, especially in engineering design contexts, and offer insights to guide future implementation of and improvements to authentic education initiatives, particularly the EPICS program. Despite certain limitations, the research opens avenues for future investigations into diverse aspects of authentic education in STEM and beyond.  </p>

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