META-EPISTEMOLOGICAL DEFINITION OF MATHEMATICS AND ITS IMPLICATION TO THE MATHEMATICS TEACHING METHODOLOGY

Mathematics philosophers do not have a consensus understanding about the definition of Mathematics. An attempt to define Mathematics began in the days of Aristotle who stated that, “Mathematics is the science of quantity”. Aristotle’s definition prevailed until the 18 th century when abstract topics in mathematics were discovered, the topics that had no direct relationship with quantities. In the 19 th century, philosophers began to propose new definitions which however philosophically differ in many ways. Since then up to date, the metaphysical and epistemological status is not well known, and hence the nature and scope of mathematics that could describe precisely mathematics is not known. Characterizing mathematics meta-epistemologically provides the philosophical foundation into which mathematics can be defined in a wide secure philosophical foundation and solve the everlasting problem in defining mathematics. It is realized that precise philosophical definitions describe metaphysical nature of a thing together with its epistemological scope. In this basis, it is realized that the proposed definitions of mathematics do not satisfy the basis of definitions neither completely satisfy philosophical basis of definitions Platonism's philosophy of mathematics and Aristotle’s assertion that epistemology is the study of things that exist and happen provide the meta-epistemological basis with which any academic discipline, including mathematics, can be defined in terms of its nature and scope as the meaning of the term definition requires to develop its philosophical truth. Platonism assertion that what exists lies beyond our experience, mathematical abstractions that reflect reality have themselves a reality and mathematics has its existence fundamentally describes the materialism, realism and idealistic nature of mathematics in the form of abstract materialistic-idealistic reality different to materialistic-idealistic reality nature of many disciplines. Platonism's philosophy of mathematics and Aristotle’s assertion that epistemology is the study of things that exist and happen provide the meta-epistemological basis with which any academic discipline, including mathematics, can be defined in terms of its nature and scope as the meaning of the term definition requires to develop its philosophical truth. On the right of the meta-epistemological basis, mathematics can be viewed as the study of shape, qualities, form, structure, properties and applicability of mathematical objects derived from the object of our experience, forming the mathematical reality. Mathematics teachers’ methodology of teaching mathematics should be based on studying the attributes of mathematical objects. And the choice of mathematics teaching methods should be guided by the methods that intend to develop the domains of learning on the six attributes of a mathematical object. Keywords: Definition of Mathematics, Platonism, Nature of Mathematics, Scope of Mathematics, Metaphysical Strands; Materialism, Realism and Idealism of Mathematics, Meta-Epistemological Definition. DOI: 10.7176/JPCR/58-01 Publication date: September 30 th 2024