Eigentheory concepts are central in mathematics and physics; they serve multiple functions, such as symbolizing physical phenomena and facilitating mathematical computations. Words and meanings associated with eigentheory develop and vary over time, as do their associated symbols. In this study, we investigate how "eigen" develops over…

Background: Blended mathematical sensemaking in science ("MSS") involves deep conceptual understanding of quantitative relationships describing scientific phenomena. Previously we developed the cognitive framework describing proficiency in MSS across STEM disciplines, and specifically Physical Science. The framework was validated with…

This paper presents a methodological approach based on the use of complex networks to analyze the structure and content of curricula. We analyze the concept network built from the final year of a particular high school physics curriculum, as well as that of mathematics. We examine the most central nodes in each case, the community structures…

As part of ongoing research on student thinking about quantum mechanical concepts and formalism, we explored how students defined and made sense of expectation values. Previous research has focused on student difficulties when defining the expectation value for a generic operator and found that students conflate other quantum mechanical ideas with…

This paper introduces two theoretical constructs, open-loop covariation and closed-loop covariation, that combine covariational reasoning and causality to characterize the way that three preservice mathematics teachers conceptualize a feedback loop relationship in a mathematical task related to climate change. The study's results suggest that the…

STEM education is on demand more than ever as the workforce relies on 21st century skills and STEM disciplines. This paper presents a framework (IMS-TEAM) for integration of mathematics and science with the use of technology and modeling in an authentic context. The activity based on this framework is designed for and implemented with forty-four…

There is a long tradition of teaching science through inquiry, with broad agreement about the form it should take. Students should investigate researchable questions; gather and analyse data; and develop and represent evidence-based claims. Authoritative teacher or textbook representations are generally used to guide this learning (Buckley &…

In the same chapter of his book "Opera Geometrica," Torricelli published two discoveries: 1) initial velocity of a jet from a container increases with the square root of the depth of the hole; 2) he drew the pattern of jets from three openings at the wall of a container filled with water to constant level "H" and determined the…

Barriers to learning can affect educators and students in achieving learning objectives. One of them is the epistemological obstacle caused by the limited context used when a concept is first learned. The purpose of this study was to explore the epistemological obstacles of mathematics students in the concept of limits and functions during online…

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…

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…

Climate change put most species' survival in danger because it substantially affects the climate in which the species live, the quality of the water they drink, as well as the temperature of the air or water. When climate change increases the temperature of the climate, excessive evaporation occurs in lands, lakes, seas, and oceans. Our purpose in…

Learning to use math in science is a non-trivial task. It involves many different skills (not usually taught in a math class) that help blend physical knowledge with mathematical symbology. One of these is the idea of quantification--that physical quantities can be assigned specific numbers (with a unit). A second is to develop an intuition for…

Logarithms are notorious for being a difficult concept to understand and teach. Research suggests that learners can be supported in understanding logarithms by making connections between mathematics and science concepts such as pH. This study investigated how an integrated chemistry and mathematics lesson impacted 29 teachers' understanding of the…

Thermodynamics challenges teachers and learners. Its pervasiveness about nature, mathematical abstractness, nonnumerical relations, and complexity in applications can inhibit understanding and usage, especially by undergraduates. Perspectives are given about these obstacles, and some suggestions are made to enhance comprehension of the discipline.