Graphs are an important component in physics laboratory reports. We have noticed that our students have difficulty selecting the "scale" and the "starting value" for an axis while generating graphs on graph paper. Recommendations concerning convenient scales and starting values are found in textbooks, laboratory manuals, and…

This article presents a task providing college students opportunities to build on their high school knowledge of trigonometry to explore parametric equations and inverse trigonometric relationships within a contextual learning ladder problem.

The ideal gas law, "PV = nRT," is one of the simplest physical laws in nature that is introduced to students as early as in high school and first year in college. In this equation, "P" stands for pressure, "V" is the volume, "n" is the amount expressed in mole, "T" is the temperature in Kelvin…

One way to develop a cross-curricular lesson is to select the most common mathematical formulas used in science and carefully develop and implement tasks that allow students to make connections between the mathematical representations and theoretical/physical science concepts. The slope-intercept formula, which is used to study relationships…

A significant goal when teaching at the secondary education level is to present the generality of the procedures that are being used to describe a wide range of different physical phenomena. However, this approach is abandoned by physics instructors in many cases since the general mathematical background needed to present the above generality is…

Quadratic modeling problems are commonplace in high school mathematics courses; they typically situate quadratic patterns of change and their corresponding parabolic graph within real-world contexts. Traditional approaches to this type of problem lend themselves to making connections across different representations (e.g., Garofalo and Trinter…

The visual method in this paper solves linear inequalities in one variable by considering them initially as two competing linear expressions, each of which is then expressed as a linear equation. When the solution of these two linear equations exist, it is viewed as a highlighted area or a line. These linear equations convey the intended visual…

This paper focuses on the emergence of abstraction through the use of a new kind of motion detector--WiiGraph--with 11-year-old children. In the selected episodes, the children used this motion detector to create three simultaneous graphs of position vs. time: two graphs for the motion of each hand and a third one corresponding to their…

The drag effect on a falling ball caused by air is a conventional subject in the most well-known textbooks of classical mechanics and fluid dynamics. Further, there are some papers that employ video analysis to track objects movements in the air making it possible to obtain position data as a function of time and its graphs. However, none of them…

This paper presents preparations, execution and reflection on results for the physics part of a CSI task for the European Union Science Olympiad 2010, taking place at the University of Gothenburg. The participants were required to make a graph of the cooling of a swede ("Brassica napus"), as a proxy for the cooling of a murder victim,…

Throughout time people have been measuring the rising and setting positions of celestial objects with respect to the horizon. The motivation for this paper is to provide a link between mathematical and observational approximations for the Sun's declination (angular distance from the celestial equator). One source had students do an experiment with…

The present work presents a proposal for study and investigation, in the context of the teaching of Mathematics, through the history of linear and recurrent 2nd order sequences, indicated by: Fibonacci, Lucas, Pell, Jacobsthal, Leonardo, Oresme, Mersenne, Padovan, Perrin and Narayana. Undoubtedly, starting from the Fibonacci sequence, representing…

This paper was inspired by the work of a previous contributor on the subject of modelling plague epidemiology by comparing it to the physics of series radioactive decay, RC transients, and fluid dynamics. An Arduino-based experiment to illustrate the fluid-dynamical case is described. Attention is drawn to important differences between systems…

The present article demonstrates a way of programming using an Excel spreadsheet to teach Fourier series expansion in school/colleges without the knowledge of any typical programming language. By using this, a student learns to approximate partial sum of the n terms of Fourier series for some periodic signals such as square wave, saw tooth wave,…

For the least-squares analysis of data having multiple uncertain variables, the generally accepted best solution comes from minimizing the sum of weighted squared residuals over all uncertain variables, with, for example, weights in x[subscript i] taken as inversely proportional to the variance [delta][subscript xi][superscript 2]. A complication…