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Service Mathematics in Irish Universities: Some Findings from a Recent Study

Olivia Gill

olivia.gill@ul.ie

John O’Donoghue

john.odonoghue@ul.ie

University of Limerick, Ireland

Abstract

In this paper the authors report on a qualitative investigation into service mathematics carried out in Irish universities against a backdrop of major concerns nationally and internationally embodied in the so-called “Mathematics problem”. The enquiry involved a close inspection of how service mathematics is perceived, planned, delivered, evaluated, assessed and experienced by both lecturers and students in selected service mathematics courses in all seven Irish universities. Murphy (2002) used Brousseau’s concept of didactical contract to uncover the implicit contract present in Irish second level classrooms. The authors emulated this work to discover the hidden learning contract in university service mathematics lectures in Ireland. Major outcomes of the study include insight into the nature of the didactical contract at work in the service mathematics courses surveyed, and the development of a preliminary characterisation of service mathematics in Irish universities. Service mathematics is also an issue for adult mathematics education and impacts on it.

Adult Mathematics Education and Commonsense

Noel Colleran

North Tipperary Vocational Education Committee, Templemore, Ireland.

Noel.Colleran@sheelan.ie

John O’Donoghue

University of Limerick, Limerick Ireland

Abstract

The relationship between quantitative problem solving and commonsense has provided the basis for an expanding exploration for Colleran and O’Donoghue. For example the authors (Colleran et al., 2002, 2001) discovered the pivotal role commonsense plays in adult quantitative problem solving and suggest commonsense is an important ‘resource’ in the adult problem-solving context. In more recent papers Adult Problem Solving and Commonsense:Adult Problem Solving and Commonsense: new insights (Colleran et al., 2003b) the authors explored the valued position given to ‘higher order’ thinking as distinct from the ‘other’, ‘lower’ form of thinking, sometimes described as commonsense thinking. They also looked at the manner in which commonsense is created from ‘natural learning’ in a range of different environments. In Colleran and O’Donoghue (in press) the authors broadened the investigation to include the views of a number of researchers in the field of commonsense who suggest that commonsense is a powerful intellectual resource and provides the bedrock on which mathematical understanding is built. The authors have come to the view that the creation and use of commonsense require intelligent, creative thinking and this ‘order’ of thinking takes place naturally in the commonsense environment. Further this intelligent thinking is supported by attitudinal as well as structural elements that facilitate the individual to engage new commonsense situations so that they become natural learning environments.

Images of Mathematics in Popular Culture / Adults’ Lives:a Study of Advertisements in the UK Press

Jeff Evans

Middlesex University, London, UK

J.Evans@mdx.ac.uk

Anna Tsatsaroni

University of the Peloponnese, Corinth, Greece

tsatsaro@uop.gr

Natalie Staub

Middlesex University, London, UK

N.Staub@mdx.ac.uk

Abstract

The success of policies to attract adults back to the learning of mathematics, at various levels, is often linked to questions of motivation. However, motivations depend on relevant beliefs, attitudes and emotions about mathematics - which themselves reflect, together with experiences with maths in school and in the home, wider cultural discourses on mathematics. The work presented here is part of a larger study examining the complex relations between popular cultural products such as advertisements and films, the way that knowledge is portrayed by them, and possible consequences for people’s affective responses. The initial phase of the project (Evans, 2003, 2004) analysed small ‘opportunistic’ samples of advertisements and films. The advertisements portrayed mathematics as generally negative, whereas the films were more ambivalent. In the next phase, we produced larger samples of both advertisements and films. In this paper, we report on our search through a systematic sample of issues of UK daily newspapers for ‘mathematical’ advertisements. A notable finding was the very small number of advertisements containing images of mathematics. Those few advertisements we found were most frequently for cars, or for services to businesses. Using a discourse theoretical perspective and a hybrid methodology, we categorise advertisements according to features such as their ‘appeal’ to potential consumers - and we also produce semiotic readings of a sub-sample of advertisements, as to their ‘message’, in particular their images of mathematics, and of people doing, using, or teaching mathematics. Here we find these images to be much more varied and subtle than in the initial phase. We end by discussing some of the consequences of our analysis for perceptions, teaching and use of mathematics in today’s market economy societies.

Brazilian peasant mathematics, school mathematics and adult education

Gelsa Knijnik

Universidade do Vale do Rio dos Sinos, Brazil

gelsak@unisinos.br

Abstract

The paper analyzes adult mathematics education from a cultural perspective. Specifically, its purpose is to broaden our comprehension about this field of knowledge using as a theoretical tool-box an Ethnomathematics perspective founded on post-modern thought, post-structuralism theorizations and Wittgenstein's work developed in his book Philosophical Investigations. This Ethnomathematics perspective allows us to study the Eurocentric discourses that constitute academic mathematics and school mathematics; to analyze the effects of truth produced by the discourses of academic mathematics and school mathematics; to discuss issues of difference in mathematics education, considering the centrality of culture and the power relations that institute it; and to problematize the dichotomy between ‘high’ culture and ‘low’ culture in mathematics education. Taking elements of the empirical data produced in many years of fieldwork with peasants of the Brazilian Landless Movement who participate in adult education courses as students or as teachers, the paper discusses some aspects of this social movement, especially the educational work they are developing; it outlines the theoretical background that supports the idea that there are different mathematics; it presents and analyzes some elements of the mathematics produced by the Landless peasant form of life, establishing relations with school mathematics, problematizing curricular issues of adult mathematics education.

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