7. Intuition revived

In the preface to Mathematics as an Educational Task, Hans Freudenthal states that his educational interpretation of mathematics betrays the influence of L. E. J. Brouwer’s view on mathematics. In this chapter we explore the nature of this possible influence. According to Brouwer, intuition plays a crucial role in any form of mathematical construction, which he specifies in terms of mental acts. He finds that mathematics does not have any adequate articulation in language, and that mathematical formalisms are nothing but imprecise and mischievous depictions of genuine mathematical processes. Freudenthal characterises mathematics as a human activity, thereby subsuming the overall intuitionist outlook that Brouwer had condensed into the notion of mental activity. While Brouwer installed intuition in a central position in mathematics, Freudenthal created a vast space for intuition in all kinds of activities in mathematics education. In his writings, Freudenthal does not demonstrate any interest in socio-political issues related to mathematics. Structuralism and the Modern Mathematics Movement are manifestations of the dogma of neutrality, and so is Freudenthal’s formulation of mathematics as a human activity. However, although he does not repudiate a dogma of neutrality, he simultaneously provides ideas that help in formulating a critical mathematics education.