Almost all finite groups encountered by undergraduates can be represented as multiplicative groups of concise block-diagonal binary matrices. Such representations provide simple examples for beginning a group theory course. More importantly, these representations provide concrete models for "abstract" concepts. We describe Maple lab…

The calculation of the total surface area of prisms forms part of the Mathematics curriculum in South Africa. This paper explores Grade 8 students' errors when learning about the surface area of prisms. The study was guided by the interpretive paradigm and adopted a qualitative approach in a form of a case study design. Data from diagnostic test's…

The present study investigated the association of students' fundamental ideas and misconceptions about ontological features of atom identity and behavior with the formation of their portrayed representations of the atomic structure. Participants (n = 421) were secondary education students in the eighth, tenth, and twelfth grades. Students'…

This article chronicles the author's positive experience of conducting a liberal arts mathematics course with no testing whatsoever. The format of the course is discussed, and student responses to the format are summarized.

Young children's symbolic magnitude understanding, or knowledge of how written numerals and number words can be ordered and compared, is thought to play an important role in their mathematical development. There is consistent evidence that symbolic magnitude skills predict mathematical achievement in later childhood and adulthood. Yet less is…

Understanding the relationship between protein structure and function can be challenging for students. Molecular visualization software aids students in this problem by allowing manipulation of structures from new and deeper perspectives. In this communication, an activity using iMolview Lite, structure visualization software for portable devices,…

Polarization of light is one of the topics in the Croatian high school physics curriculum. It is taught in the final year of high school education. Twenty-seven Croatian high-school students (aged 18-19 years) were interviewed after regular instruction about their understanding of polarization of light and the model of light itself. This paper…

Productive failure has shown positive effects on conceptual and transfer measures, but no clear effects on procedural measures. It is therefore an open question whether, and to what extent, productive failure methods may be used to enhance the learning of procedural skills. A typical productive failure study focuses on a single, complex concept;…

Common divisor is one of the concepts that started to be learned in secondary school and forms the basis of many concepts. But students generally have difficulty in making sense of it. The purpose of this study is to investigate concept formation processes of common divisor through a case study on seven sixth grade students. To do this, we…

A significant goal when teaching at the secondary education level is to present the generality of the procedures that are being used to describe a wide range of different physical phenomena. However, this approach is abandoned by physics instructors in many cases since the general mathematical background needed to present the above generality is…

Despite rapid changes in education, science classrooms will remain central forums where fragmented pieces of information are brought together to construct coherent knowledge as concepts and explanatory scientific storylines. There is limited work stressing the importance of the interplay between how content is communicated through pedagogical…

Biochemistry curricula present a particular challenge to undergraduate students with abstract concepts which can lead to misconceptions that impede learning. In particular, these students have difficulty understanding enzyme structure and function concepts. Targeted learning activities and three-dimensional (3D) physical models are proposed to…

Introductory lab courses have been a staple of the physics curriculum for over 100 years. Yet these courses are now poised for change as recent research shows that they do not meet a frequent goal of enhancing student understanding of lecture content. In thinking about how to move forward, a look back at experiment courses in history seems wise.…

The laboratory experiment regarding esterification of ethylene glycol with acetic acid to ethylene glycol diacetate using resin catalysts in a continuous flow was designed to carry out the reaction in a flow through an inquiry-guided approach. Incorporating the burgeoning field of continuous flow chemistry into the educational infrastructure, the…

Anthropogenic climate change remains divisive in the United States, where skepticism of the scientific consensus is associated with conservative worldviews, resulting in political polarization. This study considers three hypotheses regarding U.S. polarization over climate change that have emerged from social psychology research and applies them to…