The term speed-accuracy tradeoff is used when an increase in response speed comes at the expense of response accuracy. Although originally a concept from experimental psychology, the speed-accuracy tradeoff has been a topic in psychological assessment, too. In the first part of the manuscript, we discuss motivational factors that may be…

This study aims to explore seventh-grade students' understanding of negative integers as they engaged in mathematics history integrated model-eliciting activities in small groups. For this educational case study, we designed model-eliciting activities based on six design principles of the models-and-modeling perspective that incorporated history…

Statistical modeling continues to gain prominence in the secondary curriculum, and recent recommendations to emphasize data science and computational thinking may soon position algorithmic models into the school curriculum. Many teachers' preparation for and experiences teaching statistical modeling have focused on probabilistic models.…

Productive problem solving, concept construction, and sense making occur through the core process of abstraction. Although the capacity for domain-general abstraction is developed at a young age, the role of abstraction in increasingly complex and disciplinary environments, such as those encountered in undergraduate STEM education, is not well…

We present adaptable activities for models of drug movement in the human body -- pharmacokinetics -- that motivate the learning of ordinary differential equations with an interdisciplinary topic. Specifically, we model aspirin, caffeine, and digoxin. We discuss the pedagogy of guiding students to understand, develop, and analyze models,…

How should our students think about external forcing in differential equations setting, and how can we help them gain intuition? To address this question, we share a variety of problems and projects that explore the dynamics of the undamped forced spring-mass system. We provide a sequence of discovery-based exercises that foster physical and…

In this article, we question the prevalent assumption that teaching and learning mathematics should always entail movement from the concrete to the abstract. Such a view leads to reported difficulties in students moving from manipulatives and models to more symbolic work, moves that many students never make, with all the implications this has for…

Engaging with mathematical modeling can support learners to collaboratively explore mathematics in integrated ways as well as generate mathematical ideas and representations that may be useful in everyday life. Although several studies provide diverse insights into teaching and learning mathematical modeling, research has yet to be conducted on…

The motivation behind this examination is to present the theoretical structure of Modeling Activities, which is believed to be a vital device for mathematics instruction. Modeling activities are defined as activities to figure out complex problems faced in real life situations that require the creation of a mathematical model as a product. In…

Metamodeling ideas move beyond using a model to solve a problem to consider the nature and purpose of a model, such as reasoning about a model's empirical basis and understanding why and how a model might change or be replaced. Given that chemistry relies heavily on the use of models to describe particulate-level phenomena, developing…

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…