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…

We share our experience and lessons learned from using Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations (SIMIODE) modeling scenarios in our Differential Equations I class at Middle Tennessee State University. Specific projects with Python codes are presented. Discussions are brought forth on how to…

This article reports on the results of an investigation of the predictive accuracy of five different mathematical models to identify at-risk students in a Business Statistics course. Low levels of students' success, especially in mathematics-related subjects such as statistics, are a salient problem in South Africa and other countries. Statistical…

The formation of students' social competence in the course of educational process in virtual educational environment represents an urgent pedagogical problem. The author proposes to present the development level of students' social competence through introducing certain variables determined on a relative scale into a mathematical model of the…

It remains a challenge for teachers to integrate modeling tasks in everyday mathematics classes. Many studies have been conducted that show the difficulties faced by teachers. One of the challenging aspects in this regard is that of assessment. In the present study, a connection between structures of learners' solution strategies and cognitive…

This study is an investigation of elementary preservice teachers' (PSTs') exploration of model breaking points in fractions. Eighty-three PSTs at two universities in the Midwestern and Southwestern regions of the USA were asked to explore the area model of fraction addition through a series of tasks and explain their reasoning in determining its…

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…

In this article, the authors describe their experiences with planning, implementing, and revising a lesson for which the goal is for students to consider the mathematical and pragmatic issues that are related to a task of maximizing the area for a fixed perimeter. The authors also wanted students to engage in the Standards for Mathematical…

This study presents a teaching experiment in which second-grade primary school students compared a city and a town according to population estimates. The activities were presented to them as Fermi problems and required an analysis of the reality to identify sub-problems that students could deal with. The students' products were analyzed from the…