Solar energy is clean, free, and abundant worldwide. The challenge, however, is to convert it to useful forms that can reduce our reliance on fossil fuels. This article presents an activity for physical science classes in which students learn firsthand how solar energy can be used to produce electricity specifically for transportation. The…

Understanding the computational concepts on which countless digital applications run offers learners the opportunity to no longer simply read such media but also become more discerning end users and potentially innovative "writers" of new media themselves. To think computationally--to solve problems, to design systems, and to process and…

The International Technology and Engineering Educators Association (ITEEA) defines STEM as a new transdisciplinary subject in schools that integrates the disciplines of science, technology, engineering, and mathematics into a single course of study. There are three major problems with this definition: There is no consensus in support of the ITEEA…

A good formula is like a good story, rich in description, powerful in communication, and eye-opening to readers. The formula presented in this article for determining the coefficients of the binomial expansion of (x + y)n is one such "good read." The beauty of this formula is in its simplicity--both describing a quantitative situation…

We describe a modeling project designed for an ordinary differential equations (ODEs) course using first-order and systems of first-order differential equations to model the fermentation process in beer. The project aims to expose the students to the modeling process by creating and solving a mathematical model and effectively communicating their…

Is anything more refreshing than going for a nice, long swim? The math scenarios presented in this article will take the reader back to hot summer days and remind the reader what a cool dip in the water feels like. Solving these problems is enjoyable and encourages the solver to think of the many ways that math is all around--even in the middle of…

To prepare a differently educated citizenry and to play meaningful roles in new forms of community-building, colleges and universities must model informed and collaborative ways of learning and working within their own institutional contexts as well as through their interactions with the broader society of which they are an integral part. The path…

Past educational reforms have failed because they didn't meet teachers where they were. They expected major changes in practices that may have been unrealistic for many teachers even under ideal professional learning conditions. Instead of promoting broad scale changes, improvement may be more likely if they are composed of small yet powerful…

The Puppy Love problem asked fifth and sixth grade students to use their prior knowledge of measures of central tendency to determine a data set when given the mean, mode, median, and range of the set. The problem discussed in this article is a task with a higher level of cognitive demand because it requires that students (1) explore and…

In this paper, we present a set of activities for an introduction to solving counting problems. These activities emerged from a teaching experiment with two university students, during which they reinvented four basic counting formulas. Here we present a three-phase set of activities: orienting counting activities; reinvention counting activities;…

This work aims to demonstrate the use of Excel spreadsheets for solving L-L extraction problems. The key to solving the problems successfully is to be able to determine a tie line on the ternary diagram where the calculation must be carried out. This enables the reader to analyze the extraction process starting with a simple operation, the…

In this undergraduate analytical chemistry experiment, students quantitatively assess the antibacterial activity of essential oils found in thyme leaves ("Thymus vulgaris") in an authentic, research-like environment. This multi-week experiment aims to instill green chemistry principles as intrinsic to chemical problem solving. Students…

The article opens with a Geoboard Triangle Quest in this form: "How many noncongruent triangles can be constructed on a 4 × 4 geoboard? How do you know? Justify your answer with significant supporting work." The use of advanced digital technologies as tools for problem solving receives much attention in the methods classes if the…

Low achievement in mathematics education has been an increasing problem in the recent years in some countries. According to a 2010 study from the U.S. Department of Education, blended learning classes produce statistically better results than their face-to-face. There is also an increasing number of students using smartphones and tablets in…

In this work, we review and share some useful technology for mathematics educators that can help to enhance their pedagogical practices to motivate students to improve their further understanding of differential equations after an initial exposure to the topic in an undergraduate class. In particular, we present some innovative ways to employ…