Types of Problems that Elicit Inductive, Abductive, and Deductive Arguments

Abstract This paper presents a relation between the types of conjecturing open problems in geometry, preferably solved using Dynamic Geometry Systems, and the types of arguments produced. The aim of this paper is to show how each type of problem can elicit the production of certain types of arguments (inductive, abductive, and deductive) during the problem-solving process. To back this idea, we use examples of specific problems (that involve the geometric object perpendicular bisector of a segment) and show solution strategies produced by students of a plane geometry course included in a pre-service mathematics teacher program (Universidad Pedagógica Nacional, Colombia). Using the argument model proposed by Toulmin to analyze these strategies, we identify the types of arguments associated with each type of problem. Finally, we indicate the typology of problems that can contribute to the didactic-mathematical knowledge of the mathematics teacher.