Evaluating the effectiveness of Advanced Programme Mathematics in preparing learners for university mathematics

Du Plessis, Hester (2015-03)

Thesis

ENGLISH ABSTRACT: In today’s hi-tech global economy the fields of science, technology and engineering are becoming increasingly and undeniably central to economic growth and competitiveness, and will provide many future jobs. Qualifications in Mathematics are crucial gateways to further education and will provide access to the Science, Technology, Engineering and Mathematics (STEM) industries. This study focuses on the optional course in Mathematics, called Advanced Programme Mathematics (APM), which is offered and assessed by the Independent Examination Board in the final three years of high school in South Africa. At present, the South African school system does not adequately prepare students for the transition from school to university Mathematics, and APM has been designed to address this gap. The research question set by this study is: To what extent does the APM course succeed in preparing learners for the rigour of first-year Mathematics in the STEM university programmes? The sample group of 439 students was selected from the 2013 cohort of first-year Mathematics students at Stellenbosch University. First, an analysis of the relevant curricula was undertaken, and then an empirical investigation was done to determine the differences in performance between first and second semester examinations of first-year university Mathematics students who took APM, and those who did not. This was followed by an investigation by means of a questionnaire into the perceptions of students on how effective APM was in easing the transition from school to university Mathematics. The research was designed according to the Framework for an Integrated Methodology (FraIM) of Plowright (2011). From an extensive international literature study, it appears that APM is definitely a predictor of post-secondary success. Since no formal research has been recorded to support this claim, this study aims to provide a sound answer to whether APM is advantageous. The effect size results of this study show that APM marks of students explain 68% of the achievement in first-semester university Mathematics when combined with NSC Mathematics marks in a general regression model. There is a significant difference between the marks of students who took APM and those who did not in first-semester university Mathematics, specifically across the National Senior Certificate (NSC) Mathematics mark categories of 80-100%. APM course-taking leads to confidence in Mathematics, which combined with good domain knowledge of calculus, ease the transition from school to university Mathematics. The study recommends that not only students who intend pursuing a career in the STEM industries should take the APM course, but also those who intend to apply for admission to any other tertiary studies, as the cognitive and other skills provided by APM will give them the required edge to perform well in higher education. Schools are called upon to provide access to APM for mathematically gifted students, and teachers and guidance counsellors should encourage learners to enrol for AMP. This will enable them to share in the manifold academic and personal benefits accruing from the course, and to help alleviate the critical shortage of graduates in careers requiring a strong Mathematics background in South Africa.

AFRIKAANSE OPSOMMING: In die hoë-tegnologie-wêreldekonomie van vandag word die gebiede van wetenskap, tegnologie en ingenieurswese toenemend en onmiskenbaar die kern van ekonomiese groei en mededingendheid wat in die toekoms baie werkgeleenthede sal bied. Kwalifikasies in Wiskunde open beslis baie deure na verdere opleiding en verleen toegang tot die Wetenskap-, Tegnologie- Ingenieurswese- en Wiskunde-industrieë. Hierdie studie fokus op die opsionele kursus in Wiskunde, genaamd Gevorderde Program Wiskunde (GPW), wat deur die Onafhanklike Eksamenraad aangebied en geassesseer word in die laaste drie jaar van hoërskoolonderrig in Suid-Afrika. Tans berei die Suid-Afrikaanse skoolstelsel nie studente genoegsaam voor vir die oorgang van skool- na universiteitswiskunde nie en GPW is ontwerp om hierdie gaping te oorbrug. Die navorsingsvraag wat hierdie studie stel, is: In watter mate slaag die GPW-kursus daarin om leerders voor te berei vir die streng vereistes van eerstejaar-Wiskunde in die Wetenskap-, Tegnologie- Ingenieurswese- en Wiskunde-universiteitsprogramme? Die toetsgroep van 436 studente is gekies uit die 2013-groep eerstejaar-Wiskundestudente aan Stellenbosch Universiteit. Aanvanklik is ᾽n analise van die relevante leerplanne onderneem, waarna ᾽n empiriese ondersoek gedoen is om die verskille in prestasie in die eerste en tweede semester eksamens vas te stel tussen eerstejaar-Wiskundestudente op universiteit wat wel GPW geneem het en diegene wat dit nie geneem het nie. Dit is gevolg deur ᾽n ondersoek deur middel van ᾽n vraelys na die persepsies van studente oor hoe effektief GPW was om die oorgang van skool- na universiteitswiskunde te vergemaklik. Die navorsing is ontwerp op grond van ‘n model vir ‘n geïntegreerde metodologie van Plowright (2011). Dit blyk uit ᾽n uitgebreide studie van internasionale literatuur dat GPW definitief ᾽n voorspeller van post-sekondêre sukses is. Aangesien geen formele navorsing om hierdie aanspraak te ondersteun nog op skrif gestel is nie, poog hierdie studie om ᾽n deurdagte antwoord te verskaf op die vraag of GPW wel tot voordeel van studente is. Die effek grootte resultate van hierdie studie dui aan dat die GPW-punte van studente 68% van prestasie in Wiskunde in die eerste semester op universiteit verduidelik as dit in ᾽n algemene regressiemodel met die Nasionale Senior Sertifikaat (NSS) punte gekombineer word. Daar is ᾽n beduidende verskil tussen die Wiskundepunte van studente wat GPW geneem het en diegene wat dit nie geneem het nie in die eerste semester op universiteit, veral in die NSS-Wiskundepuntekategorieë van 80-100%. Om die GPW-kursus te neem, lei tot selfvertroue in Wiskunde, wat saam met ᾽n goeie kennis van die Differensiaalrekening-domein, die oorgang van Wiskunde vanaf skoolvlak na universiteitsvlak vergemaklik. Op grond van die studie beveel die navorser aan dat nie slegs studente wat ᾽n loopbaan in Wetenskap-, Tegnologie- Ingenieurswese- en Wiskunde-rigtings wil volg, die GPW-kursus behoort te volg nie, maar ook diegene wat vir toelating tot enige ander tersiêre studie wil aansoek doen, aangesien die kognitiewe en ander vaardighede wat GPW ontwikkel, hulle die nodige voorsprong sal bied om goed te vaar in verdere studie. Skole word aangemoedig om toegang tot GPW aan wiskundig begaafde leerlinge te verskaf en onderwysers en loopbaanraadgewers behoort leerlinge aan te moedig om vir GPW in te skryf. Sodoende kan hulle deel in die vele akademiese en persoonlike voordele wat die kursus bied, en help om die kritieke tekort aan gegradueerdes in die studierigtings waar ‘n sterk Wiskunde agtergrond ‘n vereiste is, te help verlig.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/97080
This item appears in the following collections: