Excluded-volume interactions are ubiquitous to modeling the average size of polymers in solution. This paper shows how simulations can be used by students to explore the emergence of mathematical scaling relations from excluded-volume interactions. Simulations provide robust visual representations of the system, and can be used to investigate a…

Research synthesis on simple yet general hypotheses and ideas is challenging in scientific disciplines studying highly context-dependent systems such as medical, social, and biological sciences. This study shows that machine learning, equation-free statistical modeling of artificial intelligence, is a promising synthesis tool for discovering novel…

The study presented in this article takes a closer look at how French and German high-school students deal with a mathematical modeling problem, what blockages they encounter and how differences in the modeling processes between students from both nations can be explained by differences between the teaching and learning of mathematical modeling in…

This study aimed to examine the relationship between mathematical modelling and reflective thinking and to examine the effects of employing mathematical modelling processes on perception of mathematical modelling competencies and reflective thinking skills for real-life problem solving of gifted students participating in Project Production and…

Developing models and using mathematics are two key practices in internationally recognized science education standards, such as the Next Generation Science Standards (NGSS). However, students often struggle with these two intersecting practices, particularly when developing mathematical models about scientific phenomena. Formative…

The study aims to investigate prospective middle school mathematics teachers' mental actions related to debugging, which is one of the computational thinking skills in the modeling process. The study was conducted with a single-case embedded model. The collaborative working group consisted of three prospective mathematics teachers selected by…

Mathematical modelling is emphasised in curricula worldwide. Since 2006, mathematical modelling has been considered a fundamental process in the mathematics subject in Norwegian upper secondary schools. This study aimed to identify tensions in the approaches to mathematical modelling expressed in teacher interviews (N = 4) and framework discourses…

The research presented in this article is a systematic review of the literature on the assessment of mathematical modeling in the setting of mathematics education published in the previous five years. This research has compiled the current best information from around the world to offer an overview of the assessment of mathematical modeling for…

Inspired by the approach first employed by C.S. Holling in his classic "disc experiment," this article provides a sequence of learning activities that increase students' understanding of the mechanisms behind saturating effects in predator-prey scenarios. The proposed lesson is recommended for inclusion in courses that address…

The development of modeling skills in mathematics is essential for individuals to understand, describe, control, and predict phenomena around them. This article describes the results of an investigation to find out how an activity -- based on a Models and Modeling Perspective -- stimulates the mathematics modeling skills of undergraduate students…

Mathematical modeling is a challenging and creative process. If one considers only interim or final solutions to modeling problems or interviews modelers afterward, often only their "explicit" models are accessible -- those expressed in work products or evinced in verbal and written reflections. The inner world of tacit knowledge and its…

The goal of this research is to make a theoretical reflection about connections that contributes to the development of the model for mathematical connections originally proposed by Businskas, and extended with the contributions of other researchers. This model is used in the most relevant investigations in this field. As a consequence of the…

These notes discuss several related problems in geometry that can be explored in a dynamic geometry environment. The problems involve an interesting property of hexagons.

Contemporary scholars describe mathematical modeling as a transformation of a real-world problem to a mathematical problem and back again. This paper treats a critical issue in the modeling process: how modelers determine if the transformation from the real world to mathematics was carried out well. I present an empirically derived typology of…

A simple discrete-time two-dimensional dynamical system is constructed and analyzed numerically, with modelling motivations drawn from the zombie virus of popular horror fiction, and with suggestions for further exercises or extensions suitable for an introductory undergraduate course.