Thesis (M. Tech. (Education)) -- Central University of Technology, Free state, 2011 / This study examines the problems encountered by educators regarding the implementation of the National Curriculum Statement in mathematics in grades 10-12. The first aim of the study was to provide solutions to problems regarding training experienced by FET mathematics educators. The second aim was to identify problem areas in the NCS that frustrate mathematics educators teaching in the FET band and to identify areas that appeal to these educators. The third aim was to provide guidelines to assist educators with lesson planning in mathematics in the FET band. The fourth aim was to provide guidelines for appropriate assessment in mathematics in the FET band. The fifth aim was to provide guidelines for the effective integration of OBE in the teaching of mathematics in the FET band. The field work was executed by administering a questionnaire to a randomly selected sample of fifty two educators teaching in the FET band. Interviews were semi-structured, flexible and yielded additional information to that of the questionnaire. The questions of the interview were directly related to the objectives of the study and followed a given sequence that was adhered to in each interview process. The researcher arranged to interview one educator from each of the 15 randomly selected schools in the Motheo-district, but only 10 educators responded positively in the interview process, other educators could not avail themselves on that day. The researcher analysed the responses according to the respondent‟s personal particulars. Descriptive analysis of the sample data for section B of the questionnaire were then done, using respondent counting, percentages and the average for the responses of each statement. This study revealed that educators differ in terms of the problems that they encountered in implementing the NCS in mathematics. The findings from this study pointed out problems such as educators receiving inadequate training on implementing the NCS in mathematics. It was also revealed that educators had not been visited by the departmental officials in their schools for monitoring the implementation of the NCS in mathematics. The last finding showed that teaching and learning support material arrived late during 2008 and that there was a large shortage of such material. The result of the study provides invaluable baseline information with regard to the problems encountered by the educators in the implementation of the NCS in mathematics. On the basis of the findings of this study, a number of recommendations for the implementation of curriculum change in mathematics on FET level are given in Chapter 5.

Thesis (PhD (Curriculum Studies))--University of Stellenbosch, 2007. / This action research study was aimed at establishing the importance and role of communication, and determining to what extent it impacts on formative assessment in the mathematics classroom with particular reference to feedback. During the first cycle of research it was evident that conditions within the mathematics classroom were preventing this from being realised. If we as researchers were to assess the nature of communication patterns within the classroom situation, then those communication patterns should have existed. Our findings reflect that teachers were generally in control of all aspects of communication of their learners, and that communication was usually a type of monologue, with very limited response from learners to closed questions, (characterised by “yes” and “no” responses), which were frequently posed. The feedback from learners (perhaps inadvertently ignored), was not optimally utilised to enhance learning. Through observation it was determined that teachers’ ability to engage learners meaningfully for longer periods, or to consciously reflect upon their actions, needed to be developed. Praxis as research paradigm, which is based on reflection and appropriate response or action geared towards improving the circumstances or conditions of the people concerned (in this case teachers), underlies this study. This research is furthermore based on the following learning theories: enactivism, constructivism, facilitation theory, action learning, andragogy, reification, and situated learning...

Thesis (MEd)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: This study explored the number sense of 47 final year primary school pre-service teachers in Namibia and was motivated by the poor performance of Namibian primary school learners in both national and international standardised assessment tests. The literature review revealed that learner performance is linked to teacher subject knowledge (Ball, 1990, Ma, 1999) and that teachers’ confidence in doing and teaching mathematics influences the way they teach and their willingness to learn mathematics (Ball, 1990; Graven 2004). Number sense studies of pre-service teachers (Kaminski, 1997; Tsao, 2004; Veloo, 2010; Yang, Reys & Reys, 2009) have indicated that the development of number sense should be a focus of primary pre-service teacher education. The data in this mixed method research design were obtained from a Number Sense Questionnaire, a Written Computations Questionnaire and a Mental Calculations Questionnaire. These questionnaires were adapted from instruments developed by Professor Der-Ching Yang for 6th and 8th grade learners in Taiwan. Teacher confidence was measured by the McAnallen Confidence in Mathematics and Mathematics Teaching Survey. Six randomly selected pre-service teachers were interviewed to determine their use of number-sensible strategies. The correlation analysis shows a strong relationship between number sense and mental calculations; between number sense and confidence in both the ability to do and the ability to teach mathematics and between mental and written calculations. The overall results of this study reveal that the final year primary pre-service teachers demonstrate limited number sense and possess very few of the indicators of number sense that were described by Kalchman, Moss and Case (2001). The findings expose a lack of conceptual understanding of the domain numbers and operations, particularly in the domain of rational numbers and the operations of multiplication and division. The pre-service teachers have little or no access to a variety of flexible number-sensible strategies to solve problems and calculate mentally. They lack the fluency in basic facts and procedures to perform written calculations efficiently and correctly. Unexpectedly, the analysis of the confidence survey shows that they are confident in both their ability to do mathematics and their ability to teach mathematics. It is recommended that mental calculations and computational estimation should become a focus of primary school mathematics education. Institutions responsible for teacher training should develop the number sense of pre-service teachers and research effective and long-term professional development programmes. The confidence and willingness of the teachers to learn can be used as an important resource. / AFRIKAANSE OPSOMMING: Hierdie studie ondersoek die getalbegrip van 47 finale jaar primêre skool voordiens-onderwysers in Namibië en is gemotiveer deur die swak prestasie van die Namibiese primêre skool leerlinge in beide nasionale en internasionale gestandaardiseerde assesseringstoetse. Die literatuurstudie het aan die lig gebring dat leerlinge se prestasie gekoppel is aan onderwyservakkennis (Ball, 1990, Ma, 1999) en dat onderwysers se vertroue in hulle vermoë om wiskunde te doen en te onderrig, die manier waarop hulle onderrig en hul bereidwilligheid om wiskunde te leer beïnvloed (Ball, 1990, Graven 2004 ). Studies van voordiens primêre onderwysers se getalbegrip (Kaminski, 1997; Tsao, 2004; Veloo, 2010; Yang, Reys & Reys, 2009) toon dat die ontwikkeling van getalbegrip 'n fokus van primêre voordiensonderwyseropleiding behoort te wees. Die data in hierdie gemengde metode navorsing is verkry uit 'n Getalbegrip, 'n Skriftelike Berekeninge en 'n Hoofrekene Vraelys. Hierdie vraelyste is gebaseer op die instrumente wat ontwikkel is deur Professor Der-Ching Yang vir graad 6 en 8 leerlinge in Taiwan. Onderwyservertroue is gemeet deur die McAnallen Confidence in Mathematics and Mathematics Teaching Survey. Ses ewekansig geselekteerde voordiens-onderwysers is ondervra om te bepaal watter sinvolle strategieë hulle gebruik om vrae oor getalbegrip te beantwoord. Die korrelasie-analise toon 'n sterk verband tussen getalbegrip en hoofrekene; tussen getalbegrip en vertroue in die vermoë om wiskunde te doen en te leer, en tussen vermoë om hoofrekene en skriftelike bewerkinge te doen. Die algehele resultate van hierdie studie dui daarop dat die finale jaar primêre voordiens-onderwysers oor beperkte getalbegrip en baie min van die aanwysers van getalbegrip wat deur Kalchman, Moss en Case (2001) beskryf is, beskik. Die bevindinge toon ‘n gebrek aan begrip van die domein van getalle en bewerkings, veral in die domein van rasionale getalle en die bewerkings vermenigvuldiging en deling. Die voordiens-onderwysers beskik oor min of geen soepel strategieë om probleme op te los en hoofrekene te doen nie. Hulle beskik nie oor die vlotheit in basiese feite en bewerkings om skriftelike berekeninge doeltreffend en korrek uit te voer nie. Die vertroue wat voordiens-onderwysers uitgespreek het in hulle vermoë om wiskunde te doen en onderrig staan in sterk teenstelling met hierdie bevindige. Dit word aanbeveel dat hoofrekene en skatting 'n fokus van primêre skool wiskunde-onderwys behoort te wees. Instansies gemoeid met onderwyseropleiding behoort die getalbegrip van voordiensonderwysers te onwikkel en navorsing te doen oor effektiewe en lang-termyn programme vir professionele ontwikkeling. Onderwysers se vertroue en bereidwilligheid om te leer kan as 'n belangrike hulpbron gebruik word.

Thesis (MEd) -- Stellenbosch University, 1981. / Bibliography / Theses -- Education / Dissertations -- Curriculum studies / Theses -- Curriculum studies / No abstract available

Thesis (MEd)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: South Africa is in the midst of a mathematics and science education crisis that challenges all key role-players. The Institute for Mathematics and Science Teaching at the University of Stellenbosch (IMSTUS), was involved in several university-school partnership (systemic intervention) projects that sought to provide continuing professional development to mathematics and science teachers and to help them make a greater impact on the learners that they teach. One of these intervention projects was the Sciences and Mathematics Initiative for Learners and EducatorS (SMILES) that targeted mathematics and science teachers and learners in under-resourced schools in the Western Cape. The effects of an intervention aimed at supporting and enhancing teacher professional development will only be seen in the learners once teachers have accepted and mastered the pedagogies proposed. Professional development that does not “enthuse, support, train and renew, and encourage” will probably fail. When considering this, the question that must be asked is whether the SMILES project was in fact enthusing, supporting, training, renewing and encouraging. The purposes and aims of the SMILES project with specific reference to professional development of science teachers were to enhance teachers’ pedagogical content knowledge and address the critical issues confronting science education of which three are: constructivist teaching, understanding the nature of science, and scientific argumentation. The characteristics of effective professional development, the core features of professional development and the theoretical constructs to evaluate professional development of teachers were used in this study to evaluate the effectiveness of the model used in the SMILES project. A concurrent version of the mixed method approach was adopted for the collection and analysis of the data. Although causality is always difficult to prove in a school setting because of the many variables that affect student performance, improved student achievement is the ultimate litmus test for teacher professional development effectiveness. Analysis of the National Senior Certificate results of the project schools compared with the National and Provincial results indicated that the project schools on the whole fared better than the National results. The project schools outperformed the national and provincial results for Life Sciences in 2011, 2012 and 2013 by at least four percentage points. The highest result achieved was 85,5% in 2011. In 2012 and 2013 these results were 82,7% and 83,0% respectively. In Physical Sciences the project schools started with results below that achieved nationally (34,7%) and then ended up with a pass percentage within half a percentage point of the provincial result (72,1%). The Mathematics results were not as positive. The project schools started by achieving a 63,4% pass rate and ended with a percentage pass rate of 63,3% having initially taking a dip down to 51,3%. At the end of the intervention the Mathematics results were better than the national results but were 10% lower than the Provincial average. Although it is difficult to pin down the results solely to the effects of the intervention, the comparison with provincial and national results reasonably controls for most of the extraneous variables including variations in enrolments in these subjects. On the affective side it is almost certain that the attitude of the learners and the teachers toward their respective subjects improved during the tenure of the project. This could have had a positive effect on the National Senior Certificate results achieved by the project schools. / AFRIKAANSE OPSOMMING: Suid-Afrika is midde in 'n wiskunde en wetenskap onderwyskrisis wat alle sleutelrolspelers uitdaag. Die Instituut vir Wiskunde en Wetenskaponderwys aan die Universiteit van Stellenbosch (IWWOUS), was betrokke by verskeie universiteit-skool vennootskapsprojekte (sistemiese intervensie) wat gepoog het om voortgesette professionele ontwikkeling te bied aan wiskunde en wetenskap onderwysers en hulle te help om 'n groter impak op die leerders wat hulle onderrig, te maak. Een van hierdie intervensie-projekte was die Wetenskappe en Wiskunde-inisiatief vir leerders en opvoeders (SMILES) wat wiskunde en wetenskap onderwysers en leerders, in hulpbronarm skole in die Wes-Kaap, geteiken het. Die impak van 'n intervensie wat daarop gemik is om onderwyser professionele ontwikkeling te ondersteun en bevorder, sal eers in die leerders waargeneem kan word, wanneer onderwysers die voorgestelde pedagogieë aanvaar en bemeester. Professionele ontwikkeling wat nie "begeester, ondersteun, oplei en vernuwe asook aanmoedig” nie, sal waarskynlik misluk. Hierdie stelling in ag genome, is die vraag wat gevra moet word, of die SMILES-projek werklik onderwysers begeester, ondersteun, opgelei, vernuwe en aangemoedig het. Die doelstellings en doelwitte van die SMILES projek, met spesifieke verwysing na die professionele ontwikkeling van Wetenskap-onderwysers, was om onderwysers se pedagogiese inhoudelike kennis te versterk en om kritieke kwessies waarmee wetenskap-onderwys gekonfronteer word, aan te spreek. Drie van hierdie kwessies is, konstruktivistiese onderrig, begrip van die aard van wetenskap en wetenskaplike argumentering. Die eienskappe van effektiewe professionele ontwikkeling, die kern kenmerke van die professionele ontwikkeling en die teoretiese konstrukte om professionele ontwikkeling van onderwysers te evalueer, is in hierdie studie gebruik om die doeltreffendheid van die model wat in die SMILES-projek gevolg is, te evalueer. 'n Gelyklopend gemengde-metode benadering is gevolg vir die insameling en ontleding van die data. Hoewel oorsaaklikheid altyd moeilik is om in 'n skoolopset te bewys, as gevolg van die baie veranderlikes wat studente se prestasie beïnvloed, is verbeterde studente prestasie die uiteindelike lakmoestoets vir doeltreffendheid van professionele onderwyser-ontwikkeling. Ontleding van die Nasionale Senior Sertifikaat-uitslae van die projek-skole, in vergelyking met die nasionale en provinsiale resultate, dui daarop dat die projek-skole oor die algemeen beter gevaar het as die nasionale uitslae. Die projek-skole het die nasionale en provinsiale skole se resultate vir Lewenswetenskappe in 2011, 2012 en 2013 met ten minste vier persentasie punte oortref. Die hoogste resultaat behaal was 85,5% in 2011. In 2012 en 2013 was hierdie uitslae onderskeidelik 82,7% en 83,0%. In Fisiese Wetenskappe het die projek-skole met resultate onder wat nasionaal behaal was (34,7%) begin, en geëindig met ʼn uiteindelike slaagpersentasie binne 'n halwe persentasiepunt van die provinsiale resultate (72,1%). Die wiskunde-uitslae was nie so positief nie. Die projek-skole het begin met 'n 63,4% slaagsyfer en geëindig met 'n slaagpersentasie van 63,3% na ʼn aanvanklike insinking na 51,3%. Aan die einde van die intervensie was hul Wiskunde-resultate beter as die nasionale resultate, maar 10% laer as die provinsiale gemiddelde. Alhoewel dit moeilik is om die resultate slegs vas te pen aan die gevolg van die intervensie, dien die vergelyking met provinsiale en nasionale resultate as redelike kontroles vir meeste van die eksterne veranderlikes insluitend variasies in inskrywings in hierdie vakke. Op die affektiewe vlak is dit byna seker dat die gesindheid van die leerders en die onderwysers ten opsigte van hul onderskeie vakke verbeter het tydens die projek. Dit kon moontlik 'n positiewe uitwerking op die projek-skole se Nasionale Senior Sertifikaat resultate gehad het.

D.Ed. (Didactics) / Please refer to full text to view abstract

A thesis submitted to the Wits School of Education, Faculty of Humanities, University of the Witwatersrand in fulfilment of the requirements for the degree of Doctor of Philosophy May, 2016 / This study investigates how primary school mathematics in-service teachers respond to learners’ offers, over time, during classroom interactions. The study was a follow-up to a one-year long in-service ‘maths for teaching’ professional development course in which 33 teachers participated in 2012. Four teachers from that course were tracked in this follow-up study. Data sources within this study consisted of two cycles of observations of lessons taught by the four teachers in 2013 and 2014, and an interim video-stimulated recall (VSR) interview with each teacher, with reflections guided by the structure of Rowland et al.’s ‘knowledge quartet’. A total of 18 lessons from the four teachers were video-recorded across the 2013 and 2014 observations. The notion of ‘elaboration’ was used in this study as an interpretive lens to examine and characterise responsive teaching actions in the South African context, with the focus narrowing over the course of the PhD to contingency situations within the knowledge quartet framework, focused on responses to learner offers. In the South African literature, the terrain of elaboration is characterised by extensive gaps in teachers’ mathematical knowledge, incoherent talk, and frequent lack of evaluation of learners’ offers in the classroom. Using a grounded theory approach, I propose an ‘elaboration’ framework with three situations of responsive teaching (breakdown, sophistication and individuation/ collectivisation), which can be used as a tool to support the development of more responsive teaching in the South African context (and perhaps in other contexts where similar problems prevail). In this way, the study has contributed in terms of identifying some important ‘stages of implementation’ (Schweisfurth, 2011) that might be required to move towards the ideals of more responsive teaching that are described in the international literature, and yet remain distant from the realities of South African schooling. Using the three markers of shifts (extent, breadth and quality) in elaboration recruited in this study, drawn from the ways in which the dimensions of responsive teaching were conceptualised, I report on the different patterns of shifts in elaboration by the four teachers. The results of this analysis indicated that all four teachers made shifts in their responses to learners’ offers from 2013 to 2014 lessons in at least one or more dimensions of responsive teaching, in relation to extent, breadth and quality of elaborations. Findings from VSR interviews indicated associations between shifts in teachers’ reflective awareness, and shifts in responsive teaching actions. Theoretically, the study contributes through characterising responsive teaching actions in contexts of evidence of limited evaluation within the elaboration framework, with a language of description for identifying and developing more responsive teaching actions in a resource constrained context

Made available in DSpace on 2016-04-27T16:57:33Z (GMT). No. of bitstreams: 1 Jeane do Socorro Costa da Silva.pdf: 4928983 bytes, checksum: b76a4c8272cb0d5de95999bbd432055b (MD5) Previous issue date: 2014-11-07 / Universidade do Estado do Pará / This research of qualitative type sought to identify both the difficulties faced by Mathematics teachers who teach young people and adults classes in the metropolitan area of Belem-Para and the perceptions of Mathematics undergraduate students on the reality of this type of teaching considering what they observed in the intership. This thesis was guided by the following research question: what common elements bring the voices of teachers and undergraduate students in order to contribute to a reflexive practice from the subjects Teaching Practice and Supervised Internship of Para State University- UEPA, based on the interlocution between school and university? The study aimed at analyzing the voices of experienced teachers and beginning teachers in relation to the challenges of the practice of the formers and to the opportunities of coexistence and confrontation of these challenges even during the training process. The theoretical frameworks of this research were grounded on: Garcia, Imbernón, Nóvoa, Tardif, Zeichner e Pimenta e Lima, concerning the initial training based on the approach between university and school, grounded on the scope of practice in a reflexive perspective; and on Haddad e Di Pierro, Gadotti, Haddad, Ribeiro, Arroyo, Galvão e Di Pierro, Fonseca e Barcelos, to discuss the bases of EJA and the teaching of Mathematics in this segment. The main characters of this research were two teachers of Mathematics who work in EJA classes and four trainees of Undergraduation Course of Mathematics of UEPA. Also took part of this study fifty and seven teachers of Mathematics who work in EJA classes around the metropolitan area of Belem and fourteen undergarduate students of Mathematics course. The research revealed the importance of the participation and insertion of future teachers in different segments of teaching, such as Young and Adult Education EJA; and it also showed the importance of giving voice to the Mathematics teacher who is working with EJA classes in Belem. The results contributed to think the intership based on the analysis and reflection of teaching practice experienced in it, in order to rebuild the views, beliefs and assumptions on EJA modality, with the support of the theoretical fundamentals. The reasearch revealed the importance of planning a lesson taking into account the specific characteristics of EJA students and the previous knowledge brought by them, whether school and life experience; it also allowed the trainees to experience some difficulties related to the teaching of Mathematics in EJA classes and to seek solutions to overcome them; and at last, it enabled an approach between school and university and a link between the theoretical and practical aspects. These results imply changes of an institutional culture grounded on problematization, discussion, decision-making by the university on the basis of a regional need and with a view to ensuring the rights of citizens to attend a quality school, even outside the expected regular time / Esta pesquisa de cunho qualitativo buscou identificar as dificuldades enfrentadas pelos professores de Matemática atuantes em turmas de jovens e adultos na região metropolitana de Belém e as percepções dos alunos licenciandos em Matemática sobre a realidade dessa modalidade de ensino a partir das observações no estágio. Esta tese foi orientada pela seguinte questão de investigação: que elementos comuns trazem as vozes dos professores atuantes e dos alunos em formação inicial para a contribuição de uma prática reflexiva a partir das disciplinas Prática de Ensino e Estágio Supervisionado da UEPA e pautada na interlocução entre a escola e a universidade? O estudo teve como objetivo analisar as vozes dos professores experientes e professores iniciantes, seja em relação aos desafios da prática dos primeiros, seja em relação às oportunidades de convivência e enfrentamento desses desafios ainda durante o processo de formação. Os referenciais teóricos que subsidiaram a pesquisa basearam-se em Garcia, Imbernón, Nóvoa, Tardif, Zeichner e Pimenta e Lima no que se refere às questões voltadas para uma formação inicial que privilegie a aproximação entre a Universidade e a escola e a perspectiva reflexiva. Para a discussão dos fundamentos sobre EJA e o ensino de Matemática nesse segmento, a pesquisa apoiou-se em Haddad e Di Pierro, Gadotti, Ribeiro, Arroyo, Galvão e Di Pierro, Fonseca e Barcelos. Os protagonistas privilegiados da pesquisa foram dois professores de Matemática atuantes em turma da EJA e quatro estagiários do curso de Licenciatura em matemática da Universidade do Estado do Pará UEPA. Também participaram do estudo cinquenta e sete professores de Matemática da região metropolitana de Belém que atuavam em turmas da EJA e quatorze licenciandos do curso de Licenciatura em Matemática. A pesquisa revelou a importância da participação e inserção dos futuros professores nos diferentes segmentos de ensino, como a Educação de Jovens e Adultos e também mostrou a importância de dar voz ao professor de Matemática que está atuando nas turmas de EJA em Belém. Os resultados obtidos neste estudo contribuíram para se pensar o Estágio a partir da análise e reflexão sobre as situações da prática docente nele vivenciadas com vistas a reconstruir as visões, crenças e concepções sobre a modalidade da EJA e com o apoio da fundamentação teórica. A pesquisa revelou a importância de se planejar uma aula levando em consideração as características específicas dos alunos da EJA e os conhecimentos prévios trazidos pelos alunos, sejam eles escolares ou da experiência de vida; também possibilitou aos alunos estagiários vivenciar algumas dificuldades em relação ao ensino de Matemática na EJA e a buscar soluções para suprir tais dificuldades; viabilizou, por fim, uma aproximação entre a escola e a universidade e um elo entre os aspectos teóricos e práticos. Esses resultados implicam mudanças de uma cultura institucional assentada na problematização, na discussão, na tomada de decisões pela universidade em função de uma necessidade regional e com vistas à garantia dos direitos dos cidadãos de frequentar uma escola de qualidade, mesmo que fora do tempo regular esperado

Thesis (Ph.D.)--University of the Witwatersrand, Faculty of Humanities, School of Education, 2013 / Mathematics-for-teaching (MfT) is complex, multi-faceted and topic-specific. In this study, a Financial Mathematics course for pre-service secondary mathematics teachers provides a revelatory case for investigating MfT. The course was designed and taught by the author to a class of forty-two students at a university in South Africa. Eight students, forming a purposive sample, participated as members of two focus tutorial groups and took part in individual and group interviews. As an instance of insider research, the study makes use of a qualitative methodology that draws on a variety of data sources including lecture sessions and group tutorials, group and individual interviews, students’ journals, a test and a questionnaire. The thesis is structured in two parts. The first part explores revisiting of school mathematics with particular focus on compound interest and the related aspects of percentage change and exponential growth. Four cases are presented, in the form of analytic narrative vignettes which structure the analysis and provide insight into opportunities for learning MfT of compound interest. The evidence shows that opportunities may be provided to learn a range of aspects of MfT through revisiting school mathematics. The second part focuses on obstacles experienced by students in learning annuities, their time-related talk, as well as their use of mathematical resources such as timelines and spreadsheets. A range of obstacles are identified. Evidence shows that students use timelines in a range of non-standard ways but that this does not necessarily determine or reflect their success in solving annuities problems. Students’ use of spreadsheets reveals that spreadsheets are a powerful tool for working with annuities. A key finding with regard to teachers’ mathematical knowledge, and which cuts across both parts of the thesis, is the importance of being able to move between compressed and decompressed forms of mathematics. The study makes three key contributions. Firstly, a framework for MfT is proposed, building on existing frameworks in the literature. This framework is used as a conceptual tool to frame the study, and as an analytic tool to explore opportunities to learn MfT as well as the obstacles experienced by. A second contribution is the theoretical and empirical elaboration of the notion of revisiting. Thirdly, a range of theoretical constructs related to teaching and learning introductory financial mathematics are introduced. These include separate reference landscapes for the concepts of compound interest and annuities

After the introduction of the Basic Education Teacher Diploma (BETD) in Namibia, a number of studies were conducted on how teachers, lecturers, stakeholders and the Namibian public perceived the BETD program and its implementation. However, very few studies focussed specifically on mathematics subject content knowledge and pedagogical content knowledge in the BETD. The purpose of this study was to investigate the need for a complementary course in mathematics education to address the lack of mathematical content and pedagogical knowledge in the Namibian BETD. The study involved five mathematics school teachers, two mathematics college lecturers in the Kavango educational region and a professor of mathematics education at the University of Namibia. These participants were purposefully selected because of their knowledge and experiences with various aspects of the BETD program. The motivation for conducting this study was to gain a better understanding of some of the issues that have been raised about the BETD program, particularly the perceived inadequacy of mathematical subject content and methodology since the inception of the program. The study adopts a qualitative approach in reporting participants’ reflections. The views of the focal educators and documents such as syllabi and course outlines were the main source of data. The findings indicate that despite the training that the three BETD mathematics graduates in this study received, the level of mathematics taught in a complementary course, such as an ACE, would clearly better equip mathematics teachers to teach proficiently and facilitate access to institutions of higher learning such as universities. The results of the study revealed that there was a need for the implementation of a complementary course to the BETD in mathematics education for teachers of mathematics in Namibia. This study also provided valuable insights into what such a course could look like.