Purpose: The purpose of this study is to explore the mathematical values, mathematics educational values, and educational values involved in mathematical modeling tasks based on different mathematical modeling perspectives. Design/Approach/Methods: In this context, the present study is a qualitative research based on document analysis. The data…

The role of mathematical modelling pertains several disciplines, both STEM and non-STEM, and various fields: education, academy, work, everyday and social life. Despite its importance, it is not uncommon to see university students facing difficulties with the use of Mathematics to create models, even when mathematical entities that play a role in…

Contextual learning experiences using integrated STEM, agricultural sciences (AgS), and mathematical modeling (model eliciting activities [MEAs]) can be a powerful approach to engage students from urban areas in STEM literacy, career exploration, and community awareness. This three-study dissertation contributes to: (1) an innovative framework for…

Human reasoning about and with uncertainty is often at odds with the principles of classical probability. Order effects, conjunction biases, and sure-thing inclinations suggest that an entirely different set of probability axioms could be developed and indeed may be needed to describe such habits. Recent work in diverse fields, including cognitive…

This paper presents an international research study of long-term professional development courses on modelling. It addresses the question of scaling-up professional development. So far, there has been much research on small-scale professional development courses, but we know very little about what it means to scale up such a course and to reach…

These four chapters describe studies of using models for integer addition and subtraction. The models draw principally on the two grounding metaphors of object collection and motion along a path. A strength of all chapters is detailed analysis of how the models are and can be implemented and how they influence student's learning. Together the…

Relating mathematics learned in the classroom to real situations increases student motivation and enhances learning. In this paper, we provide an example of a classroom application of calculus to physiology in two courses: "Differential Equations" and "Calculus I for Biology and Medicine." We designed and implemented a project…

Literature typically describes mathematization, the process of transforming a real-world situation into a mathematical model, in terms of desirable actions and behaviors students exhibit. We attended to STEM undergraduate students' quantitative reasoning as they derived equations. Analysis of the meanings they held for arithmetic operations (+, -,…

The main purpose of the current study is modifying students' daily drinking water and managing waste water through modelling activities as context and modelling cycle as tool. In this study, 12 students (13-14 years old) from the lower secondary school were participated. These students were participated in two sessions (60 minutes) each week for…

The purpose of this paper is to integrate mathematical modeling and ecology by presenting an activity involving an authentic environmental problem, which is called "Pine Processionary Caterpillars Invasion." Adopting Mathematical Modeling and Education for Climate Action (EfCA) approaches, it was aimed to encourage pre-service teachers…

This is a study of student engagement with computational labs in Calculus 2. The labs task students with using MATLAB to investigate contexts such as rocket science, disease modeling, and market economics forecasting by modifying and executing provided code, guided by questions that have students report the results of their simulations or…

Background: Modeling and simulation practices have become commonplace in modern engineering, but in-depth research on the development of modeling and simulation expertise is needed to identify the learning processes involved in successfully acquiring these skills. Purpose: This study investigated student dimensions of expertise when engaged in…

This article describes a method for using the United States Census data to open a differential equations course. The question of finding a model for the United States population data gives students a first experience with creating a model using differential equations, and also understanding derivatives, what they mean, and how to calculate them in…

This paper describes an activity using a dog treat ball to introduce systems of first-order differential equations. Beads are placed in the first of two hemispherical chambers of a food-dispensing dog toy. As the ball is turned, students track the number of beads in the first chamber, the second chamber, and the exterior of the ball. Students…

In the first part of the dialogue between theories, which gave rise to a paper in this journal, we discussed the role played by normativity in didactics. In this work, with the aim of taking a step forward in this dialogue, we state explicitly some of the postulates of the anthropological theory of the didactic. They shape the object of study, the…