We discuss an investigation of student sensemaking and reasoning in the context of degenerate perturbation theory (DPT) in quantum mechanics. We find that advanced undergraduate and graduate students in quantum physics courses often struggled with expertlike sensemaking and reasoning to solve DPT problems. The sensemaking and reasoning were…

Scientific ideas are often expressed as mathematical equations. Understanding the ideas contained within these equations requires making sense of both the embedded mathematics knowledge and scientific knowledge. Students who can engage in this type of blended sensemaking are more successful at solving novel or more complex problems with these…

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 &…

Making meaning with math in physics requires blending physical conceptual knowledge with mathematical symbology. Students in introductory physics classes often struggle with this, but it is an essential component of learning how to think with math. Teaching the dimensionality of measured quantities and dimensional analysis (DA) is a valuable first…

The present review intends to show the current state of teaching quantum-related content, to analyze and compare its learning efficiency, and to give a systemized overview of quantum-educational activities in the last years. We focus on teaching and learning elements, their innovative tools, and process-oriented studies that are empirically…

To improve understanding of identities and inverses, and to provide a stronger foundation for future mathematics, Sandra Miles designed a two-part lesson that makes the relationship between identities and inverses explicit. This article illustrates Miles' teaching of the first part of the lesson, focused on addition and subtraction, and then gives…

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…

An important step in learning to use math in science is learning to see symbolic equations not just as calculational tools, but as ways of expressing fundamental relationships among physical quantities, of coding conceptual information, and of organizing physics knowledge structures. In this paper, I propose "anchor equations" as a…

Our exponentially increasing knowledge base creates many new technology challenges. Academia must therefore respond emphatically. Educating rising professionals to successfully confront these future difficulties requires innovative curricula challenges. A successful adaptation integrates STEM program protocols into core courses. Embracing…

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…

Background: Knowledge of quantum computing is arguably inaccessible to many, with knowledge of the complex mathematics involving a particular barrier to entry, creating difficulty in terms of teaching and inclusive learning for those without a high level of mathematics. Meanwhile, it is increasingly important that the knowledge of quantum…

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.

Students in upper secondary education encounter difficulties in applying mathematics in physics. To improve our understanding of these difficulties, we examined symbol sense behavior of six grade 10 physics students solving algebraic physic problems. Our data confirmed that students did indeed struggle to apply algebra to physics, mainly because…

In this article we present and discuss some theoretical and methodological elements of a wider research that analyzes the teaching practice of two teachers novice and expert from a semiotic theoretical approach. The conceptual framework of this work allows for addressing the epistemological and didactic dimensions of the teaching practice. Three…

North Korea's development of nuclear weapons and, more recently, intercontinental ballistic missiles (ICBMs) has added a grave threat to world order. The threat presented by these weapons depends critically on missile range, i.e., the ability to reach North America or Europe while carrying a nuclear warhead. Using the limited information available…