Tlali, Moeketsi F.Lika, Mohau Armstrong2024-06-112024-06-112021http://hdl.handle.net/11660/12561Thesis (Ph.D.(Curriculum Studies))--University of the Free State, 2021𝑬𝒏𝒈𝒍𝒊𝒔𝒉 This study sought to enhance the teaching and learning of algebraic expressions and equations using reasoning in grade 9. It is a participatory action research study underpinned by bricolage paradigm and construction theory. The underpinnings guide and enable learners to use what is at their disposal to construct reasoning constructs. The constructs help learners to forge rich algebraic and mathematical conceptual connections and interrelations. In this manner, the constructs help the instruction (teaching and learning) to achieve deep conceptual understanding (DBE 2011:8) rather than limiting it to procedural orientation. The evidence presented in literature about international best practices shows that procedure-oriented instruction and procedure fluency are, and should be, nested in conceptual knowledge. This study initiated the instruction that ensures that the nesting does not manifest in nature only, but throughout the teaching and learning processes as well. The initiative draws from the South African curriculum policy, CAPS, which requires that learners should achieve a deep conceptual understanding of the subject matter (DBE 2011:8). The operationalisation of reasoning to conceptualise procedural instruction draws from the underutilisation of the reasoning skill, despite it being the curriculum policy imperative. Reasoning attaches sensible meaning (Yackel 2001:1) to algebraic content matter and provides direction and cushion for logical arguments aimed at attaining high order cognition. Pursuant to the study underpinnings, the reasoning-based instruction deploys learners’ own reasoning constructs to ensure participatory and contextual conceptualisation. In the process, learners develop critical thinking and high order cognitive skills. These are the skills that the learners are expected to attain from the meaningful learning (Pramesti & Retnawati 2019:3) of algebra and mathematics inspired in the reasoning-based instruction. The study has come up with the components of solution and strategies to address the research question and challenges underlying the research. The primary challenge that guides the study, namely the non-alignment between the instruction and requirements of the curriculum policy, manifests under procedure-oriented instruction; assessment; teachers’ competences and curriculum-time contestation. In addition, the abstraction and complexity of algebra amidst insufficient basic mathematics competency, escalate the supremacy of algebra in the teaching and learning of mathematics. The net resultant thereto is an inherent sifting nature of algebra. The data analysis and interpretation presented enough evidence that the reasoning-based instruction is couched in multi-layered components of solution and strategies that respond adequately to the research question. The instruction proved the potential to break through the integrated challenges underlying algebraic instruction. The process of conceptualisation is an encompassing component of the solution. It entails contextualising and concretising textual representations of algebra in a manner that the representations make meaningful sense to learners; so much that the learners can apply algebra purposefully in advanced mathematics and related learning. Contextualisation often involves refocusing, integration and re-organisation of content matter in a manner that meets the subject and learners’ needs. Concretisation includes the use of materials and examples within learners’ reach to explain algebraic concepts. The analysis of the conditions necessary for successful implementation and that of the risks and threats likely to impede the implementation reaffirmed the sustainability of the reasoning-based instruction. The indicators of success confirmed that the study has succeeded in the reform, transformation and enhancement of the teaching and learning of algebra as sought and anticipated. The study has further empowered co-researchers to use what is at their disposal to develop sustainable solutions. It can then be concluded that the research empowered the initiatives to overcome the ‘lock-ins’ to existing protocols and approaches, which have not been effective for the majority of teachers’ and learners’ populations in South Africa and the world. ___________________________________________________________________𝑨𝒇𝒓𝒊𝒌𝒂𝒂𝒏𝒔 Hierdie studie mik daarop om 'n strategie te ontwerp om die onderrig en leerproses van algebraïese uitdrukkings en vergelykings in graad 9 te verbeter. Dir towrdsommer ook deur gebruik te maak van die redenasieproses. Dit is 'n deelnemende proses wat ondersteun word deur die opbou van die redenasieproses as bricoleur; gemik op ‘n beter begrip; eerder as om dit tot prosedurele beginsels te beperk. Die stawende literatuur oor internasionale beste praktyke, toon dat prosedureel-georiënteerde onderrig en die vloeibaarheid van prosedures gabasseer moet word in konseptuele kennis. Die gebruik van redenasies om prosedurele instruksies te konseptualiseer, spruit uit die onderbenutting daarvan, alhoewel dit 'n noodsaaklike vaardigheid is waarvoor die kurrikulumbeleid, CAPS, voorsiening maak. Daar is gevind dat die redenasieproses sinvolle betekenis aan algebraïese inhoud heg en rigting en ondersteuning bied vir logiese argumente, wat op hul beurt daarop gemik is om hoër kognisie te bereik. Ingevolge die grondvlak van hierdie studie, gebruik die strategie leerders hul eie redenasievermoëns om deelnemende en kontekstuele konseptualisering te verseker. In hierdie proses ontwikkel leerders kritiese denke en hoër-orde kognitiewe vaardighede, wat nodig is vir die betekenisvolle begrip van algebra. Die studie het met strategieë en oplossings vorendag gekom om die navorsingsvraag en die uitdagings onderligend daaraan aan te spreek. Die primêre uitdaging van die studie, naamlik die ontwrigting tussen die opdrag en vereistes van die beleid, manifesteer onder prosedure-georiënteerde onderrig, assessering, die vaardighede van onderwysers en die stryd vir kurrikulumtyd. Daarbenewens verhoog die abstraksie en kompleksiteit van algebra, te midde van onvoldoende vaardighede in basiese wiskunde, die belangrikheid van algebra in die onderrig en leer van wiskunde, en word die inherente siftigsaard daarvan blootgelê. Die navorsingsanalise en -interpretasie het genoegsame bewyse gelewer dat die redenasie-gebaseerde strategie gevestig is in strategieë en oplossings met veelvuldige lae wat voldoende reageer het op die navorsingsvraag, en die potensiaal het om die kontekstueel geïntegreerde uitdagings van hierdie studie te staaf. Die konseptualiseringsproses is 'n omvattende komponent van die oplossing. Dit behels om die kontekstualisering en konkretisering van die teksvoorstellings van algebra op 'n manier sinvol te maak vir leerders; in so ‘n mate dat leerders dit kan toepas in verwante vakrigtings soos tydens die navorsingsproses. Kontekstualisering behels dikwels die herfokus, integrasie en herorganisasie van inhoud op 'n manier wat voldoen aan die behoeftes van die leerders. Konkretisering behels die gebruik van items en voorbeelde binne leerders se bereik om algebraïese konsepte te verklaar. Die analise van die voorwaardes wat benodig word vir suksesvolle implementering, en die risiko's wat die implementering kan belemer, het die volhoubaarheid van die strategie bevestig. Die sukses het bevestig dat die studie daarin geslaag het om die onderrig- en leerproses van algebra te hervorm, te transformeer en te verbeter soos verwag is. Die studie het mede-navorsers verder bemagtig om dit wat tot hul beskikking is, te gebruik om volhoubare oplossings te ontwikkel. Daar kan dan tot die gevolgtrekking gekom word dat die navorsing die inisiatiewe bemagtig het om die houvas van bestaande protokolle en benaderings te oorkom, wat nie effektief was vir die meerderheid van die onderwysers en leerders in Suid-Afrika en die wêreld nie. ___________________________________________________________________enThesisUniversity of the Free State