Thesis (MEd)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: Research has confirmed the educational value of mathematical modelling for learners of all abilities. The development of modelling competencies is essential in the modelling approach. Little research has been done to identify and develop the mathematising modelling competency for specific sections of the mathematics curriculum. The study investigates the development of mathematising competencies during the modelling of number pattern problems. The RME theory has been selected as the theoretical framework for the study because of its focus on mathematisation. Mathematising competencies are identified from current literature and developed into models for horizontal and vertical (complete) mathematisation. The complete mathematising competencies were developed for number patterns and mapped on a continuum. They are internalising, interpreting, structuring, symbolising, adjusting, organising and generalising. The study investigates the formulation of a hypothetical trajectory for algebra and its associated local instruction theory to describe how effectively learning occurs when the mathematising competencies are applied in the learning process. Guided reinvention, didactical phenomenology and emergent modelling are the three RME design heuristics to form an instructional theory and were integrated throughout the study to comply with the design-based research’s outcome: to develop a learning trajectory and the means to support the learning thereof. The results support research findings, that modelling competencies develop when learners partake in mathematical modelling and that a heterogeneous group of learners develop complete mathematising competencies through the learning of the modelling process. Recommendations for additional studies include investigations to measure the influence of mathematical modelling on individualised learning in secondary school mathematics. / AFRIKAANSE OPSOMMING: Navorsing steun die opvoedkundige waarde van modellering vir leerders met verskillende wiskundige vermoëns. Die ontwikkeling van modelleringsbevoegdhede is noodsaaklik in 'n modelleringsraamwerk. Daar is min navorsing wat die identifikasie en ontwikkeling van die bevoegdhede vir matematisering vir spesifieke afdelings van die wiskundekurrikulum beskryf. Die studie ondersoek die ontwikkeling van matematiseringsbevoegdhede tydens modellering van getalpatrone. Die Realistiese Wiskundeonderwysteorie is gekies as die teoretiese raamwerk vir die studie, omdat hierdie teorie die matematiseringsproses sentraal plaas. Matematiseringsbevoegdhede vanuit die bestaande literatuur is geïdentifiseer en ontwikkel tot modelle wat horisontale en vertikale (volledige) matematisering aandui. Hierdie matematiseringsbevoegdhede is spesifiek vir getalpatrone ontwikkel en op ‘n kontinuum geplaas. Hulle is internalisering, interpretasie, strukturering, simbolisering, aanpassing, organisering en veralgemening. Die studie lewer die formulering van ‘n hipotetiese leertrajek vir algebra, die gepaardgaande lokale onderrigteorie en beskryf hoe effektiewe leer plaasvind wanneer die ontwikkelde matematiseringsbevoegdhede volledig in die leerproses toegepas word. Die RME ontwikkellingsheuristieke, begeleidende herontdekking, didaktiese fenomenologie en ontluikende modellering, is geïntegreer in die studie sodat dit aan die uitkoms van ‘n ontwikkelingsondersoek voldoen. Die uitkoms is ‘n leertrajek en ‘n beskrywing hoe die leerproses ondersteun kan word. Die analise het tot die formulering van ‘n lokale-onderrig-teorie vir getalpatrone gelei. Die resultate van die studie kom ooreen met navorsingsbevindings dat modelleringsbevoegdhede ontwikkel wanneer leerders deelneem aan modelleringsaktiwiteite, en bewys dat ‘n groep leerders met gemengde vermoëns volledige matematiseringsbevoegdhede ontwikkel wanneer hulle deur die modelleringsproses werk. 'n Aanbeveling vir verdere navorsing is om die uitwerking van die modelleringsperspektief op individuele leer in hoërskool klaskamers te ondersoek.