Teachers mediation of metacognition during mathematical problem solving

Pieterse, Susan-Mari (2014-12)

Thesis (MEd)--Stellenbosch University, 2014.

Thesis

ENGLISH ABSTRACT: Recent national and international assessments single problem solving out as an important but problematic factor in the current mathematical capacities of South African learners. It is evident that the problem escalates as learners progress to the Intermediate Phase. Research indicates a significant link between metacognition and successful mathematical problem solving. From a Vygotskian sociocultural perspective which formed the theoretical framework of this study, metacognition can be regarded as a higher-order function developing through interaction within social and cultural contexts known as mediation. This qualitative collective case study, informed by an interpretivist paradigm, was designed to explore and compare how Foundation and Intermediate Phase mathematics teachers mediate metacognition during mathematical problem solving. It aimed to offer a deeper understanding of the process of mediation, the complex interplay between cognition and metacognition, and how teachers differentiate the mediation process to accommodate diversity among their learners. To address this, two cases were identified involving a sample of six mathematics teachers each of an urban primary school in the Western Cape Province. The first case was Foundation Phase teachers and the second Intermediate Phase teachers. Semi-structured individual interviews, non-participant classroom observations, and semi-structured focus group interviews were used as methods to gather and triangulate data. Themes that emerged from constantly comparing the data informed the findings. The findings suggest that there are cognitive, non-cognitive and contextual factors which could influence the quality and outcomes of the mediation of metacognition during mathematical problem solving in diverse classrooms. It emphasized the significance of the active role the teacher as a more knowledgeable other plays in the mediation process. Furthermore, it underlined the importance of giving learners challenging mathematical problems requiring metacognition within their zones of proximal development. It was also found that the teacher as mediator should not only have the necessary professional knowledge and strategies, but should also consider the affective factors, perceptions and reactions of learners, during the mediation process. Keywords: metacognition, mediation, mathematical problem solving, sociocultural theory, differentiated instruction, Foundation Phase teachers, Intermediate Phase teachers.

AFRIKAANSE OPSOMMING: Onlangse nasionale en internasionale assesserings lig probleemoplossing uit as 'n belangrike, maar problematiese faktor in die huidige wiskundige prestasie van Suid-Afrikaanse leerders. Dit is duidelik dat die probleem toeneem dermate leerders na die Intermediêre Fase vorder. Navorsing toon 'n beduidende verband tussen metakognisie en suksesvolle wiskundige probleemoplossing. Vanuit 'n Vygotskiaanse sosiokulturele perspektief, wat die teoretiese raamwerk van hierdie studie gevorm het, word metakognisie as 'n hoër-orde funksie gesien wat ontwikkel deur interaksie binne die sosiale en kulturele konteks bekend as mediasie. Hierdie kwalitatiewe kollektiewe gevallestudie, ingelig deur 'n interpretivistiese paradigma, was ontwerp om te verken en te vergelyk hoe Grondslag- en Intermediêre-Fase onderwysers metakognisie tydens wiskundige probleemoplossing medieer. Dit het ten doel gehad om 'n beter begrip te bied van die proses van mediasie, die komplekse wisselwerking tussen kognisie en metakognisie en hoe onderwysers mediasie differensieer om die diversiteit van hul leerders te akkommodeer. Om dit aan te spreek was twee gevalle geïdentifiseer wat elk uit ses wiskunde-onderwysers van 'n stedelike primêre skool in die Wes-Kaap bestaan het. Een geval was Grondslagfase-deelnemers en die ander Intermediêre-Fase- deelnemers. Semi-gestruktureerde individuele onderhoude, nie-deelnemer klaskamer-waarnemings en semi-gestruktureerde fokusgroep-onderhoude was gebruik as metodes om data in te samel en te trianguleer. Temas wat ontluik het na die konstante vergelyking van data het die bevindinge ingelig. Die bevindinge het getoon dat daar kognitiewe, nie-kognitiewe en kontekstuele faktore is wat die kwaliteit en uitkomste van die mediasie van metakognisie tydens wiskundige probleemoplossing in diverse klaskamers kan beïnvloed. Die bevindinge beklemtoon die noodsaaklikheid van die aktiewe rol wat die onderwyser as die meer kundige ander speel in die mediasieproses. Verder word die belangrikheid benadruk van die daarstelling van uitdagende wiskundige probleme, wat metakognisie vereis, binne leerders se sones van proksimale ontwikkeling. Dit is ook gevind dat die onderwyser as mediator nie net oor die nodige professionele kennis en strategieë moet beskik nie, maar ook die affektiewe faktore, persepsies en reaksies van leerders in ag moet neem tydens die mediasieproses. Sleutelwoorde: metakognisie, mediasie, wiskundige probleemoplossing, sosiokulturele teorie, gedifferensieerde onderrig, Grondslagfase-onderwysers, Intermediêre Fase-onderwysers.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/96054
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