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…

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…

In this work the authors investigate the effectiveness of robotics in education. Rather than creating excitement for children when playing with robots in games, they are examining the overall learning environment where a robot acts as a teaching assistant. They designed a suitable lesson plan when groups of teenagers participate in activities…

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…

To further understand student thinking in the context of combinatorial enumeration, we examine student work on a problem involving set partitions. In this context, we note some key features of the multiplication principle that were often not attended to by students. We also share a productive way of thinking that emerged for several students who…

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…

Teachers and students commonly use various concrete representations during mathematical instruction. These representations can be utilized to help students understand mathematical concepts and processes, increase flexibility of thinking, facilitate problem solving, and reduce anxiety while doing mathematics. Unfortunately, the manner in which some…

The "Wisdom of Crowds" hypothesis has been introduced into many fields, but not into education. Groups with diverse knowledge and skills make better decisions than homogenous groups or expert groups. Diversity adds different points of view, which improve the problem solving ability of the group. The increased use of social networks makes…

A problem-solving scaffold approach to synthesis was developed and implemented in two intervention sections of Chemistry 2211K (Organic Chemistry I) at Georgia Gwinnett College (GGC). A third section of Chemistry 2211K at GGC served as the control group for the experiment. Synthesis problems for chapter quizzes and the final examination were…

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…

This paper analyses meaning-making processes in a blended setting--face-to-face interaction and web forum--purposely created for collaborative learning activity. The analysis focuses on one pair out of 14 dyads. The dyad comprises two female students aged 17 and 18 who attended a Brazilian third-year state secondary school. We envisioned…

Implementing an integrated sequence of concrete-representational-abstract depictions of mathematics concepts (CRA-I) can improve the mathematics achievement of students with disabilities, and explicit instructional strategies involving problem-solving heuristics and student verbalizations can help facilitate students' conceptual understanding of…