The training of non-specialists, particularly engineers, in mathematics requires designing specific didactic proposals that make the importance of mathematics evident. One approach to creating such proposals consists in analyzing the mathematics used in authentic contexts of engineering research and then effectuating a didactic transposition to…

Developing models and using mathematics are two key practices in internationally recognized science education standards such as the Next Generation Science Standards (NGSS, 2013). In this paper, we used a virtual performance-based formative assessment to capture students' competencies at both "developing" and "evaluating"…

This research presents the results of development and validation of the Cyclical Self-Regulated Learning (SRL) Simulation Model, a model of student cognitive and metacognitive experiences learning mathematics within an intelligent tutoring system (ITS). Patterned after Zimmerman and Moylan's (2009) Cyclical SRL Model, the Simulation Model depicts…

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…

In this paper, we present the development of an investigation on the promotion of covariational reasoning in high school students (14-15 years old) in Mexico. The study consists of designing and applying a sequence of didactic activities that simulate a real situation virtually. The activities are organized through a Hypothetical Learning…

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…

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…

We present noncompetitive adsorption as "particles in a box with one sticky wall." We start with a general model that can be modeled as a simple ordinary differential equation (ODE). To verify the ODE students run a computer simulation. The ODE's solution imperfectly fits the simulation's data. This leads to the diffusion partial…

Purpose: Many mathematical models have been shared to communicate about the COVID-19 outbreak; however, they require advanced mathematical skills. The main purpose of this study is to investigate in which way computational thinking (CT) tools and concepts are helpful to better understand the outbreak, and how the context of disease could be used…

This paper describes an investigation looking at the underlying mathematics of poker machines. The aim of the investigation is for students to get an appreciation of how poker machines are designed to ensure that in the long-term players will inevitably lose when playing. The first part of this paper describes how students can model a simple poker…

Many national science frameworks (e.g., Next Generation Science Standards) argue that developing mathematical modeling competencies is critical for students' deep understanding of science. However, science teachers may be unprepared to assess these competencies. We are addressing this need by developing virtual lab performance assessments that…

We analyzed 5th grade students' interactions with one computer-based modeling simulation to examine how they defined and prioritized variables in a dynamically simulated environment. Results revealed that exposure to the simulation environment helped students visualize continuous motions, interpret the different quantities present in the model,…

The purpose of this study was to explore students' mathematical practices while working on modeling problems using 3 interactive computer simulations. Three fifth grade students' interactions with computer-based modeling simulation were examined to identify how children defined and prioritized and coordinated variables and parameters in…

Some researchers advocate a statistical modeling approach to inference that draws on students' intuitions about factors influencing phenomena and that requires students to build models. Such a modeling approach to inference became possible with the creation of "TinkerPlots" Sampler technology. However, little is known about what…

Various approaches to the problem of computer modelling of assimilation and forgetting of the educational information are considered. With the help of the multi-component model the Ebbinghaus' curve of forgetting of poorly assimilating information to be remembered through recurrences is confirmed. It is taken into account, that while training…