Abstract: This article describes two stages of a study carried out with pre-university students, to gather information about the learning of the concept of inductive structures. The study complements two previous investigations focusing on the design of recursive algorithms, from which the study of students' understanding about the input structures of the algorithms arises as a necessity. The theoretical framework used in the three studies is the epistemology of Jean Piaget, specially works about recursive reasoning on the series of natural numbers. Our methodology of research follows principles of Piaget's experiments in which the clinical method from psychiatry was adopted. In this sense, the instructional instance is a tool for obtaining information about cognitive processes. In the first stage, two instructional instances with eight voluntary participants were conducted, in which a problem about an inductively defined set is presented and some questions are posed. The analysis of the responses of the students reveals some diffculties casting doubts on students' conceptual knowledge on the series of natural numbers. Investigating this point is the goal of the second stage where one instructional instance is conducted with seven students, and new information is gathered and analyzed. The results of current and previous studies will be used to elaborate didactic material to introduce inductive definitions, recursive algorithms and proof by induction at pre-university level. This article describes the main theoretical guidelines, the development of both stages of the study and the analysis of the diffculties and progress observed. Some conclusions and future work are included.
PPIG 2012 - 24th Annual Workshop
A Study about Students' Knowledge of Inductive Structures