The Posing of Arithmetic Problems by Mathematically Talented Students

Abstract

Introduction. This paper analyzes the arithmetic problems posed by a group of mathematically talented students when given two problem-posing tasks, and compares these students’ responses to those given by a standard group of public school students to the same tasks. Our analysis focuses on characterizing and identifying the differences between the productions of both groups, based on an analytic framework designed in this study. Method. The sample is composed of two groups of students. The first consists of 21 students identified as mathematically talented and the second of 20 secondary students in a public school. Both groups completed two tasks of posing arithmetic problems designed in this study. The results were analyzed based on three categories of analysis and variables related to the problems’ syntactic, semantic, and mathematical structure. Results. The problems posed by the group of mathematically talented students are richer than those of the group of public school students. The talented students’ problems are composed of a greater number of propositions, use different types of numbers, require more steps and different calculation processes to solve, and have a higher number of different semantic relationships. Furthermore, the results show some attributes that enable us to characterize mathematically talented students when solving problemposing tasks. Conclusion. The problem-posing instrument and the analytical diagram enabled description and exploration of the performance of a group of mathematically talented students. Moreover, the three categories of analysis used and the solvability of each problem produced ten components whose values characterize the wealth of problems that the subjects invented. Finally, statistical analysis reinforces the differences between the productions of the two study groups.