This article presents a simple, fast, and equally accurate technique for measuring the area of a circle and of an ellipse without using geometric formulas. This therefore, together with the known radius of the circle and the semi-major and semi-minor axes of the ellipse, allows for the calculation of [pi]. The experiment is easy, thrilling, and…

Analysing graphs, formulating covariational relationships, and hypothesizing systems' behaviour have emerged as frequent objectives of contemporary research in physics education. As such, these studies aim to help students achieve these objectives. While a consensus has been reached on the cognitive benefits of emphasizing the structural domain of…

Research identifies two domains by which mathematics allows learning physics concepts: a technical domain that includes algorithmic operations that lead to solving formulas for an unknown quantity and a structural domain that allows for applying mathematical knowledge for structuring physical phenomena. While the technical domain requires…

This study investigates university students' graph interpretation strategies and difficulties in mathematics, physics (kinematics), and contexts other than physics. Eight sets of parallel (isomorphic) mathematics, physics, and other context questions about graphs, which were developed by us, were administered to 385 first-year students at the…

This article presents a case study that examines the level of integration of mathematical knowledge in physics problem solving among first grade students of upper secondary school. We explore the ways in which two specific students utilize their knowledge and we attempt to identify the epistemological framings they refer to while solving a physics…

Preservice teachers in six sections (n = 87) of a sequenced, methodological and process-integrated elementary mathematics/science methods course were able to reconcile an issue centered on a similar area of epistemology. Preservice teachers participated in a science inquiry lesson on biological classification and a mathematics problem-solving…

Problem solving, which often involves multiple steps, is an integral part of physics learning and teaching. Using the perspective of the epistemic game, we documented a specific game that is commonly pursued by students while solving mathematically based physics problems: the "analytical derivation" game. This game involves deriving an…

Presents calculations after discussing exponential growth that deal with the determination of the time of exhaustion at different rates of consumption. (PR)

Presents a simpler derivation for centripetal acceleration for use when students are first introduced to the topic. (PR)

Presents a mathematical problem that, when examined and generalized, develops the relationships between power and efficiency in energy transfer. Offers four examples of simple electrical and mechanical systems to illustrate the principle that maximum power occurs at 50 percent efficiency. (MDH)

In the framework of a curriculum reform in the Netherlands, an interdisciplinary open inquiry assignment has been introduced as a part of the final secondary school examinations. We developed and evaluated a preparatory open inquiry assignment to be used in science and mathematics departments of schools, in collaboration with each other: the…

An incident light ray parallel to the optical axis of a parabolic mirror will be reflected at the focal point and vice versa. Presents a mathematical proof that uses calculus, algebra, and geometry to prove this reflective property. (MDH)

Presents a simple mathematical model in which resultant speed is the sum or difference between wind speed and runner speed and a more complex model that assumes that only a proportion of the wind's speed affects one's running speed to describe the time difference between running with and without wind. (MDH)

Considers several aspects of quantitative relationships involved in learning physics. Includes discussions of proportionality, various kinds of equality, and the need for generality. Argues that clear distinctions are necessary if the physics curriculum is to be examined with regard to pupil outcomes. (TW)

Suggests a means for narrowing the gap between the technological-school student's (twelfth-grader) mastery of pure mathematical principles and ability to apply it to electronics. Discusses factors for and against teaching applications, cooperation between mathematics and electronics teachers, test procedures, results, and analysis of findings. (YP)