21 A culture of proving in school mathematics? Celia Hoyles Institute of Education University of London United Kingdom Abstract It is commonplace in mathematics to present proving in a hierarchy of levels in which the empirical precedes the deductive. This paper questions the assumption that this is a matter of development of the latter from the former and presents an alternative sequence where the seeds of proving are sown in a computer-based construction process which requires an explicit description of relevant properties and relationships. Keywords Curriculum policies, geometry, tools, proof INTRODUCTION It is commonplace in mathematics to present proving in a hierarchy of levels in which the empirical precedes the deductive. Clearly students need to be able to distinguish empirical verification and pragmatic proof from deductive and conceptual proof (Balacheff, 1988) but the question remains as to how best might this be done. Is it a matter of development of the latter from the former or can links be forged between the two at every stage of schooling and throughout mathematical activity? Our rationale 1 is that we need to design new learning contexts which require the use of clearly formulated statements and definitions and agreed procedures of deduction but which also allow opportunities for their connection with empirical justification and the conviction this engenders. Previous work points to what might be the constituent components of such contexts: ease of transition between an enactive or visual form of proof and a sequence of deductions (Tall, 1995); Information and Communications Technologies in School Mathematics J.D. Tinsley & D.C. Johnson (Eds.) © 1998 IFIP. Published by Chapman & Hall