Construction of the common multiple concept in the domain of whole numbers

Abstract

The purpose of this research was to characterize the construction process of common multiple of two whole numbers as a part of divisibility scheme in Secondary School students. From the analysis of clinical interviews with Secondary School students when solving a word- problem and justifying their decisions, we identify two cognitive moments in the constructive process generated in some cases in the context of problem solving. These cognitive moments were characterized regarding how students generated particular cases and were or were not able to coordinate the information arising from them. The characterization provides us with information about the way in which students begin to conceive that a number can play different roles in the divisibility scheme.

Keywords

• divisibility
• multiple of a number
• common multiple of two numbers
• reflective abstraction
• construction of mathematical knowledge