5. Creative mathematical thinking through levels of mathematical activity at engineering universites

Abstract

This essay aims to establishment that mathematical creativeness at engineering education is shown during the transition from the first to the second level of mathematical activity. It is possible thanks to the development of didactic strategies that overcome the instrumental character of the subject. This approach, supported on Changeux and Connes’ ideas, is believed to be more appropriate than Poincaré’s classical model of creative mathematical, which application presents serious difficulties related to time, space, and the uncontrollable and unforeseeable character of intermediate stages. It is concluded that to overcome the first level, didactic activities that go beyond the mere application of algorisms, and projects development are needed, as well as getting emotionally involved in the learning process.