Cyril Julie

Mathematical Modelling of Social Issues in School Mathematics in South Africa

Learners’ and teachers’ engagement with the mathematical modelling of social issues is the focus of this chapter. It is contended that the mathematical modelling behaviour of both learners and teachers is dominated by mathematical modelling as a vehicle for “entry into mathematics”. This, it is suggested mitigates against the development of a “mathematical temper”. It is recommended that more emphasis be placed on mathematical modelling “as content” which would open windows of opportunity to deal with social issues in school mathematics.

Some Regional Developments in Access and Implementation of Digital Technologies and ICT

Access to and implementation of digital technologies for mathematics teaching and learning across and within countries and regions display similarities and differences. This chapter is derived from regional presentations made at the ICMI Study 17 Conference held in Vietnam in December 2006. The descriptions of the situations in four countries (Russia, Hong Kong, Vietnam, South Africa) and one region (Latin-America) give a sense of the similarities against the general background of a global goal for schooling in the twenty-first century. The complex issue of universal access to digital technologies for meaningful mathematics learning, it is suggested, requires concerted efforts to address a host of mitigating factors.

Learners' Context Preferences and Mathematical Literacy

Abstract Mathematical Literacy deals primarily with the insertion of a mathematical gaze on extra-mathematical issues and situations. These issues and situations are to a large extent determined by curriculum, learning resource and test designers. The issues and contexts learners prefer for mathematical investigation is a largely under-researched area. In order to ascertain contexts that learners would find interesting to deal with in Mathematical Literacy a study, the Relevance Of School Mathematics Education (ROSME), was embarked upon. Some of the findings of this study and how they relate to current issues in South Africa are presented in this paper. It is concluded that within their Mathematics Literacy experiences learners should also be confronted with issues and situations to which they accord priority. However, this should be done with circumspection given that schools are also places where interests are to be developed. This, in turn, calls for a curriculum where the interests of learners and those fixed by curriculum, learning resource and test designers are balanced.

The stability of learners’ choices for real-life situations to be used in mathematics

One of the efforts to improve and enhance the performance and achievement in mathematics of learners is the incorporation of life-related contexts in mathematics teaching and assessments. These contexts are normally, with good reasons, decided upon by curriculum makers, textbook authors, teachers and constructors of examinations and tests. However, little or no consideration is given to whether students prefer and find these real-life situations interesting. There is also a dearth of studies dealing explicitly with the real-life situations learners prefer to deal with in mathematics. This issue was investigated and data on students’ choices for contextual issues to be used in mathematics were collected at two time periods. The results indicate that learners’ preferences for contextual situations to be used in mathematics remained fairly stable. It is concluded that real-life issues that learners highly prefer are not normally included in the school mathematics curriculum and that there is a need for a multidisciplinary approach to develop mathematical activities which take into account the expressed preferences of learners.

Computers in education in South Africa: the state of the art

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Learners’ Dealing with a Financial Applications-Like Problem in a High-Stakes School-Leaving Mathematics Examination

Research of students’ ways of working with modelling and applications-like problems in time-restricted examinations is rare. Using ideas and notions from ethnomethodology and the sociological study of work in science, the actual scripts of examinees were analysed to tease out the examinees’ ways of working with a modelling and applications-like problem in a high-stakes school-leaving examination. The analysis was anchored around the various agencies exerted by elements present in the context of high-stakes school-leaving examinations. Three ways of working which characterised the candidates’ ways of working are focused on. It is demonstrated how the prevailing contexts of writing high-stakes examinations exercised agency for these ways of working. The pragmatic value of analysis of this nature is recommended.

Emergences and affordances as opportunities to develop teachers’ mathematical content knowledge

Teachers’ mathematical content knowledge has been under scrutiny for some time. This development is in the wake of learners’ unsatisfactory performance in national examinations and international achievement tests. A widely held belief is that one, if not the most important, of the efforts to improve and enhance the performance and achievement in mathematics of learners is addressing teachers’ mathematical content and pedagogical content knowledge through continuous professional development initiatives. The focus of this article is on the former. It describes how emergent and affording opportunities are brought to the fore from classroom observations and interactions in workshops and institutes with practising teachers. It concludes that this in situ dealing with mathematical content knowledge holds much promise for buy-in by teachers because it addresses an immediate need related to their practice.

Introduction to Section 4

The nature and extent of the implementation of digital technology in mathematics curricula along with issues of access and equity were the issues considered by one working group of this ICMI study. A summary of the discussion conducted by the working group and the findings reported in the following chapters on this theme are presented. It is clear that widespread and sustained use of digital technology is not common and that where digital technology is used there are complex and confounding equity issues.

WGA 12: The Social and Political Dimensions of Mathematics Education

Prior to the congress, the COs and AOs of WGA 12 prepared a discussion paper with possible question to be dealt with in presentations and discussions, and a proposal for the structure and format of WGA 12. Since early in the preparation of the sessions, it was possible to keep contact with presenters and registered participants via email and to distribute abstracts of presentations and the time schedule of the programme. 20 papers from 14 different countries have been accepted for presentation at WGA12, but many more had been submitted by colleagues who could not afford to attend ICME 9. During the congress WGA 12 had 45 permanent participants. The presentations and the group of participants have been divided into two subgroups: Subgroup 1” “Social and political views about mathematics and mathematics education and Mathematics for All”, and Subgroup 2: “Mathematics education in the global village and polities for social justice and equity”

Mathematical Artifact Production: Broadening the View of “Doing Mathematics”

In this paper we briefly consider the notion of doing mathematics. Based on some shortcomings of this movement, it is proposed that doing mathematics should be broadened to mathematical artifact production. This idea is explained and some insights are presented of the discoordinations South African teachers encounter when they engage in mathematics modeling as an exemplar of mathematical artifact production.