When students begin work with fraction division in fifth grade or sixth grade, they bring with them experiences from whole-number division. Many students think that a division problem should lead to a quotient that is smaller than the dividend. It is also common for students to believe that the dividend should be larger than the divisor. Many, if…

The authors developed The Paper Plane Challenge as one of a three-part response to The Aerospace Engineering Challenge. The Aerospace Engineering Challenge was the second of three multi-part activities that they had developed with the teachers during the year. Their aim was to introduce students to the exciting world of engineering, where they…

For many students, making connections between mathematical ideas and the real world is one of the most intriguing and rewarding aspects of the study of mathematics. In the Common Core State Standards for Mathematics (CCSSI 2010), mathematical modeling is highlighted as a mathematical practice standard for all grades. To engage in mathematical…

If the prospective students of probability lack a background in mathematical proofs, hands-on classroom activities may work well to help them to learn to analyze problems correctly. For example, students may physically roll a die twice to count and compare the frequency of the sequences. Tools such as graphing calculators or Microsoft Excel®…

This guide is a list of tools that can be used in continued implementation of strong programming powered by Social and Emotional Learning (SEL) competencies. This curated resource pulls from across the landscape of policy, research and practice, with a description of each tool gathered directly from its website.

To help satisfy the pressing need for technology-related professional development for in-service teachers, the Global Academic Essentials Teacher Institute (GAETI) was implemented to provide in-service foreign language and social studies teachers with content, pedagogy, and technology explorations centered on the teaching of the Common Core State…

Teachers use the word assessment to describe any method of gathering information about student learning. Whether it be formative assessment (intended to guide instructional decisions) or summative assessment (a reflection on the entirety of student learning from prior instruction), teachers are constantly working to identify what their students…

This article invites media arts and technology educators to find synergies in their classroom curriculum and practice. Encouraging the use of the National Media Arts Standards it summons teachers to develop a useful framework for technological practice that utilizes arts knowledge and pedagogies.

Many interesting research and design questions occur at the intersections of traditional disciplines, yet most coursework and research programs for undergraduate engineering students are focused on one discipline. This leads to underutilization of the potential in better preparing students through multidisciplinary projects. Identifying this…

Acid-base equilibrium is one of the most important and most challenging topics in a typical general chemistry course. This article introduces an alternative to the algebraic approach generally used in textbooks, the graphical log "C" method. Log "C" diagrams provide conceptual insight into the behavior of aqueous acid-base systems and allow…

In an open competition, students were to determine the mass of a metal cylinder hanging on a spring inside a transparent enclosure. With the time for experiments limited to 24 h due to the unexpectedly large number of participants, a few surprisingly accurate results were submitted, the best of them differing by no more than 0.5% from the true…

Human performance technology (HPT), like other concepts, models, and frameworks that we use to describe the world in which we live and the way we organize ourselves to accomplish valuable activities, is built from paradigms that were fresh and relevant at the time it was conceived and from the fields of study from which it grew. However, when the…

Researchers have speculated that children find it more difficult to acquire conceptual understanding of the inverse relation between multiplication and division than that between addition and subtraction. We reviewed research on children and adults' use of shortcut procedures that make use of the inverse relation on two kinds of problems:…

A visual proof that 1 - (1/2) + (1/4) - (1/8) + ... 1/(1+x[superscript 4]) converges to 2/3.

An idempotent satisfies the equation x[superscript 2] = x. In ordinary arithmetic, this is so easy to solve it's boring. We delight the mathematical palette here, topping idempotents off with modular arithmetic and a series of exercises determining for which n there are more than two idempotents (mod n) and exactly how many there are.