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…

We discuss common difficulties in upper-division electricity and magnetism (E&M) in the areas of Gauss's law, vector calculus, and electric potential using both quantitative and qualitative evidence. We also show that many of these topical difficulties may be tied to student difficulties with mathematics. At the junior level, some students…

We designed a sequence of seven lessons to facilitate learning of integration in a physics context. We implemented this sequence with a single college sophomore, "Amber," who was concurrently enrolled in a first-semester calculus-based introductory physics course which covered topics in mechanics. We outline the philosophy underpinning these…

Teacher educators' knowledge about metacognitive knowledge and developing expertise can provide for insights about teaching these "difficult" constructs. In this explorative study, six teacher educators' remarks regarding metacognitive knowledge and developing expertise were examined. The teacher educators filled in closed-ended and…

"Sustainability" is a very general term and the question arises how to specify it within daily laboratory work. In this regard, appropriate metrics could support a socially acceptable, ecological and economic product development. The application of metrics for sustainability should be strengthened in education, because they do not belong…

Community-based projects immerse technical writing students in intercultural communication, addressing local needs and shaping documents in human terms. Students at a South Texas university work to establish communication with clients in a city-county health department to create effective documents and disseminate family health legislation. To…

The goals of this study were to investigate the timing and the mechanism by which two types of model-centered instruction (MCI)--expert modeling (EM) and self-guided modeling (SGM)--might be made increasingly effective, efficient, and engaging for learners with different levels of expertise. The 62 pre-service and in-service evaluators who…

The article demonstrates that multiple solution tasks (MSTs) in the context of geometry can serve as a research instrument for evaluating geometry knowledge and creativity. Geometry knowledge is evaluated based on the correctness and connectedness of solutions, whereas creativity is evaluated based on a combination of fluency, flexibility, and…

This article is the story of a very non-standard, absolutely student-centered multivariable calculus course. The course advocates the so-called problem method in which the problems used are a bridge between what the learners know and what they are about to know. The main feature of the course is a unique conceptual story that runs through the…

Getting students to think about the relationships between area and perimeter beyond the formulas for these measurements is never easy. An interesting, nonroutine, and accessible problem that will stimulate such thoughts is the Lattice Octagon problem. A "lattice polygon" is a polygon whose vertices are points of a regularly spaced array.…

In this article, we report on the findings of an exploratory study into the experience of students as they learn first year engineering mathematics. Here we define engineering as the application of mathematics and sciences to the building and design of projects for the use of society [M. Kirschenman and B. Brenner, "Education for Civil…

This article reviews some key ideas about the nature of proof, kinds of proofs, and the way of reasoning called proving. This provides background for a discussion of the teaching of proof, in which some important aspects of teaching that support students' proving are described, and the ideas of a tool-box of accepted premises and local…

In this paper, we review the rules and game board for "Chutes and Ladders", define a Markov chain to model the game regardless of the spinner range, and describe how properties of Markov chains are used to determine that an optimal spinner range of 15 minimizes the expected number of turns for a player to complete the game. Because the Markov…

The development, in an introductory differential equations course, of boundary value problems in parallel with initial value problems and the Fredholm Alternative. Examples are provided of pairs of homogeneous and nonhomogeneous boundary value problems for which existence and uniqueness issues are considered jointly. How this heightens students'…

A question posed by a teacher can often serve as an effective and engaging way to start a class. Sometimes, however, interesting questions arise from comments made by students. The investigation presented in this article arose from a student's very simple question: "Is there a perfect rectangle for folding origami?" The initial investigation was…