This research investigated the viability of learning by self-managing split-attention worked examples as an alternative to learning by studying instructor-managed integrated worked examples. Secondary school students learning properties of angles on parallel lines were taught to integrate spatially separated text and diagrammatic information by…

Since the mid-20th century, the standard U.S. high school and college math curriculum has been based on two years of algebra and a year of geometry, preparing students to take classes in pre-calculus followed by calculus. Students' math pursuits have been differentiated primarily by how far or how rapidly they proceed along a clearly defined…

Most people would agree that helping students learn new information is important; however, there are numerous methods for achieving this goal, and not all of them have been proven to be effective. One method with intuitive appeal and some empirical backing is prompting students to self-explain. A self-explanation can be defined as generating…

Although it can be visualized fairly easily and its symmetry group is easy to calculate, the permutahedron is a somewhat neglected combinatorial object. We propose it as a useful case study in abstract algebra. It supplies concrete examples of group actions, the difference between right and left actions, and how geometry and algebra can work…

Psychologists, philosophers, and educators have traditionally interpreted the phenomenon of insight learning as the result of the sudden comprehension of abstract/conceptual ideas. The present article shows that such phenomenon may also follow and emerge from the kinetic movements of the human body; that is, we conceptualize insight learning as a…

This article presents an application of standard undergraduate ODE techniques to a modern engineering problem, that of using a tuned mass damper to control the vibration of a skyscraper. This material can be used in any ODE course in which the students have been familiarized with basic spring-mass models, resonance, and linear systems of ODEs.…

While the study of geometry in some shape or form has existed for many millennia, it is within the past twenty years that a shift has occurred in how geometry may be learned through computer-based interactive geometric software. Software programs like The Geometer's Sketchpad[TM], Cabri[TM], and GeoGebra[TM] allow users to construct interactive…

The present research investigated whether immediate metacognitive feedback on students' help-seeking errors can help students acquire better help-seeking skills. The Help Tutor, an intelligent tutor agent for help seeking, was integrated into a commercial tutoring system for geometry, the Geometry Cognitive Tutor. Study 1, with 58 students, found…

For developing riding skills on mountain bikes, it is important to know how the centre of mass of a bicycle and its rider changes with ground inclination or with rider position. We show here a new method for finding the location of this point by measuring the normal forces acting on the wheels in two positions with a digital weight indicator. This…

A set of axioms for classical absolute geometry is proposed that is accessible to students new to axioms. The metric axioms adopted are the ruler axiom, triangle inequality and the bisector axiom. Angle measure is derived from distance, and all properties needed to establish a consistent system are derived. In particular, the SAS congruence…

In this short note, by using one of Li and Liu's theorems [K.-H. Li, "The solution of CIQ. 39," "Commun. Stud. Inequal." 11(1) (2004), p. 162 (in Chinese)], "s-R-r" method, Cauchy's inequality and the theory of convex function, we solve some geometric inequalities conjectures relating to an interior point in triangle. (Contains 1 figure.)

Effective competition in a rapidly growing global economy places demands on a society to produce individuals capable of higher-order critical thinking, creative problem solving, connection making, and innovation. We must look to our teacher education programs to help prospective middle grades teachers build the mathematical habits of mind that…

Introduction: For decades, prior to the inception of the Common Core State Standards (CCSS), the National Assessment of Educational Progress (NAEP) was the only vehicle through which states could assess the progress of their students using a common metric. Now, 45 states, 4 U.S. territories, and the District of Columbia have adopted the CCSS to…

This case is part of a teaching experiment that sought to provide insight into how the use of mathematics technology affects the internal mathematical representations possessed by adult developmental mathematics students. Sequences of dot patterns were examined and analyzed by the participant. He then used the algebraic features of a dynamic,…

A three-step active-learning approach is described to enhance the spatial abilities of general chemistry students with respect to three-dimensional molecular drawing and visualization. These activities are used in a medium-sized lecture hall with approximately 150 students in the first semester of the general chemistry course. The first activity…