Es ist eine weit verbreitete Wahrnehmung, dass der Übergang zwischen der Mathematik der gymnasialen Oberstufe und der Mathematik an der Universität für Studierende problematisch sein kann. Besondere Verständnisschwierigkeiten in Bereich der lineare Algebra (lA) bereiten den Studierenden die verschiedenen Herangehensweisen auf diesen beiden Ebenen. Dies lässt sich auf die strukturell-axiomatischer Herangehensweisen an die lA an der Universität, im Gegensatz zu ihrer arithmetisch-geometrischen Darstellung in der Schule, zurückführen. Dies bedingt ebenfalls Unterschiede im prozeduralen und konzeptuellen Verständnis. Ziel dieser Arbeit ist es, zu untersuchen, wie Schüler konzeptuelles Verständnis, Bezug nehmend auf die Theorien von concept definition/image in Verbindung mit multiplen Modi der Beschreibung und des Denkens von Konzepten wie Bilinearität z.B. Skalarprodukt und Multilinearität z.B. Determinanten gewinnen können. Um dies zu erreichen wurde eine substanzielle Lehr-Lernumgebung unter Verwendung einer dynamischen Geometriesoftware (DGS) entwickelt. Die Lerneinheit wurde an einem Berliner Gymnasium eingesetzt und dabei ein vollständiger design-based research Zyklus durchlaufen und eine multiple-level Datenanalyse durchgeführt. Die Ergebnisse der Untersuchung zeigen nicht nur, dass eine Erweiterung der Vorstellungen der Schüler, eine Entwicklung multipler Denkmodi und ein Gewinn tieferen konzeptuellen Verständnisses in der lA erfolgreich vermittelt werden können, sondern geben auch Einblicke in ein mögliches theoretisches Modell, mit dessen Hilfe sich diese Prozesse weiter untersuchen lassen. Weiterhin werden die interaktiven Lehr-Lernmaterialien für die weitere Verwendung im Rahmen von Lehre und Forschung zur Verfügung gestellt. Es öffnen sich neue Forschungsfragen hinsichtlich lokalen Axiomatisierens in der lA der gymnasialen Oberstufe, welches auf einer Integration geometrischer, algebraischer und axiomatischer Denkmodi, unterstützt durch DGS, basieren könnte. / A common perception among researchers in mathematics education is that the transition between secondary- and tertiary level of mathematics may be problematic for the students. In particular, the exact and abstract nature of the theory of Linear algebra versus its arithmetic-geometric presentation in school appears to be difficult for the novice students. The application of properties for defining concepts at university in contrast to their usage for describing concepts in school points out a possible occurrence of obstacles for learning and discrepancies in procedural and conceptual understanding. The aim of this study is to examine how could upper-high school students develop a conceptual understanding based on concept definition and concept image in connection to multiple modes of description and thinking about concepts such as bi-linearity exemplified by the dot product of vectors and multi-linearity exemplified by determinants. In order to achieve this, I have created a specific teaching/ learning sequence in a dynamic geometry environment (DGE), then implemented it and evaluated it in a high school in Berlin, following a complete cycle of design-based research and conducting a multiple-level data analysis. The findings of the study show not only that widening students' concept images, developing multiple modes of thinking and gaining deeper conceptual understanding can successfully be mediated by dynamic geometries, but also give insights into an eventual theoretical model of how can they be further examined. Moreover, the study promotes authorized open-source interactive teaching/ learning materials for further sustainable practice and research. It opens new research questions about revisiting axiomatic approaches on local levels in upper high-school Linear algebra which may base on the integration of all three modes of description and thinking geometric, algebraic and abstract possibly facilitated by DGE. / Честа перцепција кај многумина истражувачи во областа на математичкото образование е дека транзицијата помеѓу средното и високото образование по математика може да биде проблематична за студентите. Егзакноста и апстрактноста на теоријата по Линеарна алгебра наспроти нејзината аритметичко-геометриска презентација во средното гимназиско образование се покажува како особено тешка за студентите. Примена на својствата на математичките поими за нивно дефинирање на универзитетско ниво наспроти нивното употреба за опишување на претходно дефинирани поими на училишно ниво, укажува на можна појава на тешкотии при нивното изучување и несовпаѓање на процедуралното и концептуалното разбирање на истите. Целта на оваа студија е да истражи како средношколците би можеле да развијат концептуално разбирање на поимите врз основа на концепт дефиниција и концепт слика во врска со мулти-моди на мислење, конкретно за поими како билинеарност, пр. скаларен производ на вектори, и мултилинеарност, пр. детерминанти. За да ја постигнам оваа цел, креирав наставна содржина поддржана од еден динамичен геометриски систем (ДГС) и следејќи целосен циклус на т.н. design-based research и спрoведувајќи мулти-анализа на податоци, истата ја имплементирав и евалуирав во едно средно училиште во Берлин. Резултатите од студијата укажуваат не само на фактот дека проширувањето на концепт сликите на учениците, развојот на мулти-моди на мислење и стекнувањето на длабоко концептуално разбирање на поимите можат да бидат успешно посредувани од ДГС туку овозможија и увид во еден теоретски модел за тоа коко тие можат понатаму да се истражуваат. Уште повеќе, студијата промовира авторизирани open-source интерактивни материјали за предавање и учење на содржините кои може да служат за понатамошни одржливи истражувања и развој. Студијата отвора нови истражувачки прашања за средношколската Линеарна алгебра која може да се базира на интеграција на сите три моди на мислење, геометриски, алгебарски и апстрактен, поддржан од ДГС.

Students in Open Distance Learning (ODL) face a myriad of challenges including a low proficiency in English. While research has identified vocabulary as important in improving language proficiency and the pertinent role of interaction in vocabulary development, there remains a dearth of research on how to enhance vocabulary in ODL, a context which is characterised by the distance between students and the institution. In searching for an intervention that would support vocabulary development, including interaction, while taking cognisance of the distance between students and lecturers, this study explored the use of mobile learning (mlearning). Because mlearning technologies offer ubiquitous flexibility and accessibility, they were deemed fit for purpose for ODL which is established on the principles of openness, flexibility and student‐centredness. Using the design‐based research (DBR) method within a pragmatic paradigm, this study designed, implemented and evaluated mobile‐based interventions for vocabulary development. The first phase of the study involved the analysis of the problem through a literature review. The literature and theoretical framework were used to ground the second phase of DBR, which included the development of the intervention prototype in the form of a mobile‐based vocabulary development app called VocUp. The intervention was implemented, tested and refined in three iteration stages, which formed the third phase of DBR. The iterations included a VocUp only stage, followed by a WhatsApp only stage, and ended with a VocUp plus WhatsApp stage. The last phase of DBR involved a reflection and a production of artefacts and guidelines for practice in ODL. Data were collected through interviews and WhatsApp chats from students registered for a first‐year English module. The results were 1) that vocabulary should be explicitly taught, allow for rehearsal opportunities and contain assessment while acknowledging the instrumental role of interaction; 2) mobile interventions should balance the pedagogic benefits with the technological qualities; and 3) the advantages and challenges of using WhatsApp and VocUp can be successfully combined into a hybrid model of both platforms. This study’s contribution to the body to knowledge includes the newly‐designed VocUp as an artefact; a revised model of the CoI theoretical framework called MODeL as well as principles guiding the application of the MODeL in authentic ODL contexts. / English Studies / D. Litt. et Phil. (English)

Abstracts in English, Afrikaans and Zulu / Worldwide, students compete for a limited number of places at universities. By increasing the use of distance education, more students could have access to tertiary education. The problem addressed in this study related to the challenges faced by an ODL university to assess undergraduate modules in accounting sciences by way of technology-enhanced, non-venue-based alternative assessments, instead of the traditional venue-based examinations. The purpose of the current study was to develop an alternative assessment framework for ODL undergraduate accounting sciences modules as a possible solution to the assessment challenges faced by accounting graduates and universities in an ODL environment. The legitimacy of qualifications was considered by reviewing the identity verification of students and other ethical issues, as well as the influence on the accreditation by professional and other regulatory and governing bodies. Institutional and neo-institutional theories were used within the ODL context as foundational principles. Design-based research was used to develop two conceptual frameworks – one based on the theoretical elements and the other on non-venue-based alternative assessments in the ODL context. The two conceptual frameworks were evaluated using interviews conducted with ODL lecturers and members of professional accounting bodies. Thereafter, the data were analysed using thematic analysis. Triangulation was used as a final evaluation of the conceptual frameworks by analysing comments from students included in reports from an alternative assessment pilot study. The two conceptual frameworks were combined in one final framework. This final framework demonstrates how the institutional theory affects the institution and, specifically, internal issues. Due to the complexity of the ODL institution, external influences (such as technology) result in aspects of the neo-institutional theory becoming even more relevant to the current study. This complexity, together with the mimetic forces of technology and innovation, creates uncertainty. However, it became clear from the data analysis that coercive and normative forces result in ‘more certainty’. The alignment of these isomorphic forces resulted in legitimacy. Due to the importance of technology in the ODL environment, it became clear that technology should be anthropomorphically considered a stakeholder in the ODL institution. The inclusion of stakeholder theory created improved performance and the potential for innovation in order to ensure the legitimacy of qualifications. / Studente ding wêreldwyd mee vir 'n beperkte aantal plekke in universiteite. Indien die gebruik van afstandsonderrig uitgebrei word, kan meer studente toegang tot tersiêre onderwys kry. Die probleem waarop hierdie studie fokus is die uitdagings van 'n OAO-universiteit om voorgraadse modules in rekeningkundige wetenskappe te assesseer deur middel van tegnologies verbeterde, nie-lokaalgebaseerde alternatiewe assesserings in plaas van die tradisionele, lokaalgebaseerde eksamens. Die doel van die huidige studie was om 'n alternatiewe assesseringsraamwerk vir voorgraadse rekeningkundige wetenskapmodules in OAO te ontwikkel as 'n moontlike oplossing vir die assesseringsuitdagings van rekeningkundige gegradueerdes en universiteite in ’n OAO-omgewing. Die geldigheid van kwalifikasies is oorweeg deur 'n oorsig te doen oor die identiteitsverifiëring van studente en ander etiese aangeleenthede, asook die invloed op die akkreditasie deur professionele en ander regulatiewe beheerliggame. Institusionele en neo-institusionele teorieë is in die OAO-konteks as grondbeginsels gebruik. Ontwerpgebaseerde navorsing is gebruik om twee konseptuele raamwerke te ontwikkel – een gebaseer op die teoretiese elemente en die ander op nie-lokaalgebaseerde alternatiewe assesserings in die OAO-konteks. Die twee konseptuele raamwerke is geëvalueer aan die hand van onderhoude met OAO-dosente en lede van professionele rekeningkundige liggame. Hierna is die data deur middel van tematiese analise ontleed. Triangulasie is gebruik as 'n finale evaluering van die konseptuele raamwerke deur die kommentaar van studente wat in verslae van 'n alternatiewe assesseringsvoorstudie ingesluit is, te evalueer. Die twee konseptuele raamwerke is in een finale raamwerk gekombineer. Hierdie finale raamwerk demonstreer hoe die institusionele teorie die instelling en, spesifiek, interne aangeleenthede beïnvloed. As gevolg van die kompleksiteit van die OAO-instelling, veroorsaak eksterne invloede (soos tegnologie) dat die neo-institusionele teorie selfs meer relevant vir die huidige studie word. Hierdie kompleksiteit, tesame met die mimetiese magte van tegnologie en innovasie, skep onsekerheid. Dit is egter duidelik uit die data-analise dat dwang- en normatiewe magte ‘meer sekerheid’ veroorsaak. Die belyning van hierdie isomorfiese magte veroorsaak geldigheid. As gevolg van die belangrikheid van tegnologie in die OAO-omgewing, is dit duidelik dat tegnologie antropomorfies beskou moet word as 'n belanghebber in die OAO-instelling. Die insluiting van die belanghebbende teorie het verbeterde prestasie en die potensiaal vir innovasie tot gevolg gehad, om sodoende die geldigheid van kwalifikasies te verseker. / Emhlabeni wonke, abafundi bazabalazela ukuthola ithuba lokungena kwizindawo ezingamanyuvesi amancane ngenani. Ngokukhulisa izinga lokusetshenziswa kohlelo lokufunda ukude, abafundi abaningi bebangakwazi ukungena emazikweni ezemfundo aphakemeyo. Inkinga exazululwa kulolu cwaningo imayelana nezinselelo ezibhekene nenyuvesi yohlelo lwe-ODL ukuhlola amamojuli asesigabeni seziqu zokuqala kwisayensi ye-accounting ngendlela yoncedo lobuchwepheshe, ngezinye izinhlelo zokuhlola ezingenziwa endaweni eyodwa, kunokusebenzisa uhlelo olwejwayelekile lokuhlolwa okwenziwa endaweni eyodwaethize. Inhloso yocwaningo lwamanje kwaye kungukwakha esinye isakhiwo sokuhlola samamojuli esayensi ye-accounting yeziqu zokuqala, lokhu kwenziwa njengekhambi elingaxazulula izinselelo zokuhlola ezibhekene nabafundi besifundo se-accounting kanye namanyuvesi akusizinda sohlelo lwe-ODL. Udaba lokuba semthethweni kweziqu luye lwabhekwa ngokubuyekeza ukuqinisekiswa kwamagama abafundi kanye nezinye izindaba ezimayelana nemigomo yokuziphatha, kanye nomthelela phezu kokwamukelwa kwamaprofeshinali kanye nezinye izinhlaka eziqinisa umthetho kanye nezinye izinhlaka eziphetheyo. Amathiyori eziko kanye nalawo ohlelo olusha lwamaziko asetshenziswe ngaphakathi kwesizinda se-ODL njengemigomo eyisisekelo. Ucwaningo olususelwa kwidizayini lusetshenziswe ukwakha izinhlaka ezimbili zegama – olunye uhlaka lususelwe kwizinto zethiyori kanye nakwezinye izinhlelo zokuhlola ezingasuselwa ezindaweni ezimile ngaphakathi kwesizinda se-ODL. Izinhlaka ezimbili zezakhiwo ziye zahlolwa ngokusebenzisa izinhlolovo ezenziwa abafundisi be-ODL kanye namalungu wezinhlangano eziprofeshinali zesifundo se-accounting. Ngemuva kwalokho, idatha ihlaziywe ngokusebenzisa uhlelo lokuhlaziya isihloko. Unxantathu wezinhlolovo (triangulation) usetshenziswe njengohlelo lokugcina lokuhlola izakhiwo zegama ngokuhlaziya izimvo ezivela kubafundi ezixutshwe kwimibiko evela ohlelweni lokuhlolwa kwesivivinyo socwaningo.Lezi zakhiwo zamagama ezimbili zihlanganiswe kuhlaka olulodwa lokugcina. Lolu hlaka lwesakhiwo lukhombisa indlela umqondo weziko othinta ngayo iziko, ikakhulu, izinto ezingaphakathi. Ngenxa yengxubevange yeziko elinohlelo lwe-ODL, imithelela evela ngaphandle (enjengobuchwepheshe) idala izinto ezihambelana nomqondo omusha weziko oya ngokuya uhambisane nesifundo samanje socwaningo. Le ngxubevange indawonye nemimoya yobuchwepheshe kanye namaqhinga amasha, kuletha isimo esingenakuqinisekiswa. Yize kunjalo, kuya ngokucaca ukusukela ekuhlaziyweni kwedatha ukuthi imimoya ephoqayo kanye naleyo eyejwayelekile idala isimo esingaziwa. Ukuhambisana kwalawa mandla okudalwe yizinto ezisemthethweni. Ngenxa yokubaluleka kobuchwepheshe kwisizinda se-ODL, kuye kwacaca ukuthi ubuchwepheshe kufanele buthathelwe phezulu njengesidlalindima kwiziko le-ODL. Ukufakwa komqondo womdlalindima kudale umsebenzi omuhle othuthukile kanye namathuba okuveza amaqhinga amasha ukuze kuqinisekiswe isimo sokuqinisekisa iziqu ukuthi zibe semthethweni. / College of Accounting Sciences / D. Phil. (Accounting Sciences)