This keynote address explores the history and role of college math requirements with a focus on ensuring math courses serve to expand students' horizons, rather than serve as gatekeepers. It discusses the advent of general education math courses, which brought more students into math departments, which ultimately contributed to broadening the…

The Cell Phone modeling task centers on a Fermi real-world estimation question. The task and rubric can be used at different grade levels to focus on the modeling process and classroom community. Finding time and space to engage students, especially novice modelers, in mathematical modeling can be a challenge, yet the benefits of modeling are…

For 15 years, Complete College America (CCA) has been building movements for scaled systemic change and transforming institutions. While CCA has expanded their efforts over the past 15 years, they have studied the best ideas and co-designed the most promising practices to move the needle on college completion. They have learned a lot about how to…

Students with disabilities often face significant challenges in developing mathematical problem-solving skills, which are critical for academic success. Traditional problem-solving interventions have primarily focused on skill acquisition, leading to issues with knowledge application in real-world contexts. Enhanced Anchored Instruction (EAI)…

In this abstract, I share a field report. It is an administration manager's experience of how solutions to wicked problems can be developed by approaching the task with an action-learning attitude and using democratic methods in a Catholic parish association. In detail, it had to be worked out, how pastoral work can be shaped under 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…

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.

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…

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…

The importance of mathematical problem posing has been acknowledged by many researchers. In this theoretical paper, we want to capture different meanings and aspects of problem posing by approaching it from three different levels: (1) by comparing definitions, (2) by relating it to other constructs, and (3) by referring to research and teaching…

Educators recognize that parental participation is a critical factor in the success of children within a school setting. This is particularly true for parents who have children with disabilities or who are from a culturally or linguistically diverse background. However, reaching out to these families can be a difficult task even for the most…