Made available in DSpace on 2016-04-27T16:57:09Z (GMT). No. of bitstreams: 1 Marcelo Boaventura.pdf: 747797 bytes, checksum: 48d59791aadf3779843f6c584f47bff0 (MD5) Previous issue date: 2011-10-20 / The objetive of this research is to establish between geometry and a school that dealt with practical issues of Architecture, Art and Design and hás a lot of geometry to the school of Arts and Architecture Bauhaus. Whereas the educational phenomena present in this movement for Art and Architecture establish connections with Realistic Mathematics Education (E.M.R.) and Ethnomathematics, did historical research since this school and the two theories argue that knowledge can emerge from the practical issues day-to-day. We conducted two interviews with two professors of mathematics that deals with the real context and discurs the possibility of mathematics as a bridge catalyst, to explain, measure and guess the phenomena that are in different areas and social contexts, especially Art, Architecture and Design. The theoretical and methodological foundations are in dialogue with the E.M.R., Ethnomathematics and the Bauhaus. The interview was based on these theories and historical processes of the Bauhaus. The interview was based on these theories and historical processes of the teaching and learning of geometry with the three-dimension constructions as instruments of the Art and Crafts. It is a qualitative research interview as having the tools to collect data in the coding an decoding theory and practice / O objetivo desta pesquisa é estabelecer relações entre a Geometria e uma escola que lidou com questões práticas da Arquitetura, da Arte e do Design e tem muito da Geometria à escola de Artes e Arquitetura Bauhaus. Considerando que os fenômenos educacionais presentes neste movimento de Arte e Arquitetura estabelecem conexões com a Educação Matemática Realística (E.M.R.) e a Etnomatematica, fizemos uma pesquisa histórica uma vez que esta escola e a duas teorias discutem, que os conhecimentos podem emergir a partir de questões praticas do dia-a-dia. Realizamos duas entrevistas com dois professores de Matemática que lidam com questões do contexto real e que discutem a possibilidade da Matemática ser uma ponte catalisadora, para explicar, mensurar e conjecturar os fenômenos que estão nas diferentes áreas e contextos sociais em especial a Arte, Arquitetura e o Design. Os fundamentos teóricos e metodológicos estão dialogando com a E.M.R. a Etnomatemática e a Bauhaus. A entrevista pautou-se nos processos históricos dessas teorias e do processo ensino e aprendizagem de Geometria tendo como instrumentos as construções tridimensionais da Arte e do Artesanato. Trata-se de uma pesquisa qualitativa tendo a entrevista como instrumentos para a coleta de dados na codificação e decodificação da teoria com a prática

Since 1971, the Freudenthal Institute has developed an approach to mathematics education named Realistic Mathematics Education (RME). The philosophy of RME is based on Hans Freudenthal’s concept of ‘mathematics as a human activity’. Prof. Hans Freudenthal (1905-1990), a mathematician and educator, believes that ‘ready-made mathematics’ should not be taught in school. By contrast, he urges that students should be offered ‘realistic situations’ so that they can rediscover from informal to formal mathematics. Although mathematics education in Vietnam has some achievements, it still encounters several challenges. Recently, the reform of teaching methods has become an urgent task in Vietnam. It appears that Vietnamese mathematics education lacks necessary theoretical frameworks. At first sight, the philosophy of RME is suitable for the orientation of the teaching method reform in Vietnam. However, the potential of RME for mathematics education as well as the ability of applying RME to teaching mathematics is still questionable in Vietnam. The primary aim of this dissertation is to research into abilities of applying RME to teaching and learning mathematics in Vietnam and to answer the question “how could RME enrich Vietnamese mathematics education?”. This research will emphasize teaching geometry in Vietnamese middle school. More specifically, the dissertation will implement the following research tasks: • Analyzing the characteristics of Vietnamese mathematics education in the ‘reformed’ period (from the early 1980s to the early 2000s) and at present; • Implementing a survey of 152 middle school teachers’ ideas from several Vietnamese provinces and cities about Vietnamese mathematics education; • Analyzing RME, including Freudenthal’s viewpoints for RME and the characteristics of RME; • Discussing how to design RME-based lessons and how to apply these lessons to teaching and learning in Vietnam; • Experimenting RME-based lessons in a Vietnamese middle school; • Analyzing the feedback from the students’ worksheets and the teachers’ reports, including the potentials of RME-based lessons for Vietnamese middle school and the difficulties the teachers and their students encountered with RME-based lessons; • Discussing proposals for applying RME-based lessons to teaching and learning mathematics in Vietnam, including making suggestions for teachers who will apply these lessons to their teaching and designing courses for in-service teachers and teachers-in training. This research reveals that although teachers and students may encounter some obstacles while teaching and learning with RME-based lesson, RME could become a potential approach for mathematics education and could be effectively applied to teaching and learning mathematics in Vietnamese school. / Seit 1971 wurde an dem renommierten Freudenthal Institut in Utrecht ein als Realistic Mathematics Education (RME) bezeichneter mathematikdidaktischer Ansatz entwickelt. Die Philosophie von RME beruht auf Hans Freudenthals Auffassung von Mathematik als menschlicher Aktivität. Der Mathematiker und Didaktiker Prof. Hans Freudenthal (1905 – 1990) plädierte dafür, dass Mathematik an den Schulen nicht als Fertigprodukt unterrichtet werden sollte. Im Gegensatz dazu forderte er, den Schülern an ‚realistischen’ Situationen nicht-formale und formale Mathematik wieder entdecken zu lassen. Obwohl die mathematische Schulbildung in Vietnam in den letzten Jahrzehnten schon einige Fortschritte gemacht hat, steht sie noch vor großen Herausforderungen. Derzeit ist die Reform der Unterrichtsmethoden eine dringliche Aufgabe in Vietnam. Augenscheinlich ermangelt es der Mathematikdidaktik in Vietnam an dem dazu notwendigen theoretischen Rahmen. Die Philosophie von RME eignet sich grundsätzlich als Orientierung für die Reform der Unterrichtsmethoden in Vietnam. Allerdings ist die Potenz von RME für die mathematische Schulbildung in Vietnam und die Möglichkeiten, RME im Mathematikunterricht anzuwenden, noch zu klären. Das Hauptziel dieser Arbeit war zu erforschen, wie RME beim Mathematik-Lernen und -Lehren in Vietnam eingesetzt werden kann und die Frage zu beantworten: Wie kann RME den Mathematikunterricht in Vietnam bereichern? Dazu wurde insbesondere der Geometrieunterricht in der Sekundarstufe I betrachtet. Im Einzelnen beinhaltet die Untersuchung: • eine Analyse der vietnamesischen Mathematikdidaktik in der ‘Reformperiode’ (etwa von 1980 bis 2000) • die Konzeption, Durchführung und Auswertung einer Befragung von 152 Mittelschullehrern aus verschiedenen vietnamesischen Provinzen und Städten zum Mathematikunterricht in Vietnam • eine Analyse von RME einschließlich der Freudenthalschen Sicht von RME und der Charakteristika von RME • die Diskussion, wie man RME-basierten Unterrichtseinheiten gestalten und diese in den Mathematikunterricht in Vietnam integrieren kann • Test solcher Einheiten in vietnamesischen Mittelschulen • Analyse der Rückmeldungen anhand der Schülerarbeitsblätter und der Lehrerberichte • Diskussion der Chancen und Probleme von RME-basierten Unterrichtseinheiten im Geometrieunterricht vietnamesischer Mittelschulen • Diskussion von Vorschläge zur Entwicklung und zum Einsatz RME- basierter Unterrichtseinheiten in Vietnam, einschließlich von Hinweisen für Lehrende und der Konzeption von Ausbildungs- und Fortbildungskursen zu RME Die Untersuchung zeigt, dass – obwohl Lehrer wie Schüler zunächst einige Hindernisse beim Lehren und Lernen mit RME- basierten Unterrichtseinheiten zu bewältigen haben werden – RME ein mächtiger mathematikdidaktischer Ansatz ist, der wirkungsvoll im Lehren und Lernen von Mathematik in vietnamesischen Schulen angewandt werden kann.

This study investigated the deliberate use of learners‟ home languages in the teaching and learning of linear programming. The study involved a Grade 11 teacher and his Grade 11 multilingual learners in a township school in the East Rand. Data was collected through lesson observations for five consecutive days, reflective interview with teacher and clinical interview with two learners. Analysis of data revealed that the teacher used learners‟ home languages to probe learners‟ understanding of specific terms frequently used in linear programming concepts, for example terms such as, „at least‟ and „at most‟. Learners‟ responses suggest that they drew on their home languages for the meaning of these words. Learners explained the term „at least‟ in their home languages as „buncinci‟ in Isixhosa, „bonnyane‟ in Sesotho and Sepedi and „okungenani‟ in IsiZulu. Learners also used mathematical English term minimum to explain „at least‟ and maximum to explain „at most‟.

Made available in DSpace on 2018-06-27T19:13:00Z (GMT). No. of bitstreams: 3 Herton Gilvan Caminha Goerch.pdf: 2308904 bytes, checksum: f2936d28aa101377f5ca9704942be810 (MD5) Herton Gilvan Caminha Goerch.pdf.txt: 118606 bytes, checksum: 3d55b43845a8c6eeba047ff7e06bf4b6 (MD5) Herton Gilvan Caminha Goerch.pdf.jpg: 3273 bytes, checksum: 2d5d843dbc65f63fdca4f757bb2cd63d (MD5) Previous issue date: 2013-10-10 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work has as its central focus the analysis of the possibilities that Mathematical Modeling offers to the mathematical learning concepts in a class of an Agricultural Technician course in a federal institute of education situated in Alegrete-RS. The justification is supported by the possibility of adopting a teaching methodology which is able to create opportunities for students to have contact with everyday problems, developing the ability to solve them and to analyze and interpret the solutions and at the same time learn mathematical content. The proposed activities involved the modeling of field objects used in the work of a trooper who lives in the state of Rio Grande do Sul with the help of the software GeoGebra. The research was grounded in the ideas of realistic mathematics education proposed by Hans Freudhental and his approach to the ideas of mathematical modeling. The enquiry was operationalized, in a qualitative approach, based on data collected through interviews with the historian responsible for the Gaucho Museum of the city of Alegrete, participant observations of the activities with the students, reports of the subjects of the research informed in the Field Diary and documents produced by them. Based on the theoretical assumptions, their own reflections and research objectives established the data analysis. With the analysis it was possible to notice attitude changes during the research and the students commitment to the work developed. It was observed that the work with mathematical modeling based on a topic that is part of the students everyday lives and with the help of computational tools aroused the interest and motivation to study mathematical content as well as the development of abilities for investigating and understanding the socio-cultural role of mathematics. / Este trabalho tem como foco central a investigação sobre as possibilidades que a Modelagem Matemática oferece à aprendizagem de conceitos matemáticos, em uma turma de Ensino Médio do curso Técnico em Agropecuária de uma escola pública federal localizada na cidade de Alegrete, RS. A justificativa sustenta-se na possibilidade de adotar uma metodologia de ensino capaz de oportunizar aos alunos o contato com problemas do cotidiano, desenvolvendo a capacidade de resolvê-los e de analisar e interpretar as soluções e, ao mesmo tempo, aprender conteúdos matemáticos. As atividades propostas foram a modelagem de objetos campeiros usados no trabalho do tropeiro que vive no estado do Rio Grande do Sul com o auxilio do software Geogebra. A pesquisa foi ancorada nas ideias da Educação Matemática Realista proposta por Hans Freudhental e sua aproximação com as ideias da Modelagem Matemática. A investigação foi operacionalizada, numa abordagem qualitativa, baseada nos dados coletados em entrevista com historiador responsável pelo Museu do Gaúcho da cidade de Alegrete, observações participantes das atividades desenvolvidas com os alunos, relatos dos sujeitos da pesquisa registrados no Diário de Campo e dos documentos por eles produzidos. Tendo por base os pressupostos teóricos, as reflexões próprias e nos objetivos da pesquisa estabeleceu-se a análise dos dados. Com a análise foi possível perceber mudanças de atitudes durante a investigação e o comprometimento dos alunos com o trabalho desenvolvido. Percebeu-se que o trabalho com Modelagem Matemática, a partir de um tema que faz parte do cotidiano dos alunos e com o auxilio de ferramenta computacional, despertou o interesse e a motivação para estudar conteúdos matemáticos além do desenvolvimento de habilidades para a investigação e a compreensão do papel sócio cultural da Matemática.

The function concept is one of the most important concepts in the learning of mathematics (Dubinsky & Harel, 1992), yet it is considered by many researchers to be one of the least understood and most difficult concepts to master in the learning of high school mathematics (Eisenberg, 1992, Sfard, 1992). To this end, problems concerning its teaching and learning are often confronted (Mann, 2000) and few teachers know how learners come to understand functions (Yoon, 2007). As a result, most teachers teach functions using the conventional approach which starts by stating definitions followed by examples and then a few applications. The nature of this approach has not encouraged teachers to engage learners and their ways of reasoning in knowledge construction and adequately addressing their difficulties. The purpose of this study was to use design research to improve the teaching and learning of functions at grade 11 level. This was achieved by adapting design cycles of Wademan’s (2005) Generic Design Research model in which each cycle comprised different iterative APOS (Action, Process, Object, Schema) analysis, design, development and implementation of hypothetical learning trajectories (HLTs). I started by interrogating twelve grade 11 learners of a particular rural high school on the June 2011 mathematics paper 1 examination they had written to determine the APOS theory conception level each learner was operating at, and their difficulties. Learners’ difficulties from initial interviews and literature were grouped under the function definition and representation. I then designed instruction based on HLTs embedded with Realistic Mathematics Education (RME) activities and two separate tasks on the definition and representation as a form of intervention to help learners move up from their initial conception levels to the next and to overcome their difficulties. After each design cycle I interviewed learners based on the task for a particular concept and learners’ responses were analysed using APOS theory and used to design further instruction to help learners approximate the schema level of understanding concepts related to functions. The major findings of this study were that the use of learners’ conceptions and RME activities in designing instruction helped learners to progress smoothly through APOS theory conception levels though they did not fully reach the intended schema level. In addition, design research cycles and their HLTs implemented in a constructivist environment enabled learners to collectively derive working definitions of the function concept and to improve their conceptual understanding of the process of switching from a graph to an equation. Another contribution of this study has been a deeper understanding of the extent to which design research can be used to improve learners’ understanding of functions and an addition of some insights to the teaching and learning of functions. / Thesis (PhD)--University of Pretoria, 2013. / gm2014 / Science, Mathematics and Technology Education / unrestricted

The research documented in this report had a twofold purpose. Firstly, it was to design and implement an intervention based on the theory of Realistic Mathematics Education (RME) aimed at improving the mathematical understanding of learners in two Grade 8 remedial mathematics classes, by revisiting the key number concepts of place value, fractions and decimals. In doing so, a second purpose was to investigate the viability and emerging characteristics of an intervention based on the theory of RME in such a setting (i.e. with low attainers to revisit key number concepts). Pending the realisation of these immediate outcomes, more distant outcomes in subsequent research would be: that learners' understanding and academic performance in mathematics improves and to develop a local instruction theory in using the RME theory to revisit the concepts of place value, fractions and decimals with low attaining learners in order to improve their understanding in this regard. Grade 8 low attainers were selected as the target group for this research as a result of the pending implementation of Mathematical Literacy as a compulsory subject for all learners, possibly from 2006. Currently in South Africa, learners who are not meeting the required standard by the end of their Grade 9 year are able to elect not to take mathematics through Grades 10, 11 and 12. When the new Further Education and Training (FET) policy is implemented, this will no longer be the case. All learners, who do not elect to take mathematics as a subject, will have to take Mathematical Literacy as a compulsory subject throughout Grades 10, 11 and 12. Although less detailed and abstract than the subject mathematics, the Mathematical Literacy curriculum still requires learners to have an understanding of key number concepts and also contains a substantial amount of algebra. As Grade 8 is when learners start working with algebra more formally, and is also their first year at secondary school, it was decided that this would be an appropriate year to try and diagnose and remediate problems in learners' understanding of the key number concepts, if and where possible. The intention was that this would then equip learners with a more appropriate structure of conceptualised knowledge of the above-mentioned concepts on which they could further construct their understanding of algebra. The study was carried out at a local urban high school in South Africa and the research design of this study was informed by two development research approaches (van den Akker&Plomp, 1993; Gravemeijer, 1994). Also, the study was only implemented with a small number of participants, within a bounded setting and without the intention to generalise the results. It was therefore regarded as a development case study. The results appear to indicate that it is viable to apply the theory of RME with low attaining Grade 8 learners in order to revisit the key number concepts of place value, fractions and decimals. Copyright 2004, University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. Please cite as follows: Barnes, HE 2004, A developmental case study : implementing the theory of realistic mathematics education with low attainers, MEd dissertation, University of Pretoria, Pretoria, viewed yymmdd < http://upetd.up.ac.za/thesis/available/etd-12032004-103122 / > / Dissertation (MEd (Curriculum design))--University of Pretoria, 2005. / Curriculum Studies / unrestricted

Department of Curriculum Studies and Education Management / MEDCS

Thesis (PhD)--Stellenbosch University, 2012. / Includes bibliography / ENGLISH ABSTRACT: The rationale for this study emerged from a realization that conventional instructional design approaches for introducing Calculus concepts, based on the logical sequencing and structuring of the concepts, did not adequately attend to or address students’ ways of thinking. This was particularly important in a distance education environment where learners depend on instructional texts to make sense of what is being presented, often without support from tutors. The instructional design theory of Realistic Mathematics Education (RME) offered a promising approach for designing learning sequences based on actual investigations of the ways in which students think. This study’s focus was on trialling the process of RME theory-based design using the Fundamental Theorem of Calculus as an example. Curve sketching was prominent in this exercise. Applying RME required developing a hypothetical learning trajectory (HLT) while attempting to adhere to methodological guidelines of design research. In this project, the instructional designer’s conceptualization and interpretation of the derivative-integral construct has had the most immediate implications for the study. The line of inquiry has been largely didactic, in that it was framed by a need to establish ways of introducing the teaching of a mathematical concept following instructional design principles. Throughout the project, the instructional design space has been contested, broken down, rebuilt and, ultimately, enriched by the contributions of the expert teachers and the engagement of participating students. The series of design experiments have revealed knowledge about student reasoning in this learning domain in relation to four main areas of quantifying change, curve sketching, general mathematical reasoning and symbol use. The primary contribution of this research has been a deeper understanding of the extent to which RME can be used as an instruction design theory for planning and introducing a distance teaching Calculus unit. From the study, it is clear that successful adoption of the RME theory is influenced and facilitated by a number of factors, including: careful selection of the concepts and mathematical structures to be presented; a team of experts (mathematicians and mathematics subject didacticians) to research, test and develop the learning activities; opportunities for student interactions; and time and resources for effective RME adoption. More involved research is required to get to the stage of the evolution of a local instructional theory around introducing the derivative-integral relationship as expressed in the Fundamental Theorem of Calculus. / AFRIKAANSE OPSOMMING: Die rasionaal van hierdie studie het uit die besef ontstaan dat konvensionele onderrigontwerpbenaderings vir die bekendstelling van Calculus konsepte, gebaseer op die logiese ordening en strukturering van die konsepte, nie voldoende beantwoord aan die eise van hoe studente dink nie. Dit was van spesifieke belang in die geval van afstandonderwys waar hierdie studente sin moet maak van wat aangebied word, dikwels sonder die ondersteuning van tutors. Die onderrigontwerpteorie van Realistiese Wiskundeonderwys (RWO) bied belowende moontlikhede om leertrajekte te ontwerp wat gebaseer is op werklike ondersoeke van hoe studente dink. Hierdie studie se fokus was om die RWO-gebaseerde teoretiese ontwerp se proses wat die Fundamentele Stelling van Calculus as voorbeeld gebruik, uit te toets. Krommesketsing was prominent in hierdie oefening. Die toepassing van RWO het vereis dat 'n leertrajek ontwikkel moet word terwyl aan die metodologiese vereistes van die ontwikkelingsondersoekbenadering getrou gebly word. In hierdie projek het die onderrigontwerper se konseptualisering en interpretasie van die afgeleide-integraalkonstruk onmiddellike implikasies gehad vir die studie. Die lyn van ondersoek was grootliks didakties van aard. Desnieteenstaande was die instruksionele ontwerpruimte voortdurend beding, afgebreek, herbou en uiteindelik verryk deur die bydraes van die bedrewe onderwysers en die betrokkenheid van die deelnemende studente. Die reeks ontwerpeksperimente het kennis blootgelê van hoe studente in hierdie veld redeneer met betrekking tot die volgende vier hoof areas: kwantifisering van verandering, krommesketsing, algemene wiskundige beredenering en die gebruik van simbole. Die primêre bydrae van hierdie navorsing is die dieper verstaan van die mate waarin RWO gebruik kan word as 'n instruksionele ontwerpteorie vir die beplanning en bekendstelling van 'n Calculus eenheid in afstandsonderrig.Dit is duidelik vanuit die studie dat suksesvolle aanneming van die RWO teorie afhanklik is van 'n aantal faktore: 'n noukeurige seleksie van die konsepte en wiskundige strukture wat aangebied moet word; 'n span van bedrewe wiskundiges en wiskunde vakdidaktici om die leeraktiwiteite na te vors, uit te toets en te ontwikkel; geleenthede vir studente-interaksies, en tyd en bronne vir effektiewe RWO aanpassing. Verdere toegespitsde navorsing hierop is nodig om die fase te bereik van die ontluiking van 'n lokale onderrigteorie oor die bekendstelling van die afgeleide-integraal verwantskap soos uitgedruk in terme van die Fundamentele Stelling van Calculus.

The study explores Mathematics educators’ use of students’ out-of-school experiences in the teaching of Transformation Geometry. This thesis focuses on an analysis of the extent to which students’ out-of-school experiences are reflected in the actual teaching, textbook tasks and national examination items set and other resources used. Teachers’ teaching practices are expected to support students’ learning of concepts in mathematics. Freudenthal (1991) argues that students develop their mathematical understanding by working from contexts that make sense to them, contexts that are grounded in realistic settings. ZIMSEC Examiners Reports (2010; 2011) reveal a low student performance in the topic of Transformation Geometry in Zimbabwe, yet, the topic has a close relationship with the environment in which students live (Purpura, Baroody & Lonigan, 2013). Thus, the main purpose of the study is to explore Mathematics teachers’ use of students’ out-of-school experiences in the teaching of Transformation Geometry at secondary school level. The investigation encompassed; (a) teacher perceptions about transformation geometry concepts that have a close link with students’ out-of-school experiences, (b) how teachers are teaching transformation geometry in Zimbabwe’s rural secondary schools, (c) the extent to which students’ out-of-school experiences are incorporated in Transformation Geometry tasks, and (d) the extent to which transformation geometry, as reflected in the official textbooks and suggested teaching models, is linked to students’ out-of-school experiences. Consistent with the interpretive qualitative research paradigm the transcendental phenomenology was used as the research design. Semi-structured interviews, Lesson observations, document analysis and a test were used as data gathering instruments. Data analysis, mainly for qualitative data, involved coding and categorising emerging themes from the different data sources. The key epistemological assumption was derived from the notion that knowing reality is through understanding the experiences of others found in a phenomenon of interest (Yuksel & Yildirim, 2015). In this study, the phenomenon of interest was the teaching of Transformation Geometry in rural secondary schools. In the same light, it meant observing teachers teaching the topic of Transformation Geometry, listening to their perceptions about the topic during interviews, and considering how they plan for their teaching as well as how students are assessed in transformation geometry. The research site included 3 selected rural secondary schools; one Mission boarding high school, a Council run secondary school and a Government rural day secondary school. Purposive sampling technique was used carefully to come up with 3 different types of schools in a typical rural Zimbabwe. Purposive sampling technique was also used to choose the teacher participants, whereas learners who sat for the test were randomly selected from the ordinary level classes. The main criterion for including teacher participants was if they were currently teaching an Ordinary Level Mathematics class and had gained more experience in teaching Transformation Geometry. In total, six teachers and forty-five students were selected to participate in the study. Results from the study reveal that some teachers have limited knowledge on transformation geometry concepts embedded in students’ out-of-school experience. Using Freudenthal’s (1968) RME Model to judge their effectiveness in teaching, the implication is teaching and learning would fail to utilise contexts familiar with the students and hence can hardly promote mastery of transformation geometry concepts. Data results also reveal some disconnect between teaching practices as espoused in curriculum documents and actual teaching practice. Although policy stipulates that concepts must be developed starting from concrete situations and moving to the abstract concepts, teachers seem to prefer starting with the formal Mathematics, giving students definitions and procedures for carrying out the different geometric transformations. On the other hand, tasks in Transformation Geometry both at school level and the national examinations focus on testing learner’s ability to define and use procedures for performing specific transformations at the expense of testing for real understanding of concepts. In view of these findings the study recommends the revision of the school Mathematics curriculum emphasising pre-service programmes for teacher professional knowledge to be built on features of contemporary learning theory, such as RME theory. Such as a revision can include the need to plan instruction so that students build models and representations rather than apply already developed ones. / Curriculum and Instructional Studies / D. Ed. (Curriculum Studies)