Thesis (MEd)--Stellenbosch University, 2001. / ENGLISH ABSTRACT: The study of three-dimensional boxes is widely regarded as a suitable topic for entry-level geometry. In order to inform teaching and curriculum design this study takes children's intuitive knowledge of boxes as point of departure to research the following aspects: • the meaning children assign to boxes • children's ability to create and manipulate mental images • children's strategies to solve a three dimensional construction problem • possible age and gender differences • the role of measurement • possible links with Van Hiele's thought levels Revised clinical interviews were conducted with groups of six to ten children. Each child could select an object from a set provided by the researcher and had to build a box from cardboard into which the object could fit. The problem-solving processes were captured on video. The children's boxes, verbal utterences and overt manipulation of the materials as well as the empirical referent objects were analised. The researcher made use of grounded theory procedure to analise and categorise the data. The research indicates that young children are not necessarily aware of the shape and structural properties of three-dimensional boxes. It is also evident that children's ability to represent properties of shape of boxes through language, drawing and hand movements does not necessarily indicate adequate understanding of the structural properties of boxes to enable them to build a box from two-dimensional materials. The research further indicates that aspects of representation that are judged to be based on lack of knowledge of conventions in a medium such as drawing, may have deeper intuitive and conceptual roots. An alternative view of childrens spatial/geometric thought on VanHiele level 0 is described based on their assignment of meaning to geometric tasks. / AFRIKAANSE OPSOMMING: Drie-dimensionele houers word allerweë as geskikte konteks vir aanvangsmeetkunde-onderrig beskou. In hierdie studie word kinders se intuïtiewe begrip van alledaagse houers of bokse as vertrekpunt gebruik om die volgende aspekte te ondersoek met die oog daarop om inligting te bekom vir kurrikulering: • die betekenis wat kinders aan bokse (as meetkundige objekte) toeken • kinders se vermoë om 'n denkbeeld te skep en te manipuleer • kinders se strategieë om 'n drie-dimensionele konstruksieprobleem op te los • moontlike ouderdoms- en geslagsverskille • die rol wat meting speel wanneer 'n drie-dimensionele konstruksieprobleem opgelos word • moontlike ooreenkomste met Van Hiele-denkvlakke 'n Taakgerigte ondersoek (revised clinical interview) is met groepies van ses tot tien kinders op 'n slag gedoen. Elke kind kon 'n voorwerp kies uit 'n versameling en moes 'n houer of boks uit karton bou waarin die voorwerp kon pas. Die probleemoplossingsproses is met 'n videokamera afgeneem. Die kinders se voltooide houers, taaluitinge en overte hantering van die empiriese verwysingsvoorwerpe en die materiaal waarmee hulle gewerk het, is as data ontleed. Die navorser het gebruik gemaak van die analitiese prosesse wat beskryf word as begronde teorie-ontwikkeling om die data te ontleed en te kategoriseer. Die navorsmg hat aangetoon dat jong kinders nie noodwending bewus is van die vorm- en strukturele eienskappe van drie-dimensionele houers nie. Verder is dit duidelik dat kinders se voorstellings van veral vormeienskappe van houers deur middel van taal, handbewegings en tekeninge, nie impliseer dat hulle die nodige begrip van die struktuur het om so 'n houer uit tweedimensionele materiaal te kan vervaardig nie. Die navorsing het verder aan die lig gebring dat aspekte van kinders se ruimtelike kennis wat voorheen as aanduiding van gebrekkige kennis van konvensies beskou is, moontlik dieper konseptuele wortels het. 'n Alternatiewe beskouing van kinders se ruimtelik-meetkundige denke op Van Hiele Vlak 0 word ook voorgestel.

Submitted in fulfillment of the requirements of the Degree of Master of Technology: Management, Durban University of Technology, 2012. / The emphasis of geometry is of such significance that the current National Curriculum Statement has included the learning of two-and three-dimensional shape from grade R. However it is observed that teachers rely on textbooks for their knowledge of a dynamic topic such as nets of solids. Learners do not have an opportunity to explore the different orientations of solid shapes. Not many teachers use technology to assist their pedagogy. Quality processes in mathematics education emphasise the use of technology in teaching and learning. A study was performed using “Poly”, which is free open-source software for mathematics teaching and learning. This software was chosen because it was an easy to use application. It was able to show the different orientations of the solid shapes. Three-dimensional geometry can be explored using this software. The research is based on a social constructivist view of learning and the methodology used is a case study. The Piagetian and van Hiele stages of development will be the basis of the researcher’s investigation. Piaget’s theory is based on age development whilst van Hiele alludes to the different stages of geometrical development. A control group was compared to the experimental group consisting of 20 learners each. The research was conducted in KwaZulu-Natal and involved a teacher with a class of 40 learners. Qualitative and quantitative data were collected and were analysed. The data consisted of classroom observations and learner questionnaires and interviews. The findings of this study affirm that the use of technology in the teaching of geometry can enhance conceptual understanding. Classroom management breaks from routine while using Poly. Poly has the potential to improve learners' educational experiences; it can enable the effective application of constructive, cognitive and collaborative models of learning. Poly is not just a mathematical tool but also a tool for thinking and helping to enhance learners’ learning. It can serve as a vehicle for helping learners to foster fundamental geometrical concepts. The assessment of the use of computers in mathematics by the learners of the experimental classes indicates that application of computers enables increasing the interest of the learners in mathematics and introduces more variety to the studies, making them more enjoyable and interesting. / National Research Foundation