Non-routine mathematical problems and the strategies used by gifted students: A case study

Many gifted students fail to be diagnosed, preventing them from receiving an education that is adapted to their characteristics, with activities that challenge their minds. Mathematics is one of the subjects in which they can demonstrate talent, where they often exhibit high skills in solving problems, handling numbers and performing spatial representations. One of the contexts in which these characteristics can be addressed is the resolution of non-routine problems. Thus, the purpose of this exploratory, observational and descriptive case study was to present a battery of challenging activities to a 10-year-old gifted student and identify the strategies he uses when solving non-routine problems, with Pólya's method being used to guide him to reach one or more solutions. The results show that the activities proposed were challenging for the student, who used four strategies when solving the non-routine problems, with partial goals being the most widely used in problems of visual discrimination, and the use of patterns being the most frequently leveraged in numerical skills problems. This study provides teachers with resources that foster motivation among talented students and address their needs.