Browsing by Author "Davis, Zain"

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    A study of the computations done by grade 9 learners in a Western Cape high school when simplifying algebraic expressions involving the negative symbol
    (2025) Brink, Hestia; Jaffer, Shaheeda; Davis, Zain
    The computations that learners do when simplifying algebraic expressions are multiple and diverse, with some determined by reasoning aligned with mathematics whilst others rely on idiosyncratic constructs like mnemonics or solution templates. Research in mathematics education highlights symbol sense and negative number concepts as persistent difficulties in learning algebra and categorises learners' errors, but it is wanting in explanations of learners' computations and how they might relate to the way learners think. This study identifies, describes and offers possible explanations for some of the computations that learners did when attempting to simplify algebraic expressions involving the negative symbol. Grade 9 learners from one class in a Western Cape high school were given a set of algebraic expressions to simplify after which interviews were conducted with some learners to discuss their solutions. In the computational analysis of the data, cognitive science and universal algebra were used as lenses for a deeper understanding of learners' mathematical (and non-mathematical) thinking. The data indicates learners' tendency to read algebraic expressions as strings of characters constituting different types of objects, classified in this study as operators, signs, numerals, letters, and superscripts. As suggested by the literature, the negative symbol presented learners with additional challenges, given its polysemic nature in mathematics. Many learners resorted to replacing standard mathematical operations with various operation-like manipulations taking different types of objects as arguments. Plausible reasons for learners' type-sensitivity and idiosyncratic computations offered by this study include: humans' innate capacity for recognising and categorising different objects and symbols; the biases produced from language; and the reliance on existing mental structures for the assimilation of new knowledge. In considering learners' computations at a fundamental level, this study contributes to a more complete view of what learners do computationally and, importantly, why.
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    A study of the phenomena of conjoining terms and related aberrant transformations in the simplification of algebraic expressions by Grade 8 learners of two secondary schools in the Western Cape
    (2025) Adonis-Maarman, Bronwyn; Davis, Zain
    Mathematics education research on conjoining has been inconsistent with regard to the study of the phenomenon and the use of the term conjoining. This study aimed to identify justifications for the procedures implicated in producing instances of what we refer to as aberrant conjoining in early school algebra. The study took a rationalist view of knowledge acquisition and used a computational approach to analyse data obtained through a written test and semi-structured interviews with a selection of research subjects. The rationalist research orientation used rests on the proposition that humans possess biologically endowed, core domain knowledge of number, as is evident in the results of experiments carried out on human infants as well as other animals. Seventy-six Grade 8 students at two secondary schools in the Western Cape were given a test in which they were required to simplify ten algebraic expressions, all of which were sums. Eight students were selected for interviews on the basis that they had either displayed aberrant conjoining in their responses or that they had answered most items correctly. The computational analysis identified four computational principles employed in instances of aberrant conjoining: the use of type-specific computations, the treatment of constituents of terms as sets, the implicit use of string operations, and the use of addition-like monoids. Furthermore, the biologically endowed cognitive operation, merge, is implicated as generative of the concatenation of the results of type-specific computations central to aberrant conjoining, and as the ground for the system of addition-like monoids used by students. The analysis also found the use of a pedagogically exploited structure-preserving mapping between distributivity and indirect distributivity that enables students to simplify algebraic expressions, but which inadvertently contributes to the production of aberrant conjoining in its reliance on the typographically legitimate conjoining of symbols to form written algebraic expressions. Finally, the description and analysis of aberrant conjoining in the literature is interrogated, and a more robust explication of the phenomenon is offered.
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    A study of the representational use of aggregates in the pedagogic elaboration of addition and subtraction in the Department of Basic Education Grades 1 to 3 Numeracy workbooks, prescribed for use in state funded South African schools
    (2023) Wust, Heidi; Davis, Zain
    Cognitive science demonstrates that a sensitivity to aggregates (groups, collections, classes, categories) forms part of the biologically endowed human (core domain) capacity for dealing with quantity, along with an ability to compute using aggregates, both approximately and exactly. Core domain computations using aggregates serve as a basis for the growth of noncore mathematical computations and principles, following exposure to number enculturation and the counting algorithm, both of which are enhanced by the growth of linguistic competence. The study focuses on the pedagogic use of the class of small, discrete aggregates in the teaching and learning of natural number addition and subtraction across the Foundation Phase of schooling. The central concern is the computational processes that use discrete aggregates, and operations over such aggregates. The six 2021 Department of Basic Education numeracy workbooks (Mathematics in English) for Grades One to Three, prescribed for use in state-funded SA schools, constitute the archive of information from which the data is produced for the study. The study adopts a computational analytic approach conditioned by the proposition that all thought is computational, entailing the use of operations over domains of objects that serve as arguments (inputs) and values (outputs). A mathematised notion of representation—as a structure-preserving mapping—comprised the chief analytical resource for describing computations related across representing and represented computational structures. The analysis, firstly, proceeds descriptively. The unit of analysis is a Task, made up of Subtasks containing Exercises, so that the analysis of a Task proceeds by way of an analysis of its Exercises. Only Tasks employing discrete aggregates for the purposes of teaching addition and subtraction are analysed to reveal the representations used by identifying the computational structures and the relations between such structures. Typically, the representations used in Tasks entail mappings from operations over discrete aggregates to operations over the natural numbers. As a further means of gauging the extent of the range of mappings/operations and structures identified across the workbooks, the descriptive data is extended by the use of quantitative databases, summarising and totalling all identified mappings/operations and structures. The study found that: (1) operations over discrete aggregates are used extensively as a ground for addition, subtraction, natural number order relations, and number partitions, including the use of iii partitions for teaching place value in the base-ten natural number system; (2) counting is the primary computational resource for relating operations over discrete aggregates to operations over the natural numbers; (3) addition and subtraction are often derived from operations over discrete aggregates in a manner that privileges a unary rather than binary form; (4) the treatment of discrete aggregates, together with the use of partitioning, suggests that aggregates are conceived of in a manner that has more affinity with fusions than with sets; (5) the general semantic basis for addition, subtraction and partitioning appears to be the universal cognitive operation referred to as merge (and its derivatives, unmerge and purge) as used by the human conceptual-intentional system.
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    A synthesis of cognitive science research on the mental number line, and its relation to the pedagogical use of number lines in the teaching of elementary arithmetic in the Foundation Phase of schooling
    (2022) McNamara, Ellen; Davis, Zain
    In this paper, I examine how biologically endowed computational systems help to frame our experiences as it relates to using the number line in school mathematics. This study is a synthesis of the research findings in cognitive science and mathematics education to elucidate the mechanisms that underpin the connection between the mental number line in humans and its relation to the growth of mathematical knowledge in young children. This reported research drawn together here shows how we draw on core domain knowledge (the object tracking system (OTS), the approximate number line (ANS) and the mental number line (MNL) to construct mathematical ideas. The OTS allows us to track individual items, which provides us with the notion of exact number and the ANS creates an intuitive number sense from which we intuit that a collection can be assigned a cardinal value. Language mediates the integration of knowledge of the ANS and OTS to overcome the limits of the core systems and build the exact number system. I review the literature to investigate spatial numerical associations and the properties of the internal number line and to clarify the relationship between cognitive development, cultural factors and education. The synthesis concludes by using the ideas of representations and structure preservation to examine how closely the number line aligns with our natural intuitions about magnitude and number and the implications this has on education. I argue that educators need to understand how biologically innate conceptions of number guide subsequent learning and provides us with a foundation for domains such as mathematics. This insight will enable educators to select teaching models that build on from our intuitive notions of number and understand why certain concepts are difficult for children to understand.
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    The admission process : how portfolio assessment establishes the pedagogic subject of fashion design
    (2007) Dahl, Avryl; Davis, Zain
    This research draws on the work of Basil Bernstein as a theoretical structure with which to investigate the entry selection process that assesses prospective fashion design students' portfolios. It will be revealed how the three interrelated rules of the pedagogic device, namely distributive, recontextualising and evaluative rules regulate pedagogic communication and how their selective transmission and acquisition determine the pedagogic subject of fashion design. Recognition and realisation rules then orientate the panel and the prospective student to what is expected and what is legitimate within that context, and this is made explicit in various forms. During this process the selection panel manifests their expertise which acts as an indicator of what knowledge and skills are considered necessary for the discourse, which in turn determines what is applicable and who is eligible for the course. Because admission standards playa crucial role in establishing the quality of the learning program the evaluation process should be effective at predicting student potential and should be based on a set of reliable and valid criteria. My aim was to unpack a tacit practice which does not refer to explicit criteria or guideline procedures, yet defines and establishes authority and power relations as well as expertise, which serve to legitimate the discourse. This investigation is an attempt to generate academic enquiry into the field of fashion design, and attempts to demonstrate how the pedagogic subject of fashion design, produced during the selection process, defines how fashion design functions as a form of knowledge and a form of being that either summarily accepts or rejects students into the discourse. This establishes the profile of the ideal student and determines what forms of knowledge are privileged by the criteria for assessing portfolios. My aim is to identify what the criteria are for assessing portfolios; how consensus is established; how the process acts as a process of induction; and what ideological messages are contained and whose interests are served. This research has been interpreted on two levels: first, on a literal level and second, on a symbolic level to gain insight into what ideological messages are contained, which provides signification and reflect how tacit knowledge functions as an ideology or a veil of power. This supports Basil Bernstein's concept of the pedagogic device, which relays what counts as valid knowledge and serves as a symbolic ruler of consciousness, and provides the intrinsic grammar of the discourse.
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    Encountering the void: an attempted description of the dynamics of pedagogic communication in terms of the pedagogic relation between the teacher, the student and knowledge
    (2012) Canterbury, Jerome André; Davis, Zain
    This essay is a wholly theoretical engagement with the pedagogic relation. It attempts to take a small step in the direction of theorising the very complex phenomenon of the pedagogic relation. The relation is non-trivial as it is imbued with all the complications of social relations, plus the added complexity of the relation of knowledge in the social/libidinal economy of the classroom.
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    How and what are children learning in primary school science?: a study with special reference to three primary science classes
    (2004) Thomas, Rosemary; Davis, Zain
    [page 59, 60 missing] This research project arose out of my concern that primary school learners do not score well on standardised science tests even when they are taught in apparently functional, primary science classrooms. This led me to wonder whether they are learning any generalisable science concepts that they can apply in standardised tests. I decided to investigate how science is taught and what science knowledge is developed in three primary science classrooms in different areas of the Cape Flats. As a broad framework, I used the social theory of Basil Bernstein and his concepts of classification- and framing to explicate the how and the what of science teaching and learning. I observed the classroom activity of teachers and learners. Classroom activity can be viewed as how things are done as well as what is privileged and what is allowed to go on in classrooms. Classroom activity gives rise to inscriptions. In this study inscriptions were taken to mean the observable writings actions and sayings that materialise during or as a result of classroom discourse. I used these verbal, actional and written inscriptions as evidence of teaching and learning. I developed an external language of description as a tool to analyse the empirical evidence in terms of Bernstein's theory. This external language of description was realised as a set of indicators relating to a four-point scale indicating the strength of classification and framing. The resultant analysis provided a description of the practice that included a measure of the strength of the how and the what. The findings show, in terms of the how, that these classrooms are well organised and that much of the activity in the classroom makes use of and develops the process skills of science. However, in terms of the what, the findings also show that these classrooms are not strong on developing understanding of generalisable science concepts.
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    An investigation of the co-constitution of mathematics and learner identification in the pedagogic situations of schooling, with special reference to the teaching and learning of mathematics in a selection of grade 10 mathematics lessons at five scho
    (2011) Chitsike, Megan Jane; Davis, Zain
    The study is located within the broad framework of the sociology of education, specifically drawing on Bernstein's sociological theory of education and its application in the investigation of the relations between pedagogy and social justice. The specific problematic within which my study is located is the constitution of school mathematics in the pedagogic situations of schooling.
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    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.
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    Pedagogic evaluation, computational performance and orientations to mathematics: a study of the constitution of Grade 10 mathematics in two secondary schools
    (2018) Jaffer, Shaheeda; Davis, Zain; Ensor, Paula
    This study takes as its starting point Bernstein’s proposition that evaluation is central to pedagogy. Specifically, along with many researchers who draw on his work, Bernstein claims that explicit evaluative criteria are critical to the academic success of learners from working-class families and low economic status communities. The research problem stems from a hypothesis, derived from the literature, that social class differences in learner performances in school mathematics suggest differences in the functioning of pedagogic evaluation, and therefore differences in what is constituted as mathematics, and how, in pedagogic situations differentiated by social class (e.g. Dowling). The contention of this study is that insufficient finegrained analyses have been undertaken to surface the computational specificity of what it is that constitutes evaluative criteria in mathematics education studies of pedagogy. The study examines the functioning of pedagogic evaluation in what comes to be constituted as mathematics by teachers and their learners, and in the specialisations of mathematical thought in pedagogic situations. The study set out to investigate the functioning of pedagogic evaluation in two schools differentiated with respect to the social class membership of learners. Two Grade 10 teachers and their learners in each school served as research participants. Methodological resources for describing the functioning of pedagogic evaluation in terms of the computational activity of teachers and learners derive from the work of Davis, which draws on a computational theory of mind (e.g., Chomsky; Gallistel & King; Spelke). Bernstein’s theory of the pedagogic device, with its focus on who gets what knowledge and how, serves as a general descriptive frame structuring the study. The analysis reveals the following: (1) the commonly used descriptions of evaluative criteria as explicit/implicit are analytically blunt and consequently mask the complexity of criteria operative in pedagogic contexts; (2) differences as well as strong similarities in the functioning of evaluation and, therefore, differences and similarities in what is constituted as mathematics are evident in pedagogic situations differentiated with respect to social class; (3) an orientation to mathematics that constitutes mathematics as computations on the typographical elements of mathematical expressions is common to pedagogic situations involving learners from both upper-middle-class/elite families and working-class families; and (4) greater variation and inter-connectedness in computational resources is realised in pedagogic situations involving learners from upper-middle-class/elite families than in those involving learners from working-class families, where computational resources are relatively restricted and weakly connected. The differences between the two types of situations appear to be enabling of greater flexibility in mathematical thought and action for upper-middle-class/elite learners, on the one hand, and restricting for working-class learners, on the other. The contribution of the thesis is four-fold. The study: (1) provides a methodology for exploring the complexity of pedagogic evaluation by describing the computations performed by learners and teachers in mathematical terms, thus contributing to Bernstein’s account of pedagogic discourse as it applies to the teaching and learning of mathematics; (2) contributes to our understanding of the structuring effect of evaluation on learners’ mathematical thought; (3) contributes to the methodological resources developed by Davis for describing the constitution of mathematics in pedagogic situations; and (4) extends analyses of the constitution of mathematics in pedagogic situations to those populated by learners from upper middleclass/elite families in the South African context, albeit in a limited way.
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    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.
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    Pleasure and pedagogic discourse in school mathematics: a case study of a problem-centred pedagogic modality
    (2005) Davis, Zain; Muller, Johan
    [pages missing: 245 - 304] This 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.
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    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.
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    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.
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    A study of social solidarity and the constitution of school mathematics in five working class schools in the Western Cape Province of South Africa
    (2013) Matobako, Setseetso; Davis, Zain
    This study investigates how forms of social solidarity influence pedagogic practice and the manner in which they are implicated in providing information to the teacher about what it is that students have constituted as criteria for the production of legitimate text at five working-class schools in Greater Cape Town. It explores the contextual features that co-occur with social interactions in each of the five schools. It shows how each of the identified features impacts interactions of the participants during pedagogic practice as well as their importance in shaping the pedagogic communication at the classroom level. It also investigates the ways in which teachers evaluate students’ acquisition of criteria for the reproduction of school mathematics during pedagogic exchanges. Descriptions of teaching are developed in terms of the types of questions that teachers ask their students. I employ Weber’s (1949) technique of constructing ideal types to categorise teacher questions in terms of their purposes in order to investigate how the questions that teachers ask are implicated in the structuring of pedagogic communication. I examine whether or not questions target individual students or the whole class. I also establish whether or not questions that teachers use are productive to ascertain the level of students’ acquisition of criteria by looking at the type of responses students produce. The study interrogates the validity of links drawn by Dowling & Brown (2009) between Durkheim’s notions of organic and mechanical solidarity and their notions of communalising and individualising pedagogies. The results of this study suggest that the questioning strategies are implicated in the form taken by social interactions of participants during pedagogic practice. The results reveal that communalising pedagogic strategy was the most prevalent across the schools. Consequently, teachers gathered rather meagre and unreliable data about their students’ acquisition of criteria for the reproduction of mathematics texts.
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    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.
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    A theoretical re-assessment of the use of the distinction between everyday and acadamic knowledges in Basil Bernstein's theory of educational transmissions
    (2012) Mwiinga, Donald Muunze; Davis, Zain
    This project assesses a popular position at present in the Bernsteinian subfield of the Sociology of Education, that Basil Bernstein’s main ideas are sufficiently represented by frameworks constructed around the distinction between everyday knowledge/thought and academic knowledge/thought. A survey of some contemporary literature within the Bernsteinian subfield was undertaken to generate a question for the project, i.e., whether it is indeed the case that the everyday/academic knowledges distinction is a productive condensation of the major ideas of Bernstein’s theory. A historical study of Bernstein’s papers from 1958 to 2000 is undertaken with the view of unearthing what it is that gives the theory its impetus over time.
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    What is constituted as mathematics when presented in contextually embedded forms? : a study based on two activities from the 2003 Grade 9 Common Task for Assessment for Mathematics
    (2011) Ebrahim, Rushdien; Davis, Zain
    This study focuses on what comes to be constituted as mathematics when is presented in contextually embedded forms, how students constitute mathematical meaning from such texts, and what is constituted as mathematics when this particular form of mathematics is pedagogised.