We propose an introduction to the Laplace transform in which Riemann sums are used to approximate the expected net change in a function, assuming that it quantifies a process that can terminate at random. We assume only a basic understanding of probability.

Clients and practitioners alike are often confused about the ultimate purpose of action learning (AL). Because of the title of the method, many believe the primary goal of AL is to generate learning. This article clarifies the relationship between action, learning, and solutions. It also provides historical evidence to support the conclusion that…

Patterns are a ubiquitous phenomenon. They exist in nature's plant species emerging as a complete order from truncated matter. Patterns are also present in the fine arts where the aesthetic properties of form exist and conjugate through paintings and sculptures. Mathematical patterns, the focus of this position paper, dominate financial scenarios,…

Most word processors, including Google Docs™ and Microsoft® Word, include an equation editor. These are great tools for the occasional homework problem or project assignment. Getting the mathematics to display correctly means making decisions about exactly which elements of an expression go where. The feedback is immediate: Students can see…

This paper, "A critical reflection on my learning and its integration into my professional practice," was successfully submitted for a Master's programme at the University of Bath (UK) in 2010, whilst Sally was working full-time as a teacher in a large secondary school in an English town 10 miles from the city of Bath. Sally died of a…

In this article the authors describe a project during which they unpacked fraction standards, created rigorous tasks and lesson plans, and developed formative and summative assessments to analyze students' thinking about fraction multiplication. The purpose of this article is to (1) illustrate a process that can be replicated by educators…

This column presents ideas and techniques to enhance science teaching. In today's classrooms, teachers face numerous challenges. They are preparing students for jobs and careers that are not even conceived of yet. Assessments are being used to address students' college and career readiness and to promote critical thinking and problem solving.…

The degrees of freedom (DOF) concept is a powerful tool that has been taught since at least the '70s in undergraduate curriculum, typically introduced in the context of a first course on material and energy balances. The concept, however, has not been widely applied beyond the material balance domain and in general is not taught as a unified…

This article will share the intellectual journey E. Paul Torrance and I traveled in 2001, in which we explored psychology, science and ancient wisdom and traditions, including Native American and indigenous traditions, to establish a foundation for spiritual intelligence. This section will be followed by ways to develop and nurture spiritual…

Youth involved in 4-H projects have been engaged in science-related endeavors for years. Since 2006, 4-H has invested considerable resources in the advancement of science learning. The new Minnesota 4-H Science of Agriculture Challenge program challenges 4-H youth to work together to identify agriculture-related issues in their communities and to…

We present a novel guided inquiry second semester organic chemistry laboratory rearrangement experiment. Students performed the Favorskii Rearrangement to obtain methyl cyclopentanecarboxylate in good yields. The students learned about the individual steps of the Favorskii mechanism and were required to propose a complete reaction mechanism and…

Guessing, for Pólya, is an important way of getting an initial handle on a mathematical problem. An argument can be made to place guessing in any one of the first three steps of the four-step approach to problem solving as described in "How to Solve It" (Pólya 1945). It could be a part of understanding the problem, devising a plan, or…

After teaching the concept of division with remainders for many years, Vanessa Battreal, Vanessa Brewster, and Juli Dixon noticed that interpreting remainders in contextualized problems is particularly challenging for elementary school students. To effectively interpret remainders, students must attend to problem context and consider carefully…

In today's physical education classroom, many teachers feel starved for fresh, innovative activities to teach. This article presents team handball (TH) as one such activity. Although TH is not a new activity (it was first played toward the end of the 19th century in countries such as Denmark, Germany and Sweden), for many students in the United…

Often students have a difficult time when asked to use critical thinking skills to solve a problem. Perhaps students have a difficult time adjusting because teachers frequently tell them exactly what to do and how to do it. When asked to use critical thinking skills, students may suddenly become confused and discouraged because the teacher no…