Inclining to explore mathematically and pedagogically: students and teachers possessing the same characteristics

My research shows that students of mathematics who are inclined to undertake mathematical problem solving activity, and teachers who are inclined to experiment on- the-run share common personal characteristics. These characteristics are associated with what they do when something does not work. I have shown that such characteristic can be built in students as they undertake mathematical problem solving through my Engaged to Learn Approach. The focus of this paper is on recognizing, and building the characteristics that incline students to explore mathematically, and teachers to explore ‘pedagogically’. These are the characteristics of optimistic/resilient people as defined by Seligman (1995). If (as my research suggests) these characteristics are a necessary part of exploring new ideas then we need to pay as much attention to building them as we have to increasing the mathematical knowledge of teachers, and increasing their knowledge about teaching approaches that build deep understandings.