In this paper, the Singapore school calculus curriculum at the upper secondary and the pre-university levels is examined in the light of the Singapore mathematics curriculum framework. Three key features of the calculus content are discerned: (1) an intuitive approach to calculus supported by the use of technology; (2) an emphasis on techniques;…

Higher education providers need to deliver graduates with the conceptual understanding required for professional life. Conceptual understanding entails a synthesis of relevant facts, theories and practices that influence occupational performance. To help align curricula with individual student differences, this study investigates differences in…

Early childhood mathematics education takes attention for decades. The effect of qualified mathematics education during early years has an impact on children's future academic success. Main purposes of the study were twofold; to examine children's current 3D geometry thinking skills and to investigate the development of children's 3D geometry…

Our research with Grade 9 learners at a school in Soweto was conducted to explore learners' understanding of fundamental fraction concepts used in applications required at that level of schooling. The study was based on the theory of constructivism in a bid to understand whether learners' transition from whole numbers to rational numbers enabled…

Dark matter is one of the most intriguing scientific mysteries of our time and offers exciting instructional opportunities for physics education in high schools. The topic is likely to engage and motivate students in the classroom and allows addressing open questions of the Standard Model of particle physics. Although the empirical evidence of…

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…