Unpacking teachers' pedagogical content knowledge and skills to develop learners' problem solving skills

Tambara, Cosmas Toga (2015-03)

Thesis (PhD)--Stellenbosch University, 2015.

Thesis

ENGLISH ABSTRACT: In this study, the pedagogical knowledge of Foundation Phase teachers is explored (and unpacked) in order to obtain insight into their understanding of the teaching and learning of mathematics. The teacher’s knowledge is explored, as it is one of the most important variables that impacts on what is done in the classroom. The exploration is undertaken against the background of the very poor overall achievement of learners in the national systemic evaluations and in international assessment studies, which is currently a cause for great concern. This has resulted in different nation-wide intervention programmes that are aimed at improving teacher performance and effectiveness. In this study, the teacher is the focal point of the intervention. Problem-based learning (PBL), which is well-regarded as being one of the best examples of a constructivist learning environment, is introduced to a group of 15 Foundation Phase teachers. The study is an unpacking of the Foundation Phase teachers’ pedagogical knowledge and beliefs regarding, and practices in, the teaching and learning of mathematics, as well as in the use of PBL as a vehicle for the teaching and learning of mathematics. The unpacked knowledge can be used to address the challenges that are related to the improvement of the teaching and learning of mathematics in the Foundation Phase. A combination of qualitative and quantitative research methods, including questionnaires, interviews, lesson observation, and workshops, were used to explore the teachers’ current pedagogical knowledge, beliefs and practices with regard to problem-solving. It was also used to expose the teachers to PBL as an alternative approach to teaching and learning mathematics in the Foundation Phase. The study provides a body of knowledge on the Foundation Phase teachers’ pedagogical knowledge, practices and beliefs regarding the teaching and learning of mathematics in general, and approaches to problem-solving in particular, thus providing insights into some of the factors that might lie behind learner outcomes. Study findings indicate that the majority of teachers’ daily mathematical teaching culture was deep-rooted in the traditional approach (direct transmission). This approach was characterised by the teachers concerned focusing on the following of rules and procedures, and on doing demonstrations on the chalkboard, whereafter the learners were encouraged to practise what they had learned by asking them to do pen-and-paper calculations. The lessons were generally not structured to develop critical thinking and reasoning skills. In instances where the teachers created learner-centred activities that were conducive to the development of such skills, deep-rooted traditional approaches manifested themselves in the way in which the teachers showed the learners how to solve their given problem at the earliest signs of any difficulty in doing so was exhibited by the learners. In so doing, the majority of the teachers, despite initially creating learning opportunities by posing problems to their learners, they soon snatched away the selfsame opportunities from them. This was because they did not allow sufficient time for the learners to grapple with a problem, and to engage in critical thinking. After exposure to PBL, the educators were able to implement PBL so effectively that they could address the problems related to low learner achievement in mathematics, as reflected in the international assessment studies, and in the national systemic evaluations within the current South African context.

AFRIKAANSE OPSOMMING: In hierdie studie is die pedagogiese kennis van Grondslagfase-onderwysers ondersoek ten einde insig te verkry in hulle begrip van die onderrig en leer van wiskunde. Die onderwysers se kennis is ondersoek aangesien dit een van die belangrikste veranderlikes is wat 'n invloed het op dit wat in die klaskamer uitgevoer word. Die ondersoek is onderneem teen die agtergrond dat die algehele prestasie van leerders in die nasionale sistemiese evaluerings en internasionale assesseringstudies uiters swak en 'n bron van groot kommer was. Dit het gelei tot verskillende intervensieprogramme wat gemik is op die verbetering van onderwyserprestasie en -doeltreffendheid. In hierdie studie is die onderwyser die fokuspunt van die intervensie. Probleem-gebaseerde leer (PBL), wat beskou word as een van die beste voorbeelde van 'n konstruktivistiese leeromgewing, is aan 'n groep van 15 onderwysers in die Grondslagfase gebring. Die studie was ‘n poging om nuwe kennis te identifiseer ten opsigte van Grondslagfase-onderwysers se pedagogiese geloof en praktyke in die onderrig en leer van wiskunde, en die gebruik van PBL as 'n middel vir die onderrig en leer van wiskunde – kennis wat gebruik kan word om die verwante uitdagings aan te spreek ter verbetering van die onderrig en leer van wiskunde in die Grondslagfase. 'n Kombinasie van kwalitatiewe en kwantitatiewe navorsingsmetodes, wat vraelyste, onderhoude, les-waarneming en werkswinkels ingesluit het, is aangewend om die onderwysers se huidige pedagogiese sienings en praktyke met betrekking tot probleemoplossing grondig te ondersoek en dan voort te gaan om die onderwysers bloot te stel aan PBL as alternatiewe benadering tot onderrig en leer van wiskunde in die Grondslagfase. Die studie het bevind dat die meerderheid van die onderwysers se huidige onderrigkultuur een was wat diep gewortel is in die tradisionele benadering van onderrig en leer van wiskunde (direkte oordrag): dit is gekenmerk deur die onderwysers se onderrig van wiskunde deur te fokus op reëls en prosedures, demonstrasies aan die klas op die swartbord en leerders dan te laat oefen deur pen- en papierberekeninge te doen. Dié het die meerderheid van die onderwysers daagliks gedoen. Lesse is oor die algemeen nie gestruktureer om kritiese denke en beredenering te ontwikkel nie. In gevalle waar die onderwysers leerder-gesentreerde aktiwiteite geskep het wat weens hulle ontwerp bevorderlik is vir die ontwikkeling van kritiese denke en redenasie, het die diepgewortelde, tradisionele benaderings hulself gemanifesteer in die feit dat die onderwysers, met die eerste aanduiding dat die leerders sukkel, hulle te hulp gesnel het en die leerders gewys het hoe om die probleem op te los. Met dié optrede het die meerderheid van die onderwysers aanvanklik leergeleenthede geskep (deur probleme aan hulle leerders voor te hou), maar dit spoedig dan weer weggeraap weens die feit dat hulle nie genoegsame tyd toegelaat het vir hulle leerders om met idees te worstel en deel te hê aan kritiese denke nie. Blootstelling van die opvoeders aan PBL het aan die lig gebring dat opvoeders in die Grondslagfase PBL doeltreffend kan implementeer om probleme rondom lae leerder prestasie in wiskunde aan te spreek wat in internasionale assesseringstudies en in die nasionale sistemiese evaluerings binne die huidige Suid -Afrikaanse konteks weerspieël word.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/96772
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