Analysis of collisions is standardly included in the introductory physics course. In one dimension (1D), there do not seem to be any unusual issues: Typically, the initial velocities of the two colliding objects are specified, and the problem is to find the final velocities. In 1D there are therefore two unknown variables. One can write the…

Membrane separation processes, from reverse osmosis to ultrafiltration to microfiltration, are gradually receiving more and more emphasis in undergraduate chemical engineering curricula. Of these processes, ultrafiltration tends to be the most amenable to the standard chemical engineering approach of theory development, mass and/or energy…

The "big bad wolf" chased the squealing children around the playground as they looked for a place to hide. Because Mr. Lòpez and Ms. Kim had introduced the work of engineers and the engineering design process into their unit on The Three Little Pigs, they knew their preschool students would choose a structure that could withstand any…

Problem-based learning (PBL) is an innovative educational approach that dates back to the 1960s. However, the twenty-first century goal of sustainable education poses a challenge to PBL, especially as it relates to isolation. Here we discuss the underlying issue of isolation in three respects. First, the information-processing model of PBL depends…

With problem-solving as the focus and wisdom as the goal, the concept of giftedness is reconceptualized in the 21st century context. The two most prominent constructs in the field of education for the gifted, creativity and intelligence, are integrated into a view of exceptional talent as consisting of the ability and willingness to solve complex…

When organic students are asked to design a total synthesis of a molecule, they are often overwhelmed by the multitude of possible transformations. A decision tree is a useful tool to break complex problems up into simpler steps and scaffold the thinking process that many seasoned chemists take for granted. While many comprehensive resources…

As consultants who infuse the "Habits of Mind" into schools, the authors explain how spreading these habits through school can increase the whole school's well-being and feed teacher efficacy. They list seven factors that can create a "culture of efficacy" that draws on these 16 habits (thinking dispositions at the core of…

The Pearson correlation coefficient can be recovered from the two least squares regression lines y[with circumflex] = b[subscript 0] + b[subscript 1]x and x[with circumflex] = a[subscript 0] + a[subscript 1]y without any data. This can be done both algebraically and geometrically. This can be done without data even when the scales of the variables…

The simple vehicle routing problem (VRP) is a common topic of discussion in introductory operations research/management science courses. The VRP can be framed in a variety of ways, and it can be difficult to solve to optimality. For solution purposes, introductory textbooks demonstrate how Excel's Evolutionary Solver (ES) add-in produces a…

This paper reports on a project that sought to enhance problem-solving practices within a cluster of primary schools. In-service teachers' description of their approach to problem-solving suggested it was treated as an isolated practice that occurred after concepts had been taught; often focusing on teaching particular problem-solving strategies…

In this work three examples of textbook circuits (resistor-capacitor, resistor-inductor and resistor-inductor-capacitor) have been modeled by employing the Euler method for the approximate solution of differential equations using algorithms implemented in the "Python" programming language. The aim of this work was to demonstrate how…

This paper is about an experimental problem on forced oscillations, which was given to 14-year-old primary school pupils at the Slovenian national (final) level of the physics competition in April 2019. At the time when the competition took place these pupils were approaching the end of the school year, when they encountered physics as a school…

We present in this paper a pair of approaches to support mathematics educators and learners in formulating original tasks. In particular, we facilitate the posing of rich mathematical problems by using two novel methods that were created by a mathematics department at a K-12 school in the United States, and further developed alongside our students…

In this article, the authors share the potential for two types of atypical arrays (composite and partially hidden) to stimulate initial multiplicative ideas and strategies from students in a second-grade classroom. Composite arrays are defined here as nonarrays that are composed of multiple smaller complete arrays. The atypical arrays were…

This paper presents an approach to implement learning objects for teaching and learning problem-solving techniques based on computer programming. The demonstrated approach exploits computer-based interactive animations and computer graphics. The main feature of this approach is its simplicity for exploring the concepts and structures of the…