The effects of pedagogical content knowledge in learning Grade 12 mathematics using problem-based learning

Abstract

𝑬𝒏𝒈𝒍𝒊𝒔𝒉 This study investigated the effects of teacher’s pedagogical content knowledge in learning Grade 12 Mathematics using problem-based learning (PBL) in two selected secondary schools in the Amajuba district in KwaZulu-Natal. The problem behind the poor performance of Grade 12 Mathematics learners in the National Senior Certificate (NSC) for 2019, 2020, and 2021 is that most learners find it difficult to analyse and evaluate problem-based questions because they may be taught by some unqualified Mathematics teachers with insufficient MPCK and their low knowledge of subject content knowledge and low pedagogy. This study used Vygotsky's social constructivist theory and an inductive, exploratory qualitative case study approach. Data was collected by posing semi-structured interview questions to Mathematics teachers and open-ended questions to focus groups on learners and observing how Mathematics teachers interact with learners in the classroom. This was done to answer the "what" and "how" questions to generate theoretical insights into the phenomena under review. The findings suggest that teachers' MPCK equipped them to use inclusive educational strategies for teaching and learning Grade 12 mathematics, and had a positive outcome on learners' performances. Furthermore, the study's findings proposed that Mathematics teachers should be masters of the content, producing learning content to cognitively stimulate learners to work independently and strive for improved achievements in their current learning. More so, Mathematics teachers should be skilled at applying various teaching and learning methodologies appropriate to the learning abilities of all learners in the classroom so that learners can successfully acquire the content. The success of Grade 12 Mathematics learners adequately learning Mathematics depends on, amongst others, the teachers' ability to facilitate lessons by concretising abstract content using interactive activities in collaborative group learning. The study recommends that Grade 12 Mathematics teachers need training in using PBL as an instructional approach to teaching Mathematics. DBE needs to review the scope of the Grade 12 CAPS document so that PBL, as the preferred instructional strategy, can be adopted in teaching and learning Mathematics. ___________________________________________________________________ 𝑨𝒇𝒓𝒊𝒌𝒂𝒂𝒏𝒔 Hierdie navorsing het die uitwerking van onderwysers se pedagogiese inhoudskennis in die leer van graad 12 Wiskunde, deur probleemgebaseerde leer (PBL), in twee geselekteerde hoërskole in die Amajuba-distrik in KwaZulu-Natal ondersoek. Die probleem was dat gr. 12’s swak gevaar het in die Nasionale Senior Sertifikaat-eksamen (NSS) vir 2019, 2020 en 2021 omdat meeste van hulle dit moeilik vind om probleemgebaseerde vrae te ontleed en te evalueer, moontlik weens sommige ongekwalifiseerde Wiskunde-onderwysers met onvoldoende pedagogiese inhoudkennis van Wiskunde (MPCK), min vakinhoudelike kennis en lae pedagogiek. Vygotsky se sosiaal-konstruktiwistiese teorie en ’n induktiewe, verkennende kwalitatiewe gevallestudiebenadering is gebruik. Data is ingesamel deur semi-gestruktureerde onderhoudsvrae aan Wiskunde-onderwysers te stel, asook oop vrae aan fokusgroepe van leerders, en waar te neem hoe Wiskunde-onderwysers met leerders in die klaskamer omgaan. Dit is gedoen om die “wat”- en “hoe”-vrae te beantwoord om teoretiese insigte te genereer oor die verskynsels wat nagevors word. Die bevindinge dui daarop dat onderwysers se MPCK hulle toegerus het om inklusiewe strategieë vir die onderrig en leer van graad 12 Wiskunde te gebruik, wat ’n positiewe uitkoms op leerders se prestasies gehad het. Die navorsing stel verder voor dat Wiskunde-onderwysers kenners van die inhoud moet wees en leerinhoud moet gebruik om leerders kognitief te stimuleer om onafhanklik te werk en te streef na verbeterde prestasies in hul huidige studies. Dit is selfs belangriker dat Wiskunde-onderwysers vaardig is in die toepassing van verskeie onderrig- en leermetodologieë wat geskik is vir die leervermoëns van alle leerders in die klaskamer, sodat leerders die inhoud suksesvol kan verstaan. Die sukses van graad 12 Wiskunde-leerders wat Wiskunde voldoende bemeester, word onder meer bepaal deur die onderwyser se vermoë om lesse te fasiliteer deur abstrakte inhoud konkreet te verduidelik deur interaktiewe aktiwiteite in samewerkende groepleer te gebruik. Die navorsing beveel aan dat graad 12 Wiskunde-onderwysers opleiding benodig om PBL as ’n onderrigstrategie tot die onderrig van Wiskunde te gebruik. Die Departement van Basiese Onderwys moet die omvang van die Caps-dokument vir graad 12 hersien sodat PBL as die voorkeur onderrigstrategie in die onderrig en leer van Wiskunde ingesluit kan word. ___________________________________________________________________