Fostering mathematical reflective abilities through high school teaching activities

Abstract

The reflective ability in mathematics is a highly individual mental process, which is engaged in the course of certain types of mathematics activity. This article describes the basic meaning, characteristics, and developmental features of reflectivity in mathematics. It is suggested that reflective ability in mathematics and its relations with other mathematical abilities helps improve students' long term mathematical and creative capacities. The authors develop a trial reflective component to high school mathematics education in order to determine the degree of short-term mathematics improvement measured by examination success, as well as long-term benefits to the student, thus promoting mathematics curriculum reform.