From Searle’s Chinese room to the mathematics classroom: technical and cognitive mathematics
Employing Searle’s views, I begin by arguing that students of Mathematics behave similarly to machines that manage symbols using a set of rules. I then consider two types of Mathematics, which I call Cognitive Mathematics and Technical Mathematics respectively. The former type relates to concepts and meanings, logic and sense, whilst the latter relates to algorithms, heuristics, rules and application of various techniques. I claim that an upgrade in the school teaching of Cognitive Mathematics is necessary. The aim is to change the current mentality of the stakeholders so as to compensate for the undue value presently attached to Technical Mathematics, due to advances in technology and its applications, and thus render the two sides of Mathematics equal. Furthermore, I suggest a reorganization/systematization of School Mathematics into a cognitive network to facilitate students’ understanding of the subject. The final goal is the transition from mechanical execution of rules to better understanding and in-depth knowledge of Mathematics.