The concurrent development of mathematical modelling and engineering technician competencies of first-year engineering technician students

De Villiers, Lidamari (2018-12)

Thesis (PhD)--Stellenbosch University, 2018.

Thesis

ENGLISH ABSTRACT : Mathematics contributes significantly towards engineering education, denoting the prominance of possessing mathematical competence. Motivation for the study originated from observing students’ modest levels of mathematical reasoning and understanding, problem-solving and meta-cognitive abilities. A gap in literature was exposed for enhancing engineering technician students’ competencies to proceed towards successful mathematical thinkers and doers. This study serves to fill this gap, by answering the research question regarding the extent to which engineering technician and mathematical modelling competencies can co-develop, to produce a deeper understanding of mathematics within the context of a mathematical modelling course for first-year engineering technician students who are not strong in mathematics. The study aimed to develop a qualitative and quantitative profile that characterises the design in practice, commanding Design-Based Research methodology. Twelve first-year engineering technician students, volunteered to partake in a mathematical modelling course of one semester. They worked in small groups on model-eliciting activities that required the construction of models to describe, analyse and solve real-world problems. Qualitative data sources included video and audio recordings, observation instruments, informal discussions, students’ written work, and field notes. Analysis was done throughout the experiment. The students revealed improvements in all the competency categories, with the most prominent development occurring in generalising (cognitive) and management (meta-cognitive) competencies. Mathematical ideas and higher-order thinking develop interactively, and the characteristics of being deeply involved in solving model-eliciting activities allowed for the stimulation of reflective activities. Explanations on how the competencies advanced, exposed an intricate web of teacher beliefs, classrooms norms that foster socio-constructivist forms of learning and teaching, and modeleliciting activities designed to develop higher-order understanding. Combined with formative assessment methods to describe the nature of the students’ constructs, a local instructional theory was constructed that explains how mathematical modelling and engineering technician competencies can co-develop through mathematical modelling, and how to support competence development for improved mathematical reasoning and understanding.

AFRIKAANSE OPSOMMING : Wiskunde dra beduidend by tot ingenieursopleiding, wat die belangrikheid van wiskundige bevoegdhede impliseer. Motivering vir die studie spruit uit die waarneming van studente se beskeie vaardighede van wiskundige beredenering en begrip, probleemoplossing en metakognitiewe vermoëns. 'n Gaping is blootgelê in die literatuur om suksesvol ingenieurstegnici se vaardighede te ontwikkel tot suksesvolle wiskundige denkers en gebruikers. Die studie dien om hierdie leemte te vul deur die navorsingsvraag te beantwoord oor die mate waarin ingenieurstegniese en wiskundige modelleringsbevoegdhede gelyktydig kan ontwikkel om 'n dieper begrip van wiskunde te lewer, binne die konteks van 'n wiskundige modelleringskursus vir eerstejaar ingenieurstegnikus studente wat nie vaardig in wiskunde is nie. Die studie poog om 'n kwalitatiewe en kwantitatiewe profiel te ontwikkel wat die ontwerp in die praktyk op die voorgrond plaas en dus ontwerp-gebaseerde navorsing onderskryf. Twaalf eerstejaar ingenieurstegniese studente wat 'n oorbruggingsprogram gevolg het, het vrywillig aan 'n wiskundige modelleringskursus van een semester deelgeneem. Hulle het in groepies aan modelleringsaktiwiteite gewerk wat model-konstruksie vereis het om werklike probleme te beskryf, ontleed en op te los. Kwalitatiewe databronne sluit in video- en klankopnames, waarneming- en refleksie-instrumente, informele besprekings, studente se geskrewe werk en veldnotas. Voortdurende analise is verder ontwikkel deur Gevallestudie Navorsing. Die studente het verbeterings in al die bevoegdheidskategorieë gewys, met die prominentste ontwikkeling in veralgemenings- (kognitief) en bestuurs- (meta-kognitief) bevoegdhede. Wiskundige idees en hoër-orde denke is deur dinamiese interaktiwiteit ontwikkel, en die eienskappe van modelleringsontlokkende aktiwiteite (MOAe) stimuleer reflektiewe aksies. Besprekings oor hoe die bevoegdhede ontwikkel het, het die komplekse web van onderwyseroortuigings, klaskamer-norme wat sosio-konstruktivisme ondersteun, en MOAe wat ontwerp is om hoër-orde begrippe te ontwikkel, blootgelê. Gekombineer met formatiewe assesseringsmetodes, is 'n Lokale Onderrigteorie (LOT) opgestel wat verduidelik hoe ingenieurstegniese en wiskundige modelleringsbevoegdhede kan ontwikkel via wiskundige modellering, en ook hoe om ondersteuning te bied vir beter wiskundige beredenering en begrip.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/104864
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