Mathematics textbooks in Berlin and Hong Kong: 'Implicitly platonic' verse 'Pragmatic'

Abstract

In this paper, we will investigate how the two different schools of thoughts, i.e. implicitly platonic and pragmatic, realize their ideals through the history of mathematics in the textbooks of Berlin and Hong Kong respectively. History of mathematics has assumed an ambiguous position in the presentation and teaching of mathematics. Most would agree that mathematical maturity and the ability to solve problems using mathematics, being the main goals of mathematics education, are very different from an acquaintance of the historical development of mathematics. And unlike many other subjects whose presentation often requires mentioning the historical development of the subject, mathematical concepts are self-contained that they can be presented on their own with great clarity. The pragmatics regard this as the essence of mathematical thinking; and that mathematics necessarily involves abstraction from the concrete, reasoning logically and faultlessly, with modeling and interpretations of results being only the applications of mathematics. The implicit platonics consider such an approach being both narrow in its view and ineffective pedagogically in its implication. Modeling and interpretations of results are considered to be important aspects of mathematical ability, and they together with the reasoning process should be presented with the history of mathematics in order to highlight the interactions of mathematical ideas and our life. The former school will be illustrated by the textbook in Berlin while the latter by Hong Kong.