The pendulum was an important scientific instrument in the 17th century. It became a typical textbook problem in the 18th century. After the introduction of vectors in physics in the 1890s, the pendulum problem started to be progressively solved in the manner we know nowadays from introductory mechanics courses. Starting from "F = ma"…

Techniques for applying mathematical concepts in the real world: six rarely taught but crucial tools for analysis, research, and problem-solving. Many young graduates leave school with a solid knowledge of mathematical concepts but struggle to apply these concepts in practice. Real scientific and engineering problems are different from those found…

In Realistic Mathematics Education (RME), students should reach formal mathematics knowledge and explore mathematics based on their informal knowledge. The problems chosen in the exploration process should apply mathematics to real-life situations and be suitable for students to explore and create mathematical structures. In the current study, the…

Incorporation of the vertical jump (VJ) test in health-related fitness batteries is predicated on the availability of prediction equations to accurately estimate VJ power. The purpose was to develop and validate a generalizable equation to estimate VJ power from VJ height, body mass, age, and sex in 10- to 18-year-olds. The sample (N = 529)…

The purposes of the research were 1) to compare the scores of 7th grade students from deductive learning activities management with games on the topic of "Single Variable Linear Equations" to the standardized criteria of 75%, 2) to compare the achievement of the 7th grade students before and after using the deductive learning activities…

Algebra is considered by many to be a gateway to higher-level mathematics and eventual economic success yet students with and without disabilities often struggle to develop algebra skills. This study builds on the limited understanding of how virtual manipulatives support students with disabilities in the area of algebra by investigating their use…

This paper presents an application of the Kalman filter in signal processing in instrumentation systems when the conditions of the environment generate a large amount of interference for the acquisition of signals from measurement systems. The unwanted interferences make important use of the instrumentation system resources and do not represent…

Worked examples are effective learning tools for algebraic equation solving. However, they are typically presented in a static concise format, which only displays the major derivation steps in one static image. The current work explores how worked examples that vary in their extensiveness (i.e., detail) and degree of dynamic presentation (i.e.,…

Circular dichroism (CD) is the differential absorption of left and right circularly polarized light. It arises from molecular electron oscillations that are driven by both the light's electric and magnetic fields, where the effects are in phase for one circular polarization and out of phase for the other. We describe these interactions, which have…

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…

A case study of regression analysis based on modeling Gilliland's correlation was described for use in a computational methods course. The case study uses a familiar example to train students in nonlinear least squares regression and to use standardized residual plots for model assessment. Previously published equations for Gilliland's correlation…

The authors of this study conducted an exploratory study of the teaching and learning processes of a tutor and a student with a mild intellectual disability (MID) while working on two-step equations. The researchers focused on situations in which the participant was likely to struggle with memory and processing as well as the challenges of the…

Decades of research have documented young students' misinterpretations of the equal sign and the impediments these present for children's mathematical development. Much less is known about individual differences in adults' knowledge of the equal sign. We assessed 182 college students from developmental math courses and present analyses from a…

In this paper, the dynamic case of a system made up of two blocks connected by a string over a smooth pulley is revisited. One mass lies on a horizontal surface without friction, and the other mass has a vertical displacement. The motion equation is obtained and its solution is determined using the "Mathematica" package. Also an…

An important goal in school algebra is to help students notice the covariational nature of functional relationships, how the values of variables change in relation to each other. This study explored 102 Year 7 (12 to 13-year-old) students' covariational reasoning with their constructed graphs for figural growing patterns they had generalised. A…