This article explores inquiry-based learning (IBL) pedagogy, particularly in mathematics education, examining how it differs from problem-based learning (PBL) and case-based learning (CBL). IBL is defined as a student-centered approach involving sequenced problems or tasks that build engagement and understanding through group work. While IBL, PBL,…

Problem-solving before instruction has been shown to be a more effective learning design than traditional tell-and-practice for several mathematical concepts at the secondary school level. In particular, the more a problem-solving before instruction design follows the productive failure principles, such as comparing and contrasting…

This quasi-experimental study investigated the impact of content enrichment activities requiring higher order thinking skills (HOTS) on students' performance in answering questions across different thinking dimensions. The study involved 477 students from grades five through eight, divided into control and experimental groups. The experimental…

Differentiation of curriculum and instructional practices plays a pivotal role in meeting the educational needs of gifted students. This reality compels gifted education experts to employ various differentiation strategies. Differentiation entails modifying one or more components of the curriculum--process, content, or product--based on the…

A test method is described for determining the divisibility of non-negative integers by a prime number. The test uses an integer multiplying factor that is defined for each prime, designated as [beta], to reduce the non-negative integer that is being tested by an order of magnitude in each of a sequence of steps to obtain a series of new numbers.…

We review the history and previous literature on radical equations and present the rigorous solution theory for radical equations of depth 2, continuing a previous study of radical equations of depth 1. Radical equations of depth 2 are equations where the unknown variable appears under at least one square root and where two steps are needed to…

The cosine theorem is used in solving triangulation problems and in physics when solving problems of addition of unidirectional oscillations. However, this theorem is used only for the analytical calculation of triangles or when solving problems of adding two oscillations. Here we propose a generalization of the cosine theorem for the case of…

In this regular "American Educator" column, findings from the field of cognitive science that are strong and clear enough to merit classroom application are considered. Individuals vary in their views of what students should be taught, but there is little disagreement on the importance of critical thinking skills. In free societies, the…

The distant magnetic field of a magnetic dipole is usually derived via the magnetic vector potential and substantial vector calculus. This paper presents an alternate proof that is less mathematically intensive, and that ties together various problem-solving tricks (the principle of virtual work, observation that only instantaneous quantities…

When students are solving problems they often turn to examples when they need assistance. Examples are helpful because they illustrate how a problem can be solved. However, when examples are very similar to the problems, students default to copying the example solutions, which hinders learning. To address this, prior work has investigated the…

The purpose of this note is to describe several challenging problems in Euclidean geometry. The note also contains author's solution sketches to the two problems.

Prior research has demonstrated the importance of forecasting to creative problem-solving performance. Less is known about how case analysis and outcome valence impact forecasting performance. In this study, 266 participants were asked to assume the role of a Marketing Director of a clothing company and develop a marketing campaign for entering a…

In a recent submission to "The Physics Teacher," we related how trigonometric identities can be used to find the extremes of several functions in order to solve some standard physics problems that would usually be considered to require calculus. In this work, the functions to be examined are polynomials, which suggests the utilization of…

Metacognition, or the ability to "think about thinking," plays a significant role in the performance of first-year design students. Although the number of studies that focus on metacognition has increased in the past decade, additional studies are needed to more fully investigate metacognition and the use of metacognitive strategies in…

There are many problems whose solution requires proof that a quadrilateral is cyclic. The main reason for writing this paper is to offer a number of new tools for proving that a particular quadrilateral is cyclic, thus expanding the present knowledge base and ensuring that investigators in mathematics and teachers of mathematics have at their…