Improving teachers' technological pedagogical content knowledge for teaching Euclidean geometry using integrated information communication technologies software

Abstract

English: The study aimed at formulating a strategy to improve teachers’ technological pedagogical content knowledge (TPACK) for teaching Euclidean geometry with the aid of integrated information and communication technology (ICT) software. TPACK refers to the interaction of three knowledge domains, which are, technology, pedagogy and content knowledge. The three knowledge domains further intersect to form subsets, which are, technological content knowledge; technological pedagogical knowledge; and pedagogical content knowledge. The three knowledge domains, together with the subsets, were used to define knowledge needed for teaching with the aid of technology. Furthermore, in the context of this study, integrated ICT software tools that were employed in teaching Euclidean geometry as teaching aids were Geometer’s Sketchpad, GeoGebra and HeyMath!. The study pursued the challenges that teachers face when they use ICT software as a teaching aid; these challenges included the following: Some teachers experience difficulties keeping up with rapidly advancing software knowledge; and the majority of teachers lack sufficient knowledge and skills to explore the potential of ICT software fully. In addition, part of the problem is that teachers found Euclidean geometry too abstract and difficult to teach. Thus, the study was geared to formulating a strategy to respond to these challenges. However, the challenge is that the knowledge needed for teaching is contextually bound and complex. Thus, the study adopted bricolage as a theoretical lens for the study, mainly due to its critical commitment to making meaning of complex objects of study in their contexts. In this study, bricolage enabled me to consider a theoretical stance from the eight historical moments of qualitative research. Through the multiplicity of theoretical lenses provided by bricolage I was able to unravel the multi-layered challenges and formulate a multi-layered strategy. The multi-layered strategy was made possible by people who came together, with diverse back stories, knowledge and skills. In this study mathematics teachers who are faced with the day-to-day challenges of teaching Euclidean geometry with the aid of ICT software embarked on research to solve their own challenges. Driven by its epistemological stance on knowledge production, participatory action research created a platform for teachers, academics, and a computer programmer to engage in knowledge production activities with equality and tolerance of contrasting views. Various data generation tools were employed, ranging from audio and video recordings, learners’ scripts and data from their test scores. In order to deepen the meaning of spoken and written text, the study employed Van Dijk’s critical discourse analysis at three levels, namely, text, discursive practices and social structures. Furthermore, learners’ test scores were analysed using statistical techniques, such as boxplot, analysis of variance and statistical modelling. The study analysed the challenges experienced by teachers who teach Euclidean geometry with the aid of integrated ICT software. This was done for the purpose of proposing possible solutions and strategies that can be developed, adopted and adapted to address the challenges teachers experienced effectively. In addition, for the purpose of sustainability of the strategy formulated to improve teachers’ TPACK during and beyond the duration of the study, the conditions conducive for the strategy were investigated. The study analysed threats and risks that were embedded or inherited in the setting, to prevent them from impeding the successful implementation of the strategy. The study is transformative in nature, which created the opportunity to operationalise and evaluate the success of the strategy prior to it being considered for recommendation. Finally, some of the major findings were that teachers work in silos; and that they do not prepare sufficiently when they use ICT software as a teaching aid.

Afrikaans: Die studie se doel was om ‘n strategie te formuleer om onderwysers se tegnologiesepedagogiese- inhoudskennis (TPACK) vir die onderrig van Euklidiese meetkunde met die hulp van geïntegreerde inligtings- en kommunikasietegnogie (IKT) programmatuur, te verbeter TPACK verwys na die interaksie van drie kennisdomeine, naamlik, tegnologie-, pedagogiese en inhoudskennis. Die drie kennisdomeine sny mekaar verder om onderafdelings te vorm, naamlik tegnologie-inhoudskennis, tegnologiese pedagogiekkenis en pedagogiese inhoudskennis. Die drie kennisdomeine en die onderafdelings is gebruik om die kennis wat nodig is vir onderrig met tegnologie, te definieer. In die konteks van hierdie studie is van geïntegreerde IKT programmatuur gebruik gemaak om Euklidiese meetkunde te onderrig. Hierdie onderrighulpmiddels was Geometer’s Sketchpad, GeoGebra en HeyMath!. Die studie het ondersoek ingestel na die uitdagings wat onderwysers konfronteer wanneer hulle IKT programmatuur as onderrighulpmiddels gebruik. Hierdie uitdagings het die volgende ingesluit. Sommige onderwysers ervaar probleme om by te hou met vinnig ontwikkelede programmatuurkennis; en die meerderheid onderwysers het nie genoeg kennis en vaardighede om die potensiaal van IKT programmatuur ten volle te ondersoek nie.Verder is deel van die probleem dat onderwysers Euklidiese meetkunde te abstrak ervaar, en moeilik vind om te onderrig. Dus was hierdie studie daarop gerig om ‘n strategie te formuleer wat hierdie uitdagings sou aanspreek.Die uitdaging is egter dat die kennis wat vir onderrig nodig is, kontekstueel gebonde en kompleks is. Dus het die studie bricolage as ‘n teoretiese lens vir die studie aanvaar, hoofsaaklik weens bricolage se verbintenis tot sinmaak van komplekse onderwerpe van studie binne hulle kontekste. In hierdie studie het bricolage my in staat gestel om ‘n teoretiese standput in te neem wat die agt historiese momente van kwalitatiewe navorsing in ag neem. Deur die verskeidenheid teoretiese lense van bricolage kon ek die veelvuldige lae waaruit die uitdagings bestaan, uitrafel en ‘n veelvlakkige strategie formuleer. Die veelvlakkige strategie was moontlik gemaak deur mense wat saamgewerk het, en wat hulle diverse agtergrond-stories, kennis en vaardighede bygedra het. In hierdie studie het wiskunde-onderwysers wat met die dag-tot-dag uitdagings gekonfronteer word wat met die onderrig van Euklidiese meetkunde met die hulp van IKT programmatuur verband hou, navorsing onderneem om hulle uitdagings self aan te spreek. Aangespoor deur die metode se epistemologiese standpunt teenoor kennisskepping, het deelnemende aksienavorsing ‘n platvorm vir die onderwysers, akademici en ‘n rekenaarprogrammeerder gebied om in kennisskeppingsaktiwiteite betrokke te raak, met gelykheid en aanvaardig van uiteenlopende standpute as oogmerk. ‘n Verskeidenheid hulpmiddels is gebruik om data te genereer, van oudioen video-opnames en leerders se vraestelle, tot leerders se toetspunte. Ten einde die betekenis van gesproke en geskrewe teks te verdiep, het die studie Van Dijk se kritiese- diskoersanalise op drie vlakke aangewend, naamlik, teks, diskursiewe praktyke en sosiale strukture. Leerders se toetstellings is met die hulp van statistiese tegnieke ontleed, waaronder boxplot, ontleding van variansie en statistiese modellering. Die studie het die uitdagings wat onderwysers wat Euklidiese meetkunde met die hulp van geïntegreerde IKT programmatuur onderrig, ontleed. Dit is gedoen met die doel om moontlike oplossings en strategieë voor stel wat ontwikkel, aanvaar en aangepas kan word om die uitdagings wat onderwysers ervaar, doeltreffend aan te spreek. Verder, met die doel om te verseker dat die strategie wat geformuleer is om die onderwysers se TPACK te verbeter, gedurende en na die duur van die studie volhoubaar sal wees, is die toestande wat bevorderlik is vir die strategie ondersoek. Die studie het dreigemente en risikos wat in die situasie ingebed of oorgeërf is, ontleed, om te voorkom dat dit die sukesvolle implementering van die strategie belemmer. Die studie is tranformerend van aard, en dit het geleentheid geskep vir operasionalisering en evaluering van die sukses van die studie voordat dit vir aanbeveling oorweeg word. In die laaste plek is van die belangrikste bevindinge dat onderwysers in silos werk, en dat hulle nie voldoende voorberei wanneer hulle IKT programmatuur as onderwyshulpmiddel gebruik nie.