The Faculty Notebook, December 2003

The Faculty Notebook is published periodically by the Office of the Provost at Gettysburg College to bring to the attention of the campus community accomplishments and activities of academic interest. Faculty are encouraged to submit materials for consideration for publication to the Associate Provost for Faculty Development. Copies of this publication are available at the Office of the Provost

The dialectical tier of mathematical proof

Ralph Johnson argues that mathematical proofs lack a dialectical tier, and thereby do not qualify as arguments. This paper argues that, despite this disavowal, Johnson\u27s account provides a compel-ling model of mathematical proof. The illative core of mathematical arguments is held to strict standards of rigour. However, compliance with these standards is itself a matter of argument, and susceptible to chal-lenge. Hence much actual mathematical practice takes place in the dialectical tier

Introduction: From Practice to Results in Mathematics and Logic

1 Mathematical practice: a short overview This volume is a collection of essays that discuss the relationships between the practices deployed by logicians and mathematicians, either as individuals or as members of research communities, and the results from their research. We are interested in exploring the concept of 'practices' in the formal sciences. Though common in the history, philosophy and sociology of science, this concept has surprisingly thus far been little reflected upon in logic ..

Putting socio-cultural theories to work in supporting mathematics teachers' professional development

We discuss the contributions of socio-cultural theories to research and design of interventions directed at the professional development of mathematics teachers. We explain how these theories have been put to work in the field. We also bring to attention specific issues arising in the field for which development and adaptation of socio-cultural theory might be a useful resource

Book Review: Reckonings: Numerals, Cognition, and History by Stephen Chrisomalis

This review of Reckonings shares our thoughts on the diverse insights presented by Stephen Chrisomalis’s version of the history of numerical notation. Chrisomalis suggests that members of distinct cultural groups write numbers as an active choice in accordance with their own sociocultural contexts, which reflect the influences of historical, cognitive, social, economic, political, environmental, and cultural factors. This book integrates comparative, cognitive, and evolutionary understandings on numerical cognition with historical and linguistic evidence on the use and transformation of numeral systems through the historical advancement of numeracy. Chrisomalis offers an interesting historical perspective on numbers that builds upon three main themes: numerals, cognition, and history. Reckonings can inspire us to view the concept and constructs of numeracy through a historical and sociocultural lens