To a student in introductory physics, using vectors is at best an exercise in bookkeeping. A two-dimensional kinematics problem effectively doubles the number of equations that a student must know, and invites the student to memorize factoids: "The horizontal motion is constant," "Gravity is only in the y-direction," etc. Force…

Basis vectors e[subscript alpha] play a useful role in special and general relativity. In particular they allow an expansion of the vectorial spacetime interval dl along infinitesimal curvilinear coordinate differences dl = e[subscript alpha]d[Xi][superscript alpha]: (thus the definition e[subscript alpha] = dl/d[Xi][superscript alpha]). In this…

In high school, and also in introductory physics courses in higher levels of schooling, the law of universal gravitation of planets is introduced by postulating Johannes Kepler's three laws, and later Isaac Newton's law of the inverse of the square of the distance to the Sun. The justification of the laws is only achieved in advanced courses in…

This study aims to describe the 3D model's online modules effectiveness in the practicing mastery of conceptual knowledge in solar system learning using an instrument which tested 58 7th-grade respondents from one of the junior high schools in Jombang, East Java, Indonesia. The respondents were then divided without randomization into 29…

Three-dimensional symmetry plays a crucial role in crystallography education. The educational process can be facilitated by introducing the analysis of friezes and plane patterns such as parquets before presenting more sophisticated crystal structures. Analysis of the symmetry of parquets can serve as an opportunity to follow the full routine of…

"Representational transformation diagrams" are used to compare and contrast standard textbook presentations of vector line integrals in undergraduate courses in both mathematics and physics. These presentations are taken as the lower anchor in a learning trajectory. Two principal approaches in the lower division are identified, roughly…

While chemistry exists in three dimensions, it is presented in two. This down-conversion results in a significant loss in information and often necessitates multiple images/figures to convey the complexity, intricacy, and beauty of a given structure. Currently, three-dimensional models are built to allow students to interact with molecules.…

The equivalent resistance calculation for two circuits in cubic arrangements is solved. Emphasis is placed on the plastic (topological) properties of these circuits. In contrast, the opposite topological behaviour of an analogous arrangement is observed in the calculus of a magnetic field. It is also noted that the solved examples may be used as a…

One of the more difficult concepts introduced in the first-year undergraduate course, general chemistry, is that of chirality. Typically, left and right hands are the common, macroscopic objects of reference used to demonstrate the quality of being nonsuperimposable, followed by the use of a mirror and molecular models, to illustrate molecular…

The purpose of this study is to investigate the effect of teaching through a virtual laboratory prepared using simulations teaching materials and that are based on constructivist thought about geometrical optics upon the students' academic success and their attitudes towards physics. Quasi-experimental pretest and posttest control groups was used…

In a paper (posthumously) co-authored by Isaac Newton himself, the primacy of geometric notions in pedagogical expositions of centripetal acceleration has been clearly asserted. In the present paper we demonstrate how this pedagogical prerogative can inform the design of an experiment involving an accelerometer-equipped smartphone rotating…

The specialised uses of solid angles mean that they are quite unfamiliar quantities. This article, apart from making solid angles a little more familiar, brings out several topics of general interest, such as how units are interrelated and how equations depend on the choice of units. Although the steradian is commonly used as the unit for solid…

Fractals are geometric objects used to describe irregular shapes that have a fractional dimension and commonly appear in nature. Although several proposals for the study of perfect fractals at the basic level are present in the literature, only few proposals for the study of real fractals exist, which does not seem reasonable considering the…

The abstractness of the chemistry concept can be understood easily through chemistry learning using multiple representations. This article used the Systematic Literature Review (SLR) method to review eleven articles published from 2012 to 2021 and focused on chemistry learning using various representations. The articles are systematically obtained…

Through the implementation of the free website/smartphone application Sketchfab, we have found a simple means to introduce 3D visual tools into the chemistry classroom. Sketchfab stores 3D models and animations with free cross-platform accessibility. Blender is a free 3D modeling tool that has been used to prepare models and animations for…