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.

From Publics to Practitioners: Invention Power and Open Technoscience

Abstract

In technoscientific conditions what counts as knowledge creation is not primarily the individual experimental achievement that gives coherence to scientific practice and separates science from its publics; rather, it is a form of dispersed experimentation in more than human worlds: distributed invention power. Distributed invention power is organised and regulated through the pervasive securitisation of technoscience: surveillance and control of technoscientific fields as well as financialisation of its activities and research outputs. The securitisation of science reorders the traditional split between the public sphere, the private sector and the commons. The folding of each one of these spheres into the other underlies a constant, often antagonistic, oscillation between big science and open science. What is constitutive of the diverse movements that sustain open technoscience is not that they challenge technoscience as such but that they experiment with technoscience to create alternative forms of life.