Perceptivist mathematics education

The aim of this paper is to outline and apply a perceptivist philosophy of education and a constructivitist theory of knowledge acquisition to a problem in secondary mathematics education. A working summary of perceptivism and constructivism is provided and a program and lesson materials are discussed within the context of perceptivist-constructivist ideas. The main thesis of this paper is that the way to translate perceptivist-constructivist ideas into practice in mathematics is to emphasize activities that lead to actual perceptions. The traditional problem with this is that often the computational abilities needed to deal with reality are too much for most students to deal with. The information age innovation that makes a utilitarian mathematics education more possible now, where it was not possible previously, is the development of the personal computer. The computer can act as an information processing "step up transformer" to boost students past computation to real, perceptual mathematics. The practical part of the paper consists of lessons aimed at a partial realization of perceptivism-constructivism in the classroom. The lessons concern concepts and skills from the traditional secondary mathematics curriculum areas; arithmetic, algebra, elementary function theory and calculus. The paper concludes with a report on field tests of the materials in the secondary classrooms of the author.Education, Faculty ofGraduat