Support to mathematically highly able students in Portugal

My name is Sérgio Carlos, I live and teach secondary school Mathematics in Aveiro, which is a city in the west cost of Portugal. Ever since I started my teaching career, about 27 years ago, I was intrigued and fascinated by some students that seem to have a particular ability to grasp mathematical ideas, while others in the same classroom struggle to simply know the procedures to tackle any given task. So, to better try to understand this phenomenon, I have engaged in a PhD, completed in 2016, which focused on Excellence and Creativity in University Mathematics. 

 At this point I’m asked to share with the readers a story about my involvement with creativity and giftedness in Mathematics. After some thought I decided to talk about my own route, both as a teacher and a researcher, into this captivating subject. 

My first work experience with a group of very high achievers in Mathematics, took place between 2009 and 2012, when the Mathematics Department of Aveiro’s University created a special program for students, not yet in the university, but that were showing great promise at middle and high school math. In this program, which I developed together with university professors, there were weekly sessions of math problem solving. The problems we proposed at these sessions were not of the same type of the problems those students faced in their regular Mathematics classes. They were “out of the box” problems for which there wasn’t any predetermined set of steps or algorithm to apply, and instead the students had to discover for themselves a way to solve each one. For me, it was a source of great satisfaction and of professional fulfilment to work with those students and see how they tackled the unexpected challenges put in front of them. These sessions have strengthened my fascination with high abilities students, and I was very disappointed when the university ended this program.

Maybe this initial experience, coupled with some occasional outlier student who excelled in my own regular classes from time to time, has helped fuel my interest in the topic of high achievement and creativity in Mathematics. So much so that I ended up deciding to engage in a PhD focusing on those same topics. I must admit that it was very hard to pursue my own PhD studies while I was still teaching fulltime. Looking back, I can only explain the needed endurance during that time, with the satisfaction of learning about something that had been intriguing me for so long, which can be put as a question: “besides the natural endowment that some people have the luck to be born with (this being a necessary condition but not a sufficient one), what other conditions (both personal and of the surrounding setting of the individual) must be present to allow, and foster, excellence and creativity in math?” 

In that process, I found that the main personal traits required in a high achiever in Mathematics are motivation, the willingness to engage in work consistent with deliberate practice, and self-regulation abilities. In turn, the data from the analysis of the creative performance of very high achivers in Mathematics denoted limited creativity, probably because in the school system the students aren’t frequently required to be creative in Mathematics.  

Following the PhD completion, I was teaching at a middle school, and the next opportunity to work with high potential math students came in a project developed by myself, in which very capable middle school pupils voluntarily participated. This two-year program worked fine, both with good adherence form students and visible improvement of their problem-solving skills, and, for me, with great personal satisfaction. 

But, in Portugal, some teachers, me included, must apply to a position every four years (as a result, a teacher can continue on the same school or be assigned to a different one), and, since I got a job at another school, that was the end of that project. When I got to the new school, I tried to motivate the school board to put in motion a similar project but, unfortunately, they were not supportive of the idea. Consequently, since then I did not have the chance to work with groups of high mathematical potential students. 

In Portugal, whilst the school system is always concerned to provide the struggling students with all the support available – and rightly so – the same level of attention is not dedicated to the one´s with high ability. This happens despite the schools having legal instruments that could be applied to help these students further advancement, but most times no action is taken. I am a believer that the educational system has the responsibility to provide every student with the conditions to fulfill their potential, be it low or high. But, unfortunately, sometimes we must deal with the prevailing erroneous idea “student x is already getting excellent grades, he doesn’t need further assistance”, and sadly, this leads to the neglecting of the needs of the most capable.