The Role of Mathematical Definitions in Mathematics

Abstract

The central focus of teaching mathematics is solving problems via definitions and concern results. Problem solving is not a distinct topic, but a process that should be a focus for learning Mathematical definitions and hence in proof of results. Definitions play a key role in mathematics, but their creation and use differs from those of "everyday language" definitions. Mathematical definitions are of fundamental importance in the axiomatic formation that characterizes mathematics. Mathematics students into the field of mathematics includes their getting and of the role of mathematical definitions. Mathematical definitions have many features, some critical to their nature and others, while not necessary to the categorization of mathematical definitions, preferred by the mathematics community. Undergraduate mathematics students’ have difficulties in writing formal mathematical proofs, weak understanding of logic and/or mathematical concepts due to Mathematical definitions. In this study we first discuss a structure for thinking about mathematical definitions derived from literature in the fields of mathematics. Next, we discuss research on student understanding and use of definition and on the role of definitions in the teaching of mathematics. Finally, we discuss the implications of this research and important educational decisions that should rule the use of mathematical in the teaching of mathematics.