The role of counter examples in developing a creative learning environment in engineering mathematics

This paper extends the authors' parallel study on using counter examples for enhancing students' conceptual understanding in undergraduate engineering. mathematics, which has been undertaken in their respective universities in Germany and New Zealand. The paper deals with a practical issue encountered by many lecturers teaching first-year university engineering mathematics. A large proportion of students seem to be able to find correct solutions to test and exam questions using familiar steps and procedures. Yet they lack deep conceptual understanding of the underlying theorems and sometimes have misconceptions. In order to reduce or eliminate misconceptions, and for deeper understanding of the concepts involved, students were given several incorrect mathematical statements and were asked to construct counter examples to prove that the statements were wrong. More than 600 students from several universities in different countries were questioned regarding their attitudes towards the method of using counter examples to eliminate misconceptions and deeper conceptual understanding. The vast majority of students reported that the method was very effective and made learning mathematics more challenging, interesting and creative.