Abstract

(Objective)  This paper discusses an investigation of the meaning of “conjecture” for secondary school students, and disparities between personal meanings and those acquired in a mathematical institution.

(Methodology)  The methodology used is qualitative . A case study was carried out to improve understanding of the personal meanings of conjecture to students in the initial years of secondary education in the city of Río Cuarto, Argentina (15-16 years old). The responses of a group of students to assignments including three problems that involve the creation, contrasting, reformulation and/or validation of conjectures were analyzed, including interviews with the students. These analyses were carried out using tools from the ontosemiotic approach, determining configurations of primary objects and cognitive processes in the students’ personal practices.

(Results)  It was possible to identify semiotic conflicts in these practices, particularly disparities between personal meanings of the concept of conjecture and the meaning intended to be imparted by the mathematical institution, providing empirical indicators of the epistemic value given by students to emerging propositions in their argumentation. This made it less like ly that students would learn to doubt the scope of their initial statements and recognize the need to propose another type of argument, as was intended by the mathematical institution.

(Conclusions)  The results of this investigation showed the importance of revealing the ontosemiotic complexity of personal practices related to the formulation and validation of conjectures, and revealing the cognitive semiotic conflicts linked to personal meanings.

Keywords: Mathematics education; conjectures; argumentative practices; ontosemiotic approach; personal meanings; semiotic conflicts; epistemic value