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Physics makes powerful use of mathematics, yet the way this use is made is often poorly understood. Professionals closely integrate their mathematical symbology with physical meaning, resulting in a powerful and productive structure. But…
University students taking introductory physics are generally successful executing mathematical procedures in context, but often struggle with the use of mathematical concepts for sense making. Physics instructors note that their students…
Since its existence, the computer tool has often supported mathematicians, whether it is to implement an approximation method (numerical calculation of a root, of an integral, ...) or to simulate a phenomenon (geometric in nature,…
Symbolic equations are one of the many representations used in physics. Understanding these representations is important for students because they are how students access knowledge in physics. In this paper I build off of the work by Redish…
Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend…
Instruction in quantum mechanics is becoming increasingly important as the field is not only a key part of modern physics research, but is also important for emerging technologies. However, many students regard quantum mechanics as a…
Computation, the use of a computer to solve, simulate, or visualize a physical problem, has revolutionized how physics research is done. Computation is used widely to model systems, to simulate experiments, and to analyze data. Yet, in most…
Mathematics can serve many functions in physics. It can provide a computational system, reflect a physical idea, conveniently encode a rule, and so forth. A physics student thus has many different options for using mathematics in his…
In their study of physics beyond the first year of University -- termed upper-division in the US, many of students' primary learning opportunities come from working long, complex back-of-the-book style problems, and from trying to develop…
A primary goal of physics is to create mathematical models that allow both predictions and explanations of physical phenomena. We weave maths extensively into our physics instruction beginning in high school, and the level and complexity of…
Scientific research involves mathematical modelling in the context of an interactive balance between theory, experiment and computation. However, computational methods and tools are still far from being appropriately integrated in the high…
Previous research has found that introductory physics students perform far better on numeric problems than on otherwise equivalent symbolic problems. This paper describes a framework to explain these differences developed by analyzing…
Courses in mathematical methods for physics students are not known for including too much in the way of mathematical rigour and, in some ways, understandably so. However, the conditions under which some quite commonly used mathematical…
How students use mathematics in their physics classes has been studied extensively in the physics education literature. In addition to specific mathematical methods in specific physics contexts, possible effects of more general "cultural"…
Textbooks in applied mathematics often use graphs to explain the meaning of formulae, even though their benefit is still not fully explored. To test processes underlying this assumed multimedia effect we collected performance scores, eye…
High school science classrooms across the United States are answering calls to make computation a part of science learning. The problem is that there is little known about the barriers to learning that computation might bring to a science…
Equations are about more than computing physical quantities or constructing formal models; they are also about understanding. The conceptual systems physicists use to think about nature are made from many different resources, formal and…
Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to…
Pre-college mathematics modeling instruction often frames mathematics as being separated from reasoning about the real world -- and commonly treats reasoning mathematically and reasoning about the real-world context as separate stages of a…
Questions concerning origin of mathematical knowledge and roles of language and intuition (imagery) in mathematical thoughts are long standing and widely debated. By introspection, mathematicians usually have some beliefs regarding these…