12 - Students' Beliefs About the Evolution and Development of Mathematics

Summary

Introduction

Beliefs about the history of mathematics is a topic which is touched upon from time to time in the literature on history in mathematics education, e.g., in Furinghetti [8] and Philippou and Christou [23]. However, when scanning these samples, one soon finds that these concern the beliefs of in-service or pre-service teachers. Studies on students' beliefs about the history of mathematics seem to be rather poorly represented in the literature, if not altogether absent. One reason for this that I can think of is that, in general, studies of beliefs in mathematics education are conducted with the purpose of improving mathematical thinking, learning, and instruction. Beliefs, both cognitive and affective ones, are investigated in order to identify the ‘ingredients’ which do or do not make students capable of solving mathematical tasks or teachers capable of teaching differently and/or more effectively. Certain beliefs are identified as advantageous in the learning of certain mathematical contents, the solving of related tasks, etc., and educational studies are then conducted on how to change already existing beliefs into these more favorable ones. In this sense beliefs are regarded as means—or tools—to achieve understanding in the individuals' constructive learning process. Only rarely is providing students or teachers with certain beliefs, e.g., by changing existing ones, about mathematics or mathematics as a discipline considered as a goal in itself. And when this is done, the term ‘beliefs’ is usually not used. Instead mathematical appreciation, mathematical awareness, or providing students with a more profound image of what mathematics is, are the words or phrases more commonly used (e.g., [7, 20, 5]).