It is well known that the needle of a compass in a magnetic field deflects, and that a compass near a conductive wire carrying a stable electric current deflects its needle. The only explanation of this observation is that the current-carrying wire creates a magnetic field around it. The strength of the magnetic field at any point near the wire…

This short note discusses how the optimality conditions for minimizing a multivariate function subject to equality constraints have been covered in some undergraduate Calculus courses. In particular, we will focus on the most common optimization problems in Calculus of several variables: the 2 and 3-dimensional cases. So, along with sufficient…

If a ball rolls in a circular path on a horizontal surface at constant speed then its horizontal rotation axis changes direction with time. A simple experiment is presented showing that the torque applied to the ball is equal to the rate of change of its angular momentum, even though the magnitudes of its angular velocity and angular momentum…

What is the paradigmatic direction of teaching and learning mathematics? According to Yves Chevallard, father of the anthropological theory of the didactic, the current paradigm is characterized by an obsolescent form of monumentalism. But is a new paradigm possibly on the rise? And what is the role of powerful organizations such as the OECD? We…

Instruction in special collections and archives spaces has evolved from the once ubiquitous show-and-tell sessions, but it remains reliant on the one-shot model where classes visit the reading room to work with primary source material in a standalone session. As Nicole Pagowsky points out, "One-shots are transactional; content is requested…

Enrico Fermi is remembered for his many contributions to theoretical and experimental physics, but from an educational point of view he also popularized the use of the kind of questions we now call "Fermi problems" (or "Fermi questions"). Fermi problems (FPs) are back-of-envelope problems that arose from the need to make order…

The article gives multiple examples of types of books that can be used with learners at nearly all levels, including pre-school learners, and suggest ways that book creation can be integrated into lessons.

Teaching symmetry point groups to introductory inorganic chemistry students is often complicated by the difficulties students face with mental manipulation of complex molecules. Additionally, most textbooks provide practice in the form of random two-dimensional molecules or figures of little significance. As an alternative, an assignment is…

This edited volume brings together innovative research in the field of Science Education, fostering scientific citizenship in an uncertain world. The nineteen chapters presented in this book address diverse topics, and research approaches carried out in various contexts and settings worldwide, contributing to improving and updating knowledge on…

Mathematics coaching is complex work, and coaches must be supported to become experts in mathematics, mathematics instruction, and mathematics coaching. Using video and interview data from 12 mathematics coaches and one district administrator in one public school district in the southeastern USA, this qualitative study explores how the…

In this article we discuss some of the ethical dimensions of design-based research, which we believe should feature more prominently in CSCL scholarship. We begin by sketching out why it is important for CSCL researchers to articulate their visions of the good and how this can be accomplished in a systematic way. We then outline how ethical…

This paper addresses the rift between the teacher's sense of self as a causal agent and the experience of being in lack of control in the classroom, by way of Hans Vaihinger's philosophy of 'as if.' It is argued that understanding agential control in terms of a valuable educational fiction--a practical (ethical) fiction in Vaihinger's…

Tongue twisters are a controversial pronunciation teaching classic. Whereas some see tongue twisters difficult and frustrating for learners, others find them fun and motivating. This study was inspired by these opposing views and the fact that previous studies have failed to offer convincing proof of whether this technique works for L2…

In this article, we consider certain minimization problems. If d[subscript 1], d[subscript 2] and d[subscript 3] are the distances of a boundary or inner point to the sides of a given triangle, find the point which minimizes d[subscript 1][superscript n] + d[subscript 2][superscript n] + d[subscript 3][superscript n] for positive integer n. These…

This study examined high school chemistry students' understandings of big ideas--matter and energy, how these understandings are related to macro and submicro representations and fine-grained distinguishing characteristics of students' explanations. The study was conducted in the context of computer-based models and model-based assessments.…