The Pragmatics of Mathematics Education: Vagueness in Mathematical Discourse

The Pragmatics of Mathematics Education: Vagueness in Mathematical Discourse

The Pragmatics of Mathematics Education: Vagueness in Mathematical Discourse

The Pragmatics of Mathematics Education: Vagueness in Mathematical Discourse

Synopsis

In The Pragmatics of Mathematics Education, Tim Rowland examines students in the process of making and coming-to-know mathematics, focusing on the gap between conjecture and belief, between assertion and conviction. The unexpected finding is that vague language plays an essential role in the communication of students propositions and attitudes.

Drawing on a large, original corpus of mathematical conversations with students whose ages range from 5 to 25, the book includes reports of four empirical studies, each of which highlights how students and teachers deploy vague language in various mathematical contexts. The book offers:

-- Introduction to pragmatics and pragmatic tools

-- Understanding of vague language and what speakers achieve by using it

-- Awareness of the prevalence and function of vague language in the classroom

-- Wide-ranging psychological and philosophical discussion of induction and generalisation

-- Major reference on generic examples as a mode of proof

Excerpt

Mathematics education is established world-wide as a major area of study, with numerous dedicated journals and conferences serving ever-growing national and international communities of scholars. As it develops, research in mathematics education is becoming more theoretically orientated, with firmer foundations. Although originally rooted in mathematics and psychology, vigorous new perspectives are pervading it from disciplines and fields as diverse as philosophy, logic, sociology, anthropology, history, women's studies, cognitive science, linguistics, semiotics, hermeneutics, post-structuralism and post-modernism. These new research perspectives are providing fresh lenses through which teachers and researchers can view the theory and practice of mathematics teaching and learning.

The series Studies in Mathematics Education aims to encourage the development and dissemination of theoretical perspectives in mathematics education as well as their critical scrutiny. It is a series of research contributions to the field based on disciplined perspectives that link theory with practice. This series is founded on the philosophy that theory is the practitioner's most powerful tool in understanding and changing practice. Whether the practice concerns the teaching and learning of mathematics, teacher education, or educational research, the series offers new perspectives to help clarify issues, pose and solve problems and stimulate debate. It aims to have a major impact on the development of mathematics education as a field of study in the third millennium.

One of the major areas of growth in mathematics education research concerns the interactions between language, linguistics and mathematics. Although it has long been recognized that symbols and symbolization, and hence language, play a uniquely privileged role in mathematics and its learning and teaching, the systematic application of linguistics and discourse theory to the field has been slow to develop. I have speculated that this may be due to two factors. First of all, the dominance of mathematics education by traditional 'in the head' psychological theories has meant that mathematical talk and writing have been backgrounded while mathematical thought and cognitions have dominated the field. Secondly, thinking about mathematics has until recently been dominated by absolutist epistemologies which suggest that the role of language in mathematics is merely to describe the superhuman realm of mathematical reality. Thus the correct use of language in mathematics is often taken to be determined by immutable canons of logic. One outcome of this has been, as Tim Rowland says, neglect of the study of pragmatics and spoken mathematical discourse, because of its essential imprecision.

However, current developments have brought some of these assumptions into question. The scientific research paradigm, usually accompanied by absolutist

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