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. ___________________________________________________________________

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.

Lolu cwaningo luphenye ngomthelela wolwazi lothisha oluqukethwe ekufundiseni izibalo zeBanga le-12 besebenzisa ukufunda okusekelwe ezinkingeni (PBL) ezikoleni ezimbili zamabanga aphezulu ezikhethiwe esifundeni saseMajuba KwaZulu-Natali. Inkinga yokungenzi kahle kwabafundi beBanga le-12 ezibalweni kuMatikuletsheni (NSC) wezi-2019, nezi-2020, kanye nezi-2021 kudalwa ukuthi iningi labafundi likuthola kunzima ukuhlaziya nokuhlola imibuzo esekelwe ezinkingeni ngoba kungenzeka ukuthi ifundiswe ngothisha bezibalo abane-MPCK enganele abanolwazi oluncane lokuqukethwe esifundweni kanye nezindlela zokufundisa eziphansi. Lolu cwaningo lusebenzise itiyori ka-Vygotsky ye-social constructivist kanye ne-inductive, exploratory qualitative case study approach. Idatha yaqoqwa ngokubuza imibuzo ezinkulumeni ebezingahlelwanga phambili zibuzwa kothisha bezibalo kanye nemibuzo evulelekile emaqoqweni abafundi kanye nokubheka indlela othisha bezibalo abasebenzisana ngayo nabafundi ekilasini. Lokhu kwenzelwa ukuphendula imibuzo ethi "yini" kanye "kanjani" ukuze kukhiqizwe imininingwane yetiyori ngezenzakalo ezibuyekezwayo. Ulwazi olutholakele luveza ukuthi i-MPCK yothisha yabahlomisa ukusebenzisa amasu okufundisa abawabandakanyayo ekufundiseni nasekufundeni izibalo zeBanga le-12, futhi ibe nomphumela omuhle ekuphaseni kwabafundi. Ngaphezu kwalokho, imiphumela yocwaningo iphakamise ukuthi othisha bezibalo kufanele babe ngompetha bolwazi oluqukethwe, bakhiqize ulwazi oluqukethwe lokufunda ukuze kushukumise abafundi ngokuqonda ukuthi basebenze ngokuzimela futhi baphokophelele impumelelo ekufundeni kwabo kwamanje. Ngaphezu kwalokho, othisha bezibalo kufanele babe nekhono ekusebenziseni izindlela ezihlukahlukene zokufundisa nokufunda ezifanele amakhono abo bonke abafundi ekilasini ukuze abafundi bathole ulwazi oluqukethwe ngempumelelo. Ukuphumelela kwabafundi beBanga le-12 bezibalo ekufundeni ngokwanele izibalo kuncike, phakathi kokunye, ekhonweni likathisha lokufundisa izifundo ngokuhlanganisa ulwazi oluqukethwe olungacacile ngokusebenzisa imisebenzi yokuxoxisana ekufundweni kweqembu ngokuhlanganyela. Lolu cwaningo luncoma ukuthi othisha bezibalo beBanga le-12 badinga ukuqeqeshwa ekusebenziseni i-PBL njengendlela yokufundisa ekufundiseni izibalo. I-DBE idinga ukubuyekeza ububanzi bombhalo we-CAPS weBanga le-12 ukuze i-PBL, njengesu lokufundisa elikhethwayo, yamukelwe ekufundiseni nasekufundeni izibalo.

Diphuputso tsena di sibolla ditlamorao tsa mekgwa ya tsebo ya ho ruta ya dirutwa ya matitjhere sehlopheng sa Materiki thutong ya dipalo ba sebedisa katamelo ka ho ithuta bothata (PBL) dikolong tse pedi tse kgethilweng tsa Thuto e bohareng tsa Amajuba seterekeng sa Kwazulu-Natal. Bothata ba Mosebetsi o mobe wa barutwana thutong ya dipalo lengolong la National Senior Certificate (NSC) ka dilemo tsa 2019, 2020 le 2021 ke hore boholo ba barutwana ba fumana e le bothata ho manolla le ho hlahloba dipotso tse hlokang katamelo ka bothata hobane e ka nna yaba ba rutilwe dipalo ke matitjhere a se nang mangolo a loketseng mme ka ditsebo tse tlase (MPCK) le tsebo ya bona e tlase ya dikateng le mekgwa ya ho ruta. Diphuputso tsena di sebedisa lewa la Vygotsky la kaho ya setjhaba (Social Constructivist) le mokgwa wa katamelo wa inductive exploratory. Ditaba di bokelletswe ka ho botsa dipotso tse sekgeqe tsa dipatlisiso ho matitjhere a dipalo tsa dikarabo ka ditlhaloso ho sehlopha sa teko sa barutwana le ho lebella hore na matitjhere a sebetsa jwang le barutwana ka sehlopheng. Sena se entswe ho arabela dipotso tsa “ho tla jwang?” le ho etsahetse jwang?” ho hlahisa lewa la lesedi ho seo e leng thahasello ya mofuputsi. Ditshibollo di hlahisa hore matitjhere (MPCK) a hlomellwe ka hore a sebedise mekgwa ya ho ruta a kenyelletsa bohle le barutwana ba sehlopha sa Materiki mme mokgwa ona o bonahala o hlahisa diphetho tse ntle. Ho feta moo, dikgothaletso tsa diphuputso tsena ke hore matitjhere a dipalo e be ditsebi tsa dikateng tsa thuto ya dipalo, hape e be bahlahisi ba dikateng tse ithutwang ho hlabolla dikelello tsa barutwana hore ba etse mosebetsi ka boikemelo le ho leka ho ntlafatsa katleho ya bona diphuputsong tsa bona ha jwale. Hape matitjhere a dipalo a lokela ho hlomellwa ka ho sebedisa mekgwa e fapaneng ya ho ruta le ho ithuta mekgwa e lokelang ho ruta le ho ithuta mekgwa e lokelang ho ruta barutwana ba nang le bokgoni bo sa tshwaneng ka sehlopheng e le hore barutwana ba atlehe ho utlwisisa dikateng tsa thuto ho se bothata, katleho ya ba sehlopha sa Materiki dipalong e itshetlehile ka, hara tse ding, dietsuwa tsa sehlopha se ithutang ka ho kopanela mosebetsi. Diphuputso tsena di kgothaletsa hore matitjhere a dipalo a sehlopha sa Materiki a kwetliswe ka PBL e le mokgwa wa katamelo ya ho ruta dipalo. DBE e lokela ho hlahloba botjha moedi wa Materiki wa tokomane ya CAPS e le hore PBL, e le mokgwa o kgothaletswang wa ho ruta, e ka ba ona o nkwang e le mokgwa wa ho ruta le ho ithuta dipalo.