This article is about utilizing the process of building and exploiting models as a framework for inquiry in mathematics education research. We introduce and discuss a model of such a process and compare this model with key methodological features of design research in mathematics education. We argue that despite several communalities, educational…

We consider the following hypothesis: whereas, the institutions in charge of the teaching of mathematics for future professional mathematicians (IPM, in short) share a "didactic paradigm" (strongly based on logical arguments), there does not seem to be such a thing in secondary mathematics education. In this work, we analyse the notion…

Articulated pedagogical and didactic strategies allow improving academic quality and strengthen individual and institutional cognitive processes such as student retention. Mathematical modelling, articulated with complementary actions, contributes to teaching and learning processes within situations that go beyond the classroom since they are…

In this study, we examined one experienced mathematician's class practices, with particular attention to cognitive model described in genetic decomposition. Our findings indicate that students only had limited opportunities to be familiar with the first three steps in genetic decomposition, which may potentially lead students to answer limit tasks…

Minimal guidance or maximal independence? How can teachers achieve that complex balance when teaching mathematics? In this pre-and post-test quasi-experimental research study, the authors explored the above broad questions in Grade 10 Financial Mathematics following guided discovery and mathematical modelling principles. Fifty-four (54) Grade 10…

The purpose of the work described in this paper is to emphasize the importance of using mathematical models and mathematical modelling in order to be able to understand and to learn possible behaviours in epidemic situations such as that of the COVID-19 pandemic, besides suggesting modelling techniques with which to evaluate certain sanitary…

This curated collection covers a selection of PRIMUS articles published over a roughly 12-year period that focus on modeling and applications. The collection includes sections on individual projects, courses with a significant modeling component, and modeling and applications in extracurricular settings and throughout the curriculum.

Though there is an extensive research literature on understanding and assessing individual modeling competencies, less attention has been given to characterizing the social context of the classroom in which modeling occurs. Yet a classroom's culture of modeling--its negotiated system of beliefs and values about the nature of modeling and what…

This article presents a synthesis of existing literature on ethnomodeling and the ways in which it extends mathematical modeling research in mathematics teacher education. We also call on the field to consider ways to connect and value culture and content in teaching mathematics. There have been increasing calls for integration of a culturally…

Recursive reasoning is a powerful tool used extensively in problem solving. For us, recursive reasoning includes iteration, sequences, difference equations, discrete dynamical systems, pattern identification, and mathematical induction; all of these can represent how things change, but in discrete jumps. Given the school mathematics curriculum's…

This paper addresses two aspects of integrating mathematics education with engineering education that may address persistence of engineering majors (and STEM majors more broadly): an emphasis on modeling as a vehicle for more authentic learning activity (Niss et al. 2007), and the need for measures that can support academic units' efforts to…

In this paper, we share our collaboration across the disciplines of mathematics and mathematics education to develop and implement a mathematical modeling task for prospective secondary mathematics teachers. Through this collaboration, we identified three key components of mathematical modeling: the "what," "how," and…

This study investigated the sources of difficulties experienced by prospective teachers in mathematical modelling in the context of a semester-long course on mathematical modelling for teachers. The data reported in this study were collected from six prospective teachers through in-depth semi-structured interviews supported by audio and videotaped…

In this theoretical paper we compare the Piagetian perspective on knowledge construction to mathematical model construction, with the aim to understand how mathematical modeling enables learning of mathematics and learning of science, as is often claimed. We do this by examining data through two lenses: (1) examining the role of cognitive conflict…

Connections among the mathematics, science, and engineering disciplines have been recognized and affirmed in national standards. For example, the application of mathematical ideas and skills within science has been highlighted in national science standards for over 20 years. More recently, the Next Generation Science Standards (NGSS; NGSS Lead…