The Formulation of Hypotheses in Mathematical Modelling Activities

Abstract

Background: The formulation of hypotheses in mathematical modeling activities, although it has been pointed out as one of the specificities of this kind of activities, it is still little discussed by the research in the area of mathematical modeling. Purpose: In this paper we look for influences on mathematical modeling activities arising from the formulation of hypotheses. Design: Our statements are based on a theoretical framework about Wittgenstein's philosophy and previous studies related to hypotheses’ formulation as well as an empirical research. Scenario and participants: Modeling activities were performed by groups of students from different degrees. Data collection: In modeling classes, data were collected through audio and video recordings. The students also delivered the written records they produced. Findings: The findings indicate three categories for the formulation of hypotheses: hypotheses are formulated based on the students' view of the situation; hypotheses are based on students' experiences; hypotheses influence students' choices at different stages of the activity's development. Conclusion: The research concludes that the hypotheses determine the idealized situation, guide the mathematization and direct the students' actions in the development of the activity. In Wittgenstein's philosophical perspective, hypotheses are a way of perceiving reality and new experiences can lead to other formulations.

Estructurando y validando una herramienta para evaluación en actividades de modelización matemática

“…O segundo critério consiste em observar se a ação de formular hipóteses, considerada uma das especificidades de atividades de modelagem matemática (Bean, 2012), é realizada pelos estudantes. Lidar, em atividades de modelagem com informações, especificidades ou características de situações da realidade ainda não conhecidas quando se inicia a abordagem matemática dessa situação e encontrar uma maneira de superá-los pode ser enfrentado mediante uma formulação de hipóteses (Almeida, Sousa e Tortola, 2021).…”