A Study of the Complexity of Problems Posed by Talented Students in Mathematics

Abstract

Problem posing and mathematical talent are topics of interest to the community of researchers in Mathematics Education, but few studies reveal talented students’ abilities to solve problem-posing tasks. The data were collected using a problem invention instrument composed of four questionnaires that include free, semi-structured tasks and problem invention structures. The sample consisted of 23 students considered as mathematically talented and 22 students from a standard public school. The results show that the problems posed by the talent group are more complex than those invented by the standard group. The former are longer and show greater diversity of ideas while also requiring more steps to be solved, presenting a higher level of complexity according to the PISA framework, and requiring significant cognitive effort. In conclusion, the problem invention instrument used and the variables defined enabled us to analyze the complexity of the problems posed by the group of talented students. The statistical analysis performed reinforces the differences found in the complexity of the productions by the two groups studied.