This work presents experiments to teach fundamentals of automation through a sequence of laboratory practices that naturally guide to development of an on/off control system. It focuses on the integration of technological and scientific concepts, based on an educational approach associated with a problem-solving technique.

Given two vectors u and v, their cross product u × v is a vector perpendicular to u and v. The motivation for this property, however, is never addressed. Here we show that the existence of the cross and dot products and the perpendicularity property follow from the concept of linear combination, which does not involve products of vectors. For our…

We aim to open up discussion about the intertwined roles of teachers and tasks that involve students communicating about mathematics when working in groups. Over many years we have observed, researched and ourselves have taught students working on mathematics in groups and find that it is often easier to pay attention to the forms of communication…

A central goal of physics education is to teach problem-solving competency, but the description of the nature of this competency is somewhat fragmentary and implicit in the literature. The present article uses recent historical scholarship on Arnold Sommerfeld and Enrico Fermi to identify and characterize two positions on the nature of physics…

Physics is often seen as an excellent introduction to science because it allows students to learn not only the laws governing the world around them, but also, through the problems students solve, a way of thinking which is conducive to solving problems outside of physics and even outside of science. In this article, we contest this latter idea and…

We deal with an application of partial differential equations to the correct definition of a wine cellar. We present some historical details about this problem. We also discuss how to build or renew a wine cellar, creating ideal conditions for the ageing process and improving the quality of wines. Our goal is to calculate the optimal depth…

Most studies on fairness behavior in preschool focus on fair resource allocation and on children's behavior when faced with fairness dilemmas. The purpose of this study is to understand preschoolers' point of view: what do they think when presented with various scenarios that call for fairness behavior? We interviewed 66 children aged 3.5-6 years,…

Open-ended design problems have become an important component in our educational landscape (Grubbs and Strimel in J STEM Teach Educ 50(1):77-90, 2015; Jonassen et al. in J Eng Educ 95:139-151, 2006; National Research Council in Education for life and work: developing transferable knowledge and skills in the 21st Century, National Academies Press,…

The literature on insight problems--problems that supposedly can only be solved by rejection of an initial faulty problem representation and sudden comprehension of another, nonobvious representation (restructuring)--suggests that the size of initial representations affects the very process of problem solving. Large initial representations impose…

The aim of the study was to examine mathematics teacher candidates' strategies used in solving non-routine problems. The research was carried out with 104 mathematics teacher candidates studying at a state university during the first term of the 2014-2015 academic year in Turkey. Data was collected through Problem Solving Test which was consisted…

This article describes two heuristic strategies for problem solving: the "use of false assumption" strategy and the "use of double false assumption" strategy. Both of these strategies have their roots deep in history. In this article, we define these two strategies and illustrate their use in a problem developed by Frances…

In this study, we continue our efforts to address students' difficulties understanding organic chemistry, particularly in connecting structure to function and using the language of chemistry to explain how and why reactions occur. For the first time, we have characterized students' work and problem-solving strategies on familiar and unfamiliar…

Finding intersections, unions, and complements of sets is an essential issue in elementary mathematics. It builds the foundation for set theory, probability, logic, and other topics. It is commonly recognized that drawing a Venn diagram, which was first introduced by the British philosopher and mathematician John Venn in 1881, is a classic and…

In the core of computational thinking (CT) practices is problem-solving. However, there is little research on connecting CT with problem solving processes. We developed a computer-based assessment on CT that can log students' problem-solving processes and administered it to a group of fifth graders as a pre- and post- measure of a robotics…

The Program for the International Assessment of Adult Competencies (PIAAC) is a cyclical, large-scale study of adult skills and life experiences focusing on education and employment. It is coordinated by the Organization for Economic Cooperation and Development (OECD) and developed by participating countries with the support of the OECD. Between…