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.