Understanding the concept of a numerical series through Pirie and Kieren model

Abstract

Several research studies have realized the difficulties faced by students for the acquisition and understanding of the concept of numerical series. The concepts of limits, infinity and the difference between the series and the sequence of partial sums are some obstacles to be overcome. This article analyzes the process that follows a group of students solving the activity about the calculi of the height and volume of a tower that involves working with harmonic series in the light of Pirie and Kieren model. Starting from Image Making level the students link different elements of the mathematical concept of numerical series. The interactions between them allow to advance between the different levels of the model to develop an understanding of the concept using the folding back mechanism.