The key difference between math as math and math in science is that in science we blend our physical knowledge with our knowledge of math. This blending changes the way we put meaning to math and even the way we interpret mathematical equations. Learning to think about physics with math instead of just calculating involves a number of general…

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…

Learning to create, use, and evaluate models is a central element of becoming a scientist. In physics, we often begin an analysis of a complicated system with highly simplified or toy models. In introductory physics classes, we tend to use them without comment or motivation. Some students infer that physics is irrelevant to their understanding of…

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…

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…

Students in one discipline often receive their scientific training from faculty in other disciplines. As a result of tacit disciplinary differences, especially as implemented in courses at the introductory college level, such students can have difficulty in understanding the nature of the knowledge they are learning in a discipline that they do…

Course syllabi are a required component of college and university courses. Syllabi present both broader course structuring practices, are a valuable "first impression" of what instructors want to offer their students, and are used as tools in course design. While best teaching practices suggest specific recommendations for syllabi…

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 effectively include math in physics in a way that reaches most students remains unsolved. In this paper, we…

Teaching about energy in interdisciplinary settings that emphasize coherence among physics, chemistry, and biology leads to a more central role for chemical bond energy. We argue that an interdisciplinary approach to chemical energy leads to modeling chemical bonds in terms of negative energy. While recent work on ontological metaphors for energy…

Energy is an abstract science concept, so the ways that we think and talk about energy rely heavily on ontological metaphors: metaphors for what kind of thing energy is. Two commonly used ontological metaphors for energy are "energy as a substance" and "energy as a vertical location." Our previous work has demonstrated that…

Educators and policy makers have advocated for reform of undergraduate biology education, calling for greater integration of mathematics and physics in the biology curriculum. While these calls reflect the increasingly interdisciplinary nature of biology research, crossing disciplinary boundaries in the classroom carries epistemological challenges…

As interdisciplinary courses are developed, instructors and researchers have to grapple with questions of how students should make connections across disciplines. We explore the issue of interdisciplinary reconciliation (IDR): how students reconcile seemingly contradictory ideas from different disciplines. While IDR has elements in common with…

Physics students can encounter difficulties in physics problem solving as a result of failing to use knowledge that they have but do not perceive as relevant or appropriate. In previous work we have demonstrated that some of these difficulties may be epistemological. Students may limit the kinds of knowledge that they use. For example, they may…

The authors appreciate Professor Slotta's responding to their critique (Slotta, this issue). For their part, they believe that Professor Slotta has misinterpreted aspects of their position. In this commentary, the authors clarify two particular points. First, they explain their use of "static ontologies," which they maintain applies. Second, they…

In a series of well-known papers, Chi and Slotta (M. T. H. Chi, 1992, 2005; M. T. H. Chi & J. D. Slotta, 1993; M. T. H. Chi, J. D. Slotta, & N. de Leeuw, 1994; J. Slotta & M. T. H. Chi, 2006; J. D. Slotta, M. T. H. Chi, & E. Joram, 1995) have contended that a reason for students' difficulties in learning physics is that students…