Taylor series play a ubiquitous role in calculus courses, and their applications as approximants to functions are widely taught and used everywhere. However, it is not common to present the students with other types of approximations besides Taylor polynomials. These notes show that polynomials construed to satisfy certain boundary conditions at…

Researchers have demonstrated a much-needed shift in pedagogical practices to incorporate literacy strategies. This dissertation provides additional empirical evidence to expand the body of research by utilizing a comparative readability analysis that examines the academic language of a popular calculus textbook. A sample from the published…

Length of the Unused Bed (LUB) methods for scaling sorbers have confusing and complicated pedagogically elements. One method limits feeds to C/C[subscript F] < 0.3; a limitation not stated in the established textbooks. Discussed is a new LUB method with no limitation on the feed C/C[subscript F]. It fixes the pedagogically confusing and…

We discuss the limits of the equation of the period of a simple pendulum, T[subscript s] = 2[pi][square root]l/g, frequently used in high-school and university classrooms to measure the acceleration of gravity. We evaluate the relative error in determining the acceleration of gravity with this simple equation instead of a more realistic one,…

Capitalizing on cognitive load theory and learning by analogy, we propose two instructional methods to learn a complex linear equation (e.g. two-step equation) by building on prior knowledge of a simpler linear equation (e.g. one-step equation). We will examine the proposal theoretically in this paper. In line with the design principles of…

This study explores the worked-example instruction (WEI) and the van Hiele teaching phases (VHTP) pedagogies to advance students' acquisition of procedural and conceptual understanding of solving simultaneous equations. The quasi-experimental study involved two groups of high school students (age=15): 157 students in total with 72 in one group and…

Consider a chain of length L that hangs in a U shape with end A fixed to a rigid support and free end E released from rest starting from the same initial height (call it y = 0) as A. Figure 1 sketches the chain after end E has fallen a distance y. Points O and A are assumed to be close enough to each other and the chain flexible enough that the…

The present study examines the effectiveness of incorporating worked examples with prompts for self-explanation into a middle school math textbook. Algebra 1 students (N = 75) completed an equation-solving unit with textbooks either containing the original practice problems or in which a portion of those problems were converted into a combination…

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…

Understanding equivalence is fundamental to STEM disciplines, yet misunderstandings and misconceptions inhibit students from fully appreciating or leveraging the concept. Using the game-based algebraic notation system, From Here to There! (FH2T), students explore ideas of equivalence by dynamically transforming expressions or equations among…

GeoGebra is a dynamic geometric software developed for the support of mathematics teaching. The aim of this research was to study the effect of GeoGebra on mathematics achievement in relation to the linear equations and explore the perception of students towards the use of GeoGebra in teaching mathematics. Forty students were participating in this…

Problems of optimization in natural science, technology, economics, and management are of great interest. Students also usually find them intriguing. However, the selection of such problems in introductory undegraduate physics textbooks is very limited and should be broadened. To that end, a model of traffic flow optimization, simple enough for…

Background: The format of a mathematics problem often influences students' problem-solving performance. For example, providing diagrams in conjunction with story problems can benefit students' understanding, choice of strategy, and accuracy on story problems. However, it remains unclear whether providing diagrams in conjunction with symbolic…

Many studies have shown that visual representations can enhance student understanding of STEM concepts. However, prior research suggests that visual representations alone are not necessarily effective across a broad range of students. To address this problem, we created a novel, scaffolded form of diagrammatic self-explanation in which students…

In order to show how formal analogies between different physical systems play an important conceptual work in physics, this paper analyzes the evolution of Einstein's thoughts on the structure of radiation from the point of view of the formal analogies he used as "lenses" to "see" through the "black box" of Planck's…