Inquiry and Modeling for Teaching Mathematics in Interdisciplinary Contexts: How Are They Interrelated?

Abstract

International research has pointed out the importance of integrating mathematical modeling and inquiry processes into the teaching and learning of mathematics. This paper aims to present an integrative model that enables analyzing the characteristics inquiry and modeling processes share in the same model with a view to using them when designing and implementing interdisciplinary teaching sequences. After presenting a synthesis of the literature review, our theoretical approach to inquiry and modeling for the analysis of an interdisciplinary teaching sequence will be introduced. We focus here on the case of an inquiry situation in an archaeological context where mathematics and history are interrelated. It was implemented at secondary school level with students aged 13–14. We use this particular case study to analyze the appearance of both processes, in order to look for coincidences, concatenations and synergies. The main result is an integrative model for the joint analysis of both processes.

Norms That Regulate the Theorem Construction Process in an Inquiry Classroom of 3D Geometry: Teacher’s Management to Promote Them

“…On the other hand, we agree with Yackel [8], Stylianides et al [29], and Sala et al [30] in that the management of inquiry classrooms implies having deep knowledge about mathematics and argumentation. However, the study allowed us to see this idea can be complemented, specifying pieces of didactic-mathematical knowledge and competences that a teacher must develop relative to norms [5,24].…”

Inquiry and Mathematical Modelling with Real-Archaeological Objects in Secondary Education

“…This first approach to an integrative model, which could be useful for the study of learning situations where both inquiry and modelling processes emerge, started a path that this investigation aims to develop and delve into. As it is seen for the first time in the work presented in [9], both inquiry and modelling have subprocesses showing a notorious family resemblance between them and, from the perspective of Realistic Mathematics Education (see [7]), we can assert that both processes arise from situations which present realistic and authentic contexts (see a broader explanation in Section 2.3).…”

“…This author describes inquiry competency as one of methodological (which is focused on the learning of strategies and working methods that allow students to solve problems in school and, eventually, in adult life) and transversal (which is achieved by students throughout the work done in the different subjects of curriculum) nature [5]. Moreover, Sala-Sebastià et al [9] developed a model to characterise the inquiry process in terms of seven subprocesses (see Figure 1).…”

“…We stress the dynamic and cyclic nature of this model, in which students constantly validate their hypotheses and construct new ones. As the authors explain in the work presented in [9], the inquiry comes from the motivation to solve a problem-situation beyond the wording of the task. This is the starting point of the inquiry cycle and when students are expected to develop some of (or all) the seven subprocesses of the cycle, progressing (and/or receding; for this reason, the arrows are bidirectional) throughout the cycle.…”

“…However, despite the family resemblance (in terms of [8]) between some of the subprocesses concerning each of the inquiry and modelling processes, studies of both of them have been conducted separately until a recently published article [9]. This first approach to an integrative model, which could be useful for the study of learning situations where both inquiry and modelling processes emerge, started a path that this investigation aims to develop and delve into.…”