Building passion and potential for creative learning in higher education involves deliberately seeking to understand, appreciate, and teach for creativity. Recognizing the urgent need for creativity and problem solving skills, and understanding that instructors must embrace creative learning for themselves first, is central. Creativity cannot be…

New assessments that measure deeper learning--whether students understand challenging content and are able to apply that knowledge to think critically, solve problems, communicate their understanding, and work with their peers--are essential if students are to develop the competencies they need to succeed in an increasingly complex world. Such…

Social scientists use adjacency tables to discover influence networks within and among groups. Building on work by Moler and Morrison, we use ordered pairs from the components of the first and second singular vectors of adjacency matrices as tools to distinguish these groups and to identify particularly strong or weak individuals.

The art gallery problem asks for the maximum number of stationary guards required to protect the interior of a polygonal art gallery with "n" walls. This article explores solutions to this problem and several of its variants. In addition, some unsolved problems involving the guarding of geometric objects are presented.

While contemplating ways to extend the author's ninth-grade honors geometry students' thinking and knowledge about area and perimeter, he discovered an interesting type of problem based on Erickson's (2001) rectangle problem, which he had been using for ten years. Erickson's original problem involves creating random rectangles with lengths and…

When elementary ordinary differential equations (ODEs) of first and second order are included in the calculus curriculum, second-order linear constant coefficient ODEs are typically solved by a method more appropriate to differential equations courses. This method involves the characteristic equation and its roots, complex-valued solutions, and…

It is important to let students see the value of mathematics in design--and how mathematics lends perspective to problem solving. In this article, the author describes a water-service challenge which enables students to design a water utility system that uses surface runoff into an open reservoir as the potable water source. This challenge…

A simple partial version of the Fundamental Theorem of Calculus can be presented on the first day of the first-year calculus course, and then relied upon repeatedly in assigned problems throughout the course. With that experience behind them, students can use the partial version to understand the full-fledged Fundamental Theorem, with further…

This paper presents a theoretical basis for cultivating engineering education as a complex system that will prepare students to think critically and make decisions with regard to poorly understood, ill-structured issues. Integral to this theoretical basis is a solution space construct developed and presented as a benchmark for evaluating…

This article describes the technique of introducing a new variable in some calculus problems to help students master the skills of integration and evaluation of limits. This technique is algorithmic and easy to apply.

The focus of this special section is on the processes involved when solving information-based problems. Solving these problems requires from people that they are able to define the information problem, search and select usable and reliable sources and information and synthesise information into a coherent body of knowledge. An important aspect…

In the current time of globalization, collaboration among people in virtual environments is becoming an important precondition of success. This trend is reflected also in the educational domain where students collaborate in various short-term groups created repetitively but changing in each round (e.g. in MOOCs). Students in these kind of dynamic…

Teaching design to middle and high school students can be challenging. One of the first procedures in teaching design is to help students gather information that will be useful in the design phase. An early stage of engineering design as described by Lewis (2005), calls for the designer to establish the state of the art of the problem. During this…

As the National Middle School Association wrote, "No other age level is of more enduring importance because the determinants of one's behavior as an adult, self concept, learning interests and skills, and values largely are formed in this period of life." During this influential time in the lives of gifted adolescents, it is important to…

Open-ended questions, as discussed in this article, are questions that can be solved or explained in a variety of ways, that focus on conceptual aspects of mathematics, and that have the potential to expose students' understanding and misconceptions. When working with teachers who are using open-ended questions with their students for the…