Browsing by Subject "Mathematics Education"

Now showing 1 - 20 of 21
  • Thumbnail Image
    Item
    Open Access
    Action research : an exploration
    (1987) Colyn, Wendy May
  • Thumbnail Image
    Item
    Open Access
    Bridging the boundaries? A study of mainstream mathematics, academic support and "disadvantaged learners" in an independent, secondary school in the Western Cape
    (1998) Swanson, Dalene M; Ensor, Paula
    A small-scale study was conducted within a historic and traditional, independent, all-boys secondary school in the Western Cape, the focus of which is the exploration of subject positions potentially available to the black male students of the "Black Scholarship Programme" in their study of school mathematics. This includes an examination of the particular nature of the schooling ethos and culture, and its role in creating and maintaining boundaries, producing and reproducing forms of power and control which assist in holding these black students to positions of subordination. It is proposed that the hierarchical and differentiating rituals and codes within the school context provide the means by which the Black Scholarship students are constructed as disadvantaged. Particular emphasis is placed on the discourse of mathematics within the Academic Support Programme of the school, designed to assist these black students in "bridging the gap" in their academic knowledge and experience; and in the differentiated nature of the mathematics discourse available to the Black Scholarship students within the Mainstream Programme. There is an examination of the power relations between these two discourses and other discourses within the social domain which shape the way in which these students are positioned in terms of deficit and disadvantage. Four students of the Black Scholarship Programme were interviewed in their initial year at the secondary school (Standard Six) as were the two teachers of the Academic Support Programme. The discussions were taped and transcribed and formed the basis of the analysis. Field notes were taken of discussions with academic staff within the Mathematics Department and school documentation reflecting school policies and discussions within the school were used, where relevant, in relation to the Black Scholarship students and mathematics. The methodological framework was drawn, in the main, from the work of Basil Bernstein and Paul Dowling in focusing on context, discourse and subjectivity. The study was used to interrogate previous research work in the area of Social Inequality and Mathematics Education. It also raised questions about taken-for-granted assumptions, both within the school as well as the wider community, regarding race, social class, language and cultural difference. The study attempts to investigate and bring into focus how "difference" is created and maintained, produced and reproduced within the context of the school, providing boundaries rather than bridges, and how this difference is recontextualised into disadvantage in relation to the Black Scholarship students and mathematics.
  • Thumbnail Image
    Item
    Open Access
    Building a model of "spatial ability" : an analysis of grade 5 and 6 learners' strategies for solving "spatial" activities
    (1999) Bennie, Catherine Jane; Breen, Chris
    This study explores the notion of "spatial ability" from the perspective of mathematics education. A review of the literature on "spatial ability" is used to compile a preliminary model of the phenomenon. Certain questions related to interaction in space arising from the literature review are noted in this model. Three aspects of this interaction are the focus of the empirical study. The results of the research are used to shed light on the preliminary model of "spatial ability". The three themes of the empirical study can be described as follows: the visualisation of "objects" from different perspectives (in "small-scale" space); the visualisation of "objects" from different perspectives (in "large-scale" space): and the representation of a three-dimensional "object" in a two-dimensional net. The results of the study suggest that a range of strategies can be used on the same "spatial" activity, and that a learner can adopt a variety of different strategies on a set of activities. Of the ten strategies identified in the study, some appear to rely on the manipulation of visual imagery, while others suggest that the manipulation process has been generalised resulting in a more "abstract" strategy. Interesting features related to the use of physical manipulation in solving spatial tasks and the communication of visual processes in the form of drawings and verbal responses are discussed. These results are used to expand the preliminary model of "spatial ability". This updated model suggests that a learner who has mastered four "abilities" and has a working knowledge of visual conventions will be able to interact successfully in the visual world. The different strategies identified in the empirical study are required during this interaction in space. The researcher also identifies areas for further research in. the field of "spatial ability" and reflects on the methodology associated with the assessment of this phenomenon. The potential value of the results of the study for use in mathematics education is discussed.
  • Thumbnail Image
    Item
    Open Access
    A case study investigation of how assessment practices construct teachers' and pupils' views of mathematics
    (1995) Cilliers, Peter Steven; Ensor, Paula
    Assessment practices are an integral part of schooling. The prominence of assessment within schooling in providing information to students and teachers about students' "ability" in learning school subjects, raises an important question: what sort of influence do assessment practices have on how school subjects are perceived by students and teachers? This dissertation focuses on two themes - the way in which assessment practices construct school mathematics, and the way in which these constructions of school mathematics work dynamically with assessment practices to produce descriptions of students.
  • Thumbnail Image
    Item
    Open Access
    Demographic profile and perceived in-service education and training needs of secondary Mathematics teachers in the Limpopo Province
    (2003) Rakumako, Angeline Mosenya; Laugksch, Rudiger C
    It is now generally acknowledged that effective and sustainable in-service education and training (INSET) programmes require, first, adequate information to be available on teachers' demographics and, second, for teachers' views on professional development to be taken into consideration. Neither kind of information is currently available for Mathematics teachers in the Limpopo Province of South Africa in a reliable manner. Consequently, this study has as its objectives 1) to determine the demographic profile of secondary Mathematics teachers in the Limpopo Province, 2) to establish the perceived INSET needs of these teachers, and 3) to examine possible associations between demographic profiles and perceived INSET needs of secondary Mathematics teachers in the Limpopo Province.
  • No Thumbnail Available
    Item
    Open Access
    Gender differences in mathematics : a discourse analysis
    (1993) MacLeod, Catriona
    The majority of perspectives from which the study of gender and mathematics has been approached have failed to move beyond the· individual/society divide. The contradictory nature of subjectivity and the operation and interpenetration of power and knowledge in the production of that subjectivity has n~t been taken into account. This thesis is based on the theoretical framework of post-structuralistn. The literature concerning gender differences in mathematics is criticized from this framework. In particular, the work of Walkerdine and her colleagues, which highlights the processes within the classroom which allow girls to succeed in mathematics but never actually be successful, is of interest. The methodology of choice in this study is that of discourse analysis which makes clear both the positionings available to the participants as well as the power relations formed. The sample was drawn from a topachieving Std 8 Higher Grade class in an affluent Model C school. This sample represents a theoretically salient sample as the literature points to the 'differences' being most pronounced in the upper levels of mathematics education. The analysis clearly highlights the double-bind within which girls find themselves in the mathematics classroom. The apparent equality of opportunity and non-sexism is counteracted by the positioning of girls as hard-working but without natural flair in mathematics. The characteristics that make it possible to achieve in mathematics are ascribed to males. The resistance to t~is powerful 'disciplinary technology' is the invoking of the feminist discourse, which was done by some of the females in the study.. It appears that there are very real barriers to girls' participation and achievement in mathematics. These barriers lie within the power relations and discourses/knowledges surrounding gender issues and mathematics education.
  • Thumbnail Image
    Item
    Open Access
    Investigating a geometry course for in-service teachers
    (2004) Agherdien, Gabeba; Breen, Chris
    This study focused on Foundation Phase teachers' pedagogical and content knowledge. It investigated the impact that a geometry course (Shape and Space), had on the teachers levels of understanding of Shape and Space. The course was conducted over 5 days. A literature search revealed a few different tools in designing the course, the majority of which referred to either Van Hiele or Hoffer. Our course design however was instructed by the requirements of the Revised National Curriculum Statement (RNCS) and had to follow it closely.
  • Thumbnail Image
    Item
    Open Access
    An investigation of mathematical misconceptions through an analysis of Grade 7 learners' responses to test items on decimals, percentages and measuremnt
    (2001) Tawodzera, George; Ensor, Paula; Gumedze, Freedom Nkhululeko
    This research dissertation emerges as a component of a broader research study, which sought to determine the impact of a mathematics textbook, Maths for all (Mfa) on teaching and learning, in general, and on learners' performance, in particular. The impact evaluation study focused on Grade 7 learners, from a sample of formerly DET primary classrooms in townships near Cape Town. It focused particularly on the teaching of decimals, percentages and measurment which 14 teachers in these schools agreed to teach in the second term of 2000. The 538 learners, from 10 experimental classrooms (with access to Mfa) and 4 control classrooms (with no access to Mfa), were given a pre-test at the beginning of the second term, and the same test as a post-test towards the end of the same term of the year 2000. The present study aims to analyse possible patterns of error in learners' responses to the test and investigate whether these patterns suggest underlying misconceptions held by the learners on decimals, percentages and measurement. As a secondary aspect, the study also set out to evaluate the test instrument as a measure of achievement and of potential misconceptions.
  • Thumbnail Image
    Item
    Open Access
    Knowledge used for teaching counting: A case study of the treatment of counting by two Grade 3 teachers situated in schools serving working class communities in the Western Cape Province of South Africa
    (2021) Nwaoha-Peterside, Fortune; Davis, Zain
    Knowing how to correctly count, is fundamental to the future mathematics success of young children. Earlier studies show that many South African primary school students underperform in mathematics even when evaluated with task below grade level. Reports suggest that this is a problem stemming from the poor pedagogic, and or content knowledge of classroom mathematics teachers. Shulman (1986; 1987) refers to this area of knowledge as Pedagogic Content Knowledge (PCK). In the field of mathematics teaching and learning, Ball, Thames and Phelps (2008) refer to it as Mathematics Knowledge for Teaching (MKfT). Teachers' mathematics PCK, comprises of three core knowledge domain: (i) Teacher's Knowledge of Content and Teaching (KCT); (ii) Teacher's Knowledge of Content and Student (KCS); and (iii) teacher's Knowledge of Content and Curriculum (KCC). Teachers' KCS was considered in this study as it concerns what teachers know about what learners know and how they learn. The general interest of this project was to study the construction of experience of mathematics (non-core domain knowledge) by genetic endowment on the basis of contextual data. More specifically, the particular interest of the study is on the construction of the experience of counting in the pedagogic situations of Grade 3 schooling. For that purpose, video records of mathematics teaching in two schools situated in working-class communities were analysed. The study adopted an Integrated Causal Model approach which drew on resources from different disciplines such as mathematics education, cognitive science, evolutionary psychology and mathematics. The study was partly framed by Bernstein's pedagogic device, particularly with respect to his notion of evaluation, as well as the inter-related constructs of PCK, MKfT and KCS. The theoretical resources used to describe computations were drawn largely from Davis (2001, 2010b, 2011a, 2012, 2013a, 2015, 2018) and related work on the use of morphisms as elaborated in Baker et al. (1971), Gallistel & King, (2010), Krause (1969) and Open University (1970). These resources were used to produce the analytic framework for the production of and analysis of data. The analysis describes the computational activities of teachers and learners during the recorded lessons, specifically the computational domains made available pedagogically. In so doing, I was able to provide more illumination on what is described as teacher's KCS for teaching counting at the Grade 3 level. From the generated data, the study finds that counting proper was restricted to the constitution and identification of very small ordered discrete aggregates which can be handled by human core domain object tracking system and approximate number system, and that an implicit reliance on numerical order derived from computations on aggregates was central to the teaching and learning of counting.
  • Thumbnail Image
    Item
    Open Access
    Mathematics, pedagogy and textbooks : a study of textbook use in Grade 7 mathematics classrooms
    (2001) Jaffer, Shaheeda; Ensor, Paula
    This dissertation is concerned with a systematic description of the recontextualization of the practices of a textbook, Maths for all Grade 7 Learner's Activity Book, when it is incorporated into grade 7 mathematics teachers' classroom practices. In particular, the research described here focuses on the impact of the textbook on four grade 7 mathematics teachers' classroom practices. My study forms a sub-project of a larger research project which explores the impact of the textbook, Maths for all Grade 7 Learner's Activity Book, in 14 grade 7 mathematics classrooms. The research design of my study comprised two aspects: an analysis of a chapter from the textbook, Maths for all Grade 7 Learner's Activity Book, and an analysis of its use in classrooms. Data collected included a textbook chapter on measurement and the accompanying chapter in the teacher's guide, questionnaires (learner, teacher and school), teacher interviews, video recordings of observed lessons and learner notebooks. Drawing largely on Paul Dowling's Social Activity Theory and Paula Ensor's extension of this work in her study on teacher education, a theoretical model was developed for the analysis of data. The theoretical model was supplemented with theoretical concepts from Basil Bernstein's sociological theory of pedagogic discourse. While the model was developed in relation to the content and use of a specific textbook, the model can potentially be used for other mathematics textbooks or textbooks from other disciplines. Analysis shows that the textbook, which embodies an inductive, exploratory pedagogy, cannot on its own achieve learner's apprenticeship into mathematics, or teacher's apprenticeship into its privileged mode of teaching mathematics. The analysis of the teachers' use of textbook shows that in most cases, the privileged pedagogy of the textbook differed considerably from the preferred pedagogy of the teachers. Most teachers preferred a deductive pedagogy and used the textbook in ways which fragmented the mathematical knowledge presented to learners, reduced the mathematical complexity of the textbook tasks and consequently transformed the pedagogic intentions of the textbook. The research therefore concludes that the transformative role of the textbook needs to be accompanied by teacher development programmes.
  • Thumbnail Image
    Item
    Open Access
    Pleasure and pedagogic discourse in school mathematics : a case study of a problem-centred pedagogic modality
    (2005) Davis, Zain; Ensor, Paula
    thesis is concerned with the production of an account of the relation between the reproduction of specialised knowledge and the moral discourse within pedagogic practice. The internal mechanism that knots together knowledge and moral discourse is elaborated by way of an analysis of texts produced by the originators of a pedagogic modality they refer to as the "problem-centred approach." The particular texts analysed are: (1) the Grade 1 to 4 textbooks and the corresponding teacher's guides, and (2) video records, supplied by the originators, of what they consider to be exemplary realisations of the pedagogy in practice of the "approach." The thesis opens with a discussion of a proposition, derived from Bernsteinian studies of curriculum and pedagogy, stating that everyday and academic know ledges are incommensurable, and from which it is claimed that the insistent contemporary attempts at incorporating the everyday into the academic in curricula and pedagogy, under the banner of "relevance," are educationally problematic. Against the Bernsteinian position, a central feature of the "problem-centred approach" is the extensive recruitment of extra-mathematical referents for the purposes of the reproduction of school mathematics. A more general examination of school mathematics texts that recruit the everyday reveal that such texts also associate the everyday with the pleasure of the student, so rendering "relevance," and hence moral discourse, as utilitarian. The manner in which the moral discourse operates within pedagogy was described in terms of Hegel's theory of judgement and Freudian-Lacanian accounts of imaginary and symbolic identification. Hegel enabled a description of pedagogic discourse at the level of the instructional content, and Freud-Lacan at the level of moral discourse. Hegel also enabled the location of the point at which the moral attaches to the instructional. What our analysis revealed is as follows: (1) the "problem-centred approach" is a competence-type pedagogy that employs strategies encouraging an initial imaginary identification with the everyday and pleasure, which is used to effect symbolic identification with school mathematics; (2) moral discourse drives pedagogic judgement by means of the imaginary-symbolic dialectic pertaining to identification; (3) evaluation drives pedagogic judgement aimed at the knowledge statements produced by students; and that (4) while the moral discourse is a pervasive and formally necessary component of pedagogy, it is ultimately embedded in the organisation and elaboration of the instructional contents, working in the service of the reproduction of instructional contents, but in accord with dominant ideological imperatives.
  • Thumbnail Image
    Item
    Open Access
    The recontextualising of pedagogic discourse: a case study drawn from an inservice mathematics education project
    (1995) Davis, Zain; Ensor, Paula
    The dissertation is concerned with the production of a systematic account of the recontextualising of pedagogic discourse across two contexts: mathematics INSET provision and school mathematics teaching. Drawing on the work of sociologists Basil Bernstein and Paul Dowling, an attempt is made to construct a theoretical model which is applied to produce a reading of the interactions between an INSET provider and a teacher, and the teacher and school students. The dissertation opens with a description and discussion of the conceptualising of the research project, the production of data, and the use of the literature survey and theoretical resources in the production of a methodology. The second chapter presents a review of the literature on INSET in which three chief components of conceptions of good INSET practice are highlighted: teachers should define their own needs; INSET should be concerned with the professional development of teachers, where professionalism implies an exclusion or marginalising of academic concerns; and INSET should be school-focused. The chapter moves on to consider NGO-provided INSET and concludes with a discussion of INSET in terms of Bernstein's categories horizontal and vertical discourses. In the third chapter, elements of Bernstein's code theory and Dowling's language of description are appropriated to construct a model which contextualises the study, produces an account of the transmission and acquisition of pedagogic discourse which attends to the interactions between transmitters and acquirers, and generates data for analysis. The chapter concludes with a summary of the model. Chapter 4 is devoted to an analysis of written materials from an INSET course which the teacher attended as well as the interactions between the INSET provider and teacher. An analysis of the use of wall displays and the arrangement of the classroom is produced in chapter 5, followed by an analysis of the interactions between the teacher and students. The analysis focuses on the way in which the utterances of the transmitter and acquirer are redescribed to produce pedagogic texts. The dissertation is concluded in chapter 6 which opens with a discussion of the resources and strategies implicated in the recontextualising of pedagogic discourse after which a summary of the analysis is produced. The last section of the chapter discusses the limitations of the research and the model.
  • Thumbnail Image
    Item
    Open Access
    The recruitment of the 'everyday' in fourteen Grade 7 mathematics classrooms
    (2004) Nakidien, Mogamat Toyer; Ensor, Paula
    Bibliography: leaves 97-101.
  • Thumbnail Image
    Item
    Open Access
    A small-scale investigation into teachers' access to the regulating principles underlying the "new mathematics" curriculum in the Junior Primary phase
    (1995) Long, Caroline; Ensor, Paula
    This research project focuses on the "new primary mathematics" curriculum that has been implemented in the schools in the Western Cape over the past six years. The specific question I addressed was, 'What access do teachers have to the regulating principles underpinning the 'new primary mathematics' curriculum". The term "regulating principles" is drawn from the work of Paul Dowling (1993;98). In terms of this research, the regulating principles are the theoretical underpinnings to the new curriculum, which include substantially a theory of learning. I explore access to the regulating principles through semi-structured interviews with six teachers, who have implemented this new approach with different degrees of success, as measured in their own terms. I also investigate the official Teachers' Guide for Mathematics (Cape Education Department, 1993) for explicitness of theoretical underpinnings. An analysis of the teachers' guide indicated that the regulatory principles were not made explicit and the research indicates that the teachers in my sample have restricted access to these principles. I conclude that teachers who have little access to the regulating principles are constructed as a subordinate voice in relation to teacher educators, and must of necessity rely on procedure for their practice and be subject to external validation. This raises questions as to the successful implementation of the curriculum, in that it limits access by teachers to the educational debates surrounding theories of knowledge and theories of learning, and so inhibits teacher involvement in curriculum implementation. It also limits the ability of teachers to interrogate their own practice.
  • Thumbnail Image
    Item
    Open Access
    Students, texts and mathematics : an analysis of mathematics texts and the construction of mathematics knowledge
    (2001) Allie-Ebrahim, Ferial; Davis, Zain
    This study deals with a systematic description of student production of mathematics texts and focused on written texts that appeared to be legitimate yet could not be upheld by a principled verbal description. A search of the literature on the analysis of students texts revealed that semiotic analysis, was not only scarce, but ideally suited to examining the social organisation of school mathematics practice. This study examines how student texts produced in response to typical school mathematics problems can, via a systematic analysis of texts, index the construction of mathematics knowledge. It outlines Dowlings' model of Social Activity Theory (1998) to produce a textual analysis which focuses on textual strategies to distribute message. These strategies and the message underpin the analysis. Practices that establish the message distributed indexes mathematics knowledge and curriculum practices. The notion of a mathematising gaze informing school practice was explored and was related to the construction of existing and pre-existing mathematics knowledge. To locate the effects of a mathematics gaze that could produce texts that lacked discursive elaboration in verbal discriptions, a comprehensive list of ideal types were developed to act as an interface between the empirical text produced that acted as a reading for constructive description of the theoretical terrain.
  • Thumbnail Image
    Item
    Open Access
    A study of the constitution of Grade 8 mathematics within the context of the Revised National Curriculum Statement in five Western Cape schools
    (2013) Arendse, Nicole; Jaffer, Shaheeda
    This dissertation is an investigation into the constitution of school mathematics within the context of the Revised National Curriculum Statement in a selection of Grade 8 mathematics lessons in five working-class schools in the Western Cape Province of South Africa. The study is located within the broad framework of the sociology of education, specifically drawing on Bernstein's (1996) sociological theory of education and his pedagogic device. This study focuses on the way in which the content of the evaluative rule of the pedagogic device is realised in the particular selection of schools. My theoretical framework relies on of the work of Davis (2010a, 2010b, 2010c, 2011a, 2011b, 2011c, 2012, 2013a & 2013b) and Bernstein (ibid.). These theoretical resources were drawn on to describe and analyse the mathematical activity in the five schools as well as serving as a means for generating analytical resources for describing the constitution of mathematics. In my analysis I present an account of the computational activity of teachers and their learners and the regulation of mathematical activity in fifteen Grade 8 mathematics lessons. I use these descriptions of computational activity to discuss the realisation of content against a general background of curriculum reform that has de-emphasised explicit use of formal definitions. I explore what mathematical content was recognised and constituted in relation to topics announced by teachers and use the mathematics encyclopaedia as a resource to ascertain the content that substitutes for formal mathematical definitions, axioms and propositions.
  • Thumbnail Image
    Item
    Open Access
    Teachers' attributions and beliefs about girls, boys and mathematics : a comparative study based on 40 Afrikaans-speaking secondary mathematics teachers in the Western Cape
    (1998) Roelofse, Rosina Catherina; Ensor, Paula; Meyer, JHF
    This dissertation is concerned with teachers' beliefs regarding boys, girls and mathematics. The present study is a partial replication of a study conducted by Fennema et al (1990) and the results are compared. The present study extended the work of Fennema et al (1990) through an exploration of the structure of the data. Forty female teachers in the Western Cape region were interviewed. They were asked to identify their two most and least successful boys and girls in mathematics and to attribute causation for success and failure. They _were also asked to respond to 20 characteristics on a "Likert type" response format. The results generated from the present study concluded that teachers believed their female students to be their more successful mathematics students. They attributed the most successful girls' achievement mainly to effort whereas with the most successful boys, achievement was attributed to ability and effort. Both the most successful boys and girls failures on mathematics tasks were attributed to the difficulty of the task. Achievement of the least successful girls was attributed mainly to teacher's help and for the boys it was attributed to teacher's help and task. For both these groups, ability and to a lesser extent, effort, are given as the main reasons for failure on mathematics tasks. Very little difference was found between teachers' responses regarding the characteristics of their best boy and best girl mathematics students. When exploratory factor-analysis was performed a difference was found in the factor-solutions for the boys and the girls. This study suggests that there might be a difference in teachers' beliefs regarding boys and girls achievement in mathematics that is worthy of further exploration.
  • Thumbnail Image
    Item
    Open Access
    Teachers, learners and mathematics : an analysis of HSRC research reports on mathematics education 1970-1980
    (1997) Galant, Jaamiah; Ensor, Paula
    The dissertation is concerned with the production of a systematic analysis of HSRC research reports into mathematics education in South Africa between 1970 and 1980. Drawing on the theoretical language of Dowling (1995), the analysis focuses on the (re)production of voice and message in the reports. This entails an analysis of positioning strategies that il1ark out voices in the texts and distributing strategies that distribute message across voices. Voices include bureaucratic, academic, teacher and learner voices and knowledge and practices that constitute message distributed to voices relate to mathematical knowledge, pedagogic knowledge and curriculum innovation practices. Positioning and distributing textual strategies with respect to learner and teacher sub-voices are related to the (re)production of theories of instruction that constitute models of acquirers, transmitters and pedagogic contexts and define pedagogic competence in particular ways. The (re)production of theories of instruction in turn are related to the reproduction of social relations in the broader society. It is hoped that the analysis illustrates the generality of Dowling's language for analysing texts. The substantive focus of the study is the analysis of the reports and the language developed in the analysis is used to make some suggestive comments about current mathematics curriculum development in South Africa. It is hoped, in particular, that the focus in this study on discourses in mathematics education in South Africa in the 1970s will contribute to the documenting of the history of mathematics curriculum development in South Africa.
  • No Thumbnail Available
    Item
    Open Access
    The school mathematics textbook as an instantiation of the pedagogic discourse of school mathematics
    (1999) Press, Karen; Davis, Zain
    The research focus of this dissertation is the manner in which textual strategy present in a school mathematics textbook contribute to the production of the pedagogic discourse of school mathematics. The dissertation undertakes an analysis of a chapter of a Std 5 mathematics textbook, and seeks through this analysis to demonstrate two things: firstly, the contribution of textual strategies specific to the textbook genre to the production of school mathematics discursive practices; and secondly, that the semiotic tools selected for the analysis can be applied productively to the analysis of school textbooks. The analysis is situated within the framework of Bernstein's theory of pedagogic discourse. School mathematics is seen as such a pedagogic discourse, and the hypothesis is made that school mathematics textbooks instantiate this discourse in particular ways that are determined, at least in part, by their formal and structural features. The semiotic theories of Eco, Luke and Hodge and Kress are recruited to provide elements of a language of description for the school mathematics textbook. In particular, the analysis examines how a chapter of the textbook constructs its own model reader and model author, how it produces literacy practices and narratives that contribute to the construction of school mathematics· as a discursive practice, how it defines the rules for reading its messages and how these rules are in tum susceptible to modification by logonomic systems present in contexts where the textbook may be used. The analysis demonstrates that formal and structural features of the textbook contribute significantly to the production of subject positions for the learner of school mathematics, and thus to the production of the discursive practice of school mathematics. The dissertation concludes that further research into the use of textbooks in empirical settings is necessary to test the reliability and validity of the semiotic tools used, but argues that within the limitations of the present research framework, these tools have shown their productivity as elements of a language of description for school textbooks.
  • Thumbnail Image
    Item
    Open Access
    Understanding University of Technology foundation students' perspectives on their learning in mathematics, with a focus on group work
    (2007) Armien, Mogamat Noor; Le Roux, Kate; Breen, Chris
    This study investigates students' perceptions of their learning experiences at the Cape Peninsula University of Technology (CPUT) as well as their perceptions of their previous high school learning experiences. Eight first time entering Black township-schooled foundation Civil Engineering students were interviewed. The students indicated that they had difficulties with the medium of instruction, English. It also appears that certain teaching and learning practices at school do not prepare students for study at a tertiary institution. Social factors, such as transport and residence issues, were also named as issues influencing students' learning. An important focus of the study was on students' perceptions of group work, since the study took place during a period in which a group work intervention was conducted in the class from which the eight participants were selected. Seven of the eight participating students in the study made use of some form of group work at high school. The students had a positive disposition towards group work at school and towards the group work intervention programme at CPUT. They also had particular views of what group work is. The study also claims that students benefited from group work and that group work had a positive effect on students' performances in Mathematics. This study advocates for and contributes to a theoretical perspective on student communities, an aspect of the community perspective (Allie et al., 2007) on student learning. Group work as a form of participation that was investigated in this study was beneficial in student learning. Thus the theoretical perspective for the study, student communities, is appropriate. The study makes a contribution to the existing theoretical perspective in that it provides some insight into the school communities from which students entering higher education come; it suggests what classroom communities at tertiary level might look like; and it argues for the importance of the development of student communities outside the classroom.