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The effect of a problem based learning approach on the teaching and learning of composition and inverses of functions in a foundation programme

Chirimbana, Moses (2014-12)

Thesis (PhD)--Stellenbosch University, 2014.


ENGLISH ABSTRACT: The purpose of the study was to investigate The effect of the Problem-Based Learning Problem Based Learning (PBL) approach in the teaching of composition and inverse functions in a foundation programme. PBL is a philosophical approach to teaching and learning where problems drive the learning. The study was important because it was trying to find out if PBL can improve students’ performance in compositions and inverses of functions at the bridging course for undergraduate mathematics at Oshakati Campus. The study intended to come up with a PBL model suitable for FP mathematics in the teaching of compositions and inverses of functions. The study was done on Science Foundation students who are registered for FP. Eighty students were randomly selected from the foundation students registered for the 2013 academic year. The students were randomly assigned into the experimental and the comparison groups of 40 each. In this study the comparison group of the Foundation students was predominantly taught through the traditional lecture approach while the experimental group was predominantly taught using a hybrid PBL approach. The study also attempted to establish the students’ perceptions with regard to the relevance of inverses and compositions of functions as a concept in a topic that determines their academic destination. It also attempted to ascertain how the PBL approach could best be implemented in order to improve FP students’ understanding of inverses and composition of functions; how Bridging course for undergraduate mathematics (FP) students experience the PBL approach in the teaching and learning of inverses and composition of functions compared to those who are taught using the lecture method and how FP students’ performance on inverses and composition of functions as a result of their PBL experience compare to those who are taught using the lecture method. This study used the concurrent nested mixed methods (qualitative and quantitative) research designs. A quasi experimental design was adopted through the administration of a pre-post-test on experimental and comparison groups. The other designs or methods included a questionnaire survey, focus group interviews, non-participant lesson observation and a group research project on compositions and inverses of functions. The experimental group was then mainly taught through a hybrid PBL approach while the comparison group mainly through the lecture approach for a period of three months. The findings of this research study showed that experimental group students performed significantly better in the overall results analysis but there were no significant differences in performance between the two groups for some Hypothetical Learning Trajectory (HLT) domains on compositions and inverses of functions. It is recommended that PBL should be implemented in the other foundation programme subjects. However, the role of the conventional teaching approaches cannot be undermined in the teaching and learning of compositions and inverses of functions since the students who were taught using this method also improved their performances, and as such these conventional teaching approaches should be used together with PBL in order to get the best results on FP students’ mathematics performance. This study recommends further research on how PBL can be implemented in other FP subjects. This study also recommended that PBL should be implemented right at the beginning of the year when the FP students start their classes in the foundation programme.

AFRIKAANSE OPSOMMING: Die doel van die studie was om die effek van die probleemgebaseerde leer (PBL) benadering in die onderrig van die samestelling en inverse funksies in 'n Stigting program te ondersoek. PBL is 'n filosofiese benadering tot onderrig en leer waar probleme ry die leer. Die studie is belangrik omdat dit probeer het om uit te vind of PBL kan studente se prestasie in komposisies en inverses van funksies te verbeter by die Stigting Program op Oshakati-kampus. Die studie bedoel om vorendag te kom met 'n PBL model wat geskik is vir fondament in die onderrig van komposisies en inverses van funksies. Die studie is gedoen op Science Foundation studente by Oshakati-kampus van die Universiteit van Namibië. Tagtig studente is lukraak gekies uit die fondament studente wat geregistreer is vir die 2013 akademiese jaar. Die studente is ewekansig toegewys in die eksperimentele en die vergelyking groepe van 40 elk. In hierdie studie is die vergelyking groep van die Stigting studente is hoofsaaklik geleer word deur die tradisionele lesing benadering terwyl die eksperimentele groep was hoofsaaklik geleer met behulp van 'n hibriede PBL benadering. Die studie het ook probeer om vas te stel uit wat die studente se persepsies met betrekking tot die toepaslikheid van inverses en komposisies van funksies is soos 'n konsep in 'n onderwerp wat bepaal hul akademiese bestemming. Dit het ook probeer om vas te stel hoe die PBL benadering kan die beste om FP studente se begrip van inverses en samestelling van funksies te verbeter geïmplementeer word; hoe FP studente die PBL benadering in die onderrig en leer van inverses en samestelling van funksies in vergelyking met diegene wat geleer is met behulp van die lesing metode en hoe FP studente se prestasie op inverses en samestelling van funksies as 'n gevolg van hul PBL ervaring vergelyk met dié wat geleer is met behulp van die lesing-metode. Hierdie studie gebruik om die konkurrente geneste gemengde metodes (kwalitatiewe en kwantitatiewe) navorsing ontwerpe. 'N quasi eksperimentele ontwerp is aangeneem deur die administrasie van 'n pre-na-toets op eksperimentele en vergelyking groepe. Die ander ontwerpe of metodes het 'n vraelys opname, fokusgroeponderhoude, nie-deelnemer leswaarneming, en 'n groep navorsingsprojek oor komposisies en inverses van funksies. Die eksperimentele groep is dan hoofsaaklik geleer deur middel van 'n kruising PBL benadering terwyl die vergelyking groep hoofsaaklik deur die lesing benadering vir 'n tydperk van drie maande. Die bevindinge van hierdie navorsing het getoon dat die eksperimentele groep studente uitgevoer aansienlik beter in die algehele resultate analise, maar daar was geen betekenisvolle verskille in prestasie tussen die twee groepe vir 'n paar MTT gebiede op komposisies en inverses van funksies. Die studie het ook bevind dat PBL aan die begin van die jaar reg geïmplementeer moet word wanneer die FP studente begin hul klasse in die fondament program. Dit word aanbeveel dat PBL in al die ander fondament program vakke moet geïmplementeer word. Tog kan die rol van die konvensionele onderrig benaderings nie ondermyn word in die onderrig en leer van komposisies en inverses van funksies, en as sodanig die konvensionele onderrig benaderings moet saam met PBL word gebruik om die beste resultate op FP studente se wiskunde prestasie te kry . Hierdie studie beveel aan verdere navorsing oor hoe PBL in 'n ander fondament program vakke geïmplementeer kan word.

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