Engineers are faced with solving important problems every day and must follow a step-by-step design process to arrive at solutions. Students who are taught an effective design process to apply to engineering projects begin to see problems as an engineer would, consider all ideas, and arrive at the best solution. Using an effective design process…

Sprego is programming with spreadsheet functions. The present paper provides introductory Sprego examples which have so far only been available in Hungarian. Spreadsheet environments offer both a programming tool which best serves beginner and end-user programmers' interest, and an approach which lightens the burden of coding and language details.…

The 1998 paper by Martin Mühlenbrock, Frank Tewissen, and myself introduced a multi-agent architecture and a component engineering approach for building open distributed learning environments to support group learning in different types of classroom settings. It took up prior work on "multiple student modeling" as a method to configure…

"WeBWorK" CLASS combines the best features of online homework and digital whiteboards to create a system that provides instructors with information on students' problem-solving processes, as well as their final answer. The system's utilization of tools that can sort students based on correct and incorrect homework and quiz answers and…

I describe the first stages of a process of design research in which I employ problem-based learning in a course in engineering ethics, which fulfills a requirement for students in engineering degree programs. The aim of the course is to foster development of particular cognitive skills contributing to moral imagination, a capacity to notice,…

More than 2,200 years ago, Eratosthenes, who was a Greek astronomer, geographer, and mathematician, used a simple proportion involving the distance between two ancient cities and measures of shadows cast in those cities during a summer solstice to estimate the circumference of Earth (Nicastro 2008, 25-28). Today, middle school students can use…

Children's background experiences not only make them unique individuals, but also impact their interactions with texts because of their varied schema. Teachers who work with children should keep in mind Gregory Smith's (2002) five thematic patterns (cultural studies, nature studies, real world problem solving, internship and entrepreneurial…

During the past few years, several of the authors have incorporated student problem posing as a regular instructional feature in their classrooms. When they offer their students the opportunity to construct their own problems, particularly during the course of an entire school year, they create many novel tasks. Student-created tasks not only…

We describe an important elaboration of our multiscale/multiresolution model for solving the Traveling Salesman Problem (TSP). Our previous model emulated the non-uniform distribution of receptors on the human retina and the shifts of visual attention. This model produced near-optimal solutions of TSP in linear time by performing hierarchical…

Content authenticity and correctness is one of the important challenges in eLearning as there can be many solutions to one specific problem in cyber space. Therefore, the authors feel it is necessary to map problems to solutions using graph partition and weighted bipartite matching. This article proposes an efficient algorithm to partition…

Consider a skier who goes down a takeoff ramp, attains a speed "V", and jumps, attempting to land as far as possible down the hill below (Fig. 1). At the moment of takeoff the angle between the skier's velocity and the horizontal is [alpha]. What is the optimal angle [alpha] that makes the jump the longest possible for the fixed magnitude of the…

Using calculus only, we find the angles you can rotate the graph of a differentiable function about the origin and still obtain a function graph. We then apply the solution to odd and even degree polynomials.

We show that inside every triangle the locus of points satisfying a natural proportionality relationship is a parabola and go on to describe how this triangle-parabola relationship was used by Archimedes to find the area between a line and a parabola.

A core component of applied educational and child psychology practice is the skilfulness with which practitioners are able to rigorously structure and conceptualise complex real world human problems. This is done in such a way that when they (with others) jointly work on them, there is an increased likelihood of positive outcomes being achieved…

As STEM educators, we know it is beneficial to train students to think critically and mathematically during their early mathematical lives. To this end, the author teaches the College Algebra/Precalculus course in a flipped classroom version of an inquiry-based learning style. However, the techniques described in this paper can be applied to a…