This article aims to examine the impact of an online learning environment enriched with computer activities on geometry achievement and geometric habits of mind (GHoM). The study includes reflections from an online application of a one-term computer-aided mathematics teaching course in which the participants were preservice teachers (PTs) enrolled…

Surface area and volume computations are the most common applications of integration in calculus books. When computing the surface area of a solid of revolution, students are usually told to use the frustum method instead of the disc method; however, a rigorous explanation is rarely provided. In this note, we provide one by using geometric…

Kindergarten children's (5-6 years old) ability to communicate geometric shapes, to their classmates, in different modes--verbally, gesturally, schematically--through a game, was investigated. The game motivated the children to describe the shapes in the different modes, by emerging children's thinking process, communication capacity as well as…

Every day, 27,000 trees are used to make bathroom tissue. Americans use an average of 23.6 rolls per person per year, and more than 7 billion rolls of toilet paper are sold yearly in the United States alone. Perhaps the amount of bathroom tissue used can be reduced by changing the dimensions of the paper or the core. This brief article presents…

In this article, we examine the ways in which the creation of a third space can bridge the divide between coursework and practice for preservice secondary mathematics teachers (PSTs) taking a technology, pedagogy, and content course. A university-based instructor partnered with two high school teachers to create a space in which PSTs draw upon and…

Usually, all the applications of dynamic geometry systems (DGS) presented to our students are strictly mathematical, meanwhile their interests are normally far away from mathematics. We would like to introduce here a motivating example outside the "standard applications" of DGS, presenting a completely different application of this kind…

A new transition course centered on complex topics would help in revitalizing complex analysis in two ways: first, provide early exposure to complex functions, sparking greater interest in the complex analysis course; second, create extra time in the complex analysis course by eliminating the "complex precalculus" part of the course. In…

Ontologies play an important role as knowledge domain representations in technology-enhanced learning and instruction. Represented in form of concept maps they are commonly used as teaching and learning material and have the potential to enhance positive educational outcomes. To ensure the effective use of an ontology representing a knowledge…

Students studying geometry at the secondary level are expected to read diagrams in different ways than those in elementary school. In this paper, we present an analysis of the changes in diagrammatic expectations by comparing the geometric diagrams found in Grade 1 U.S. textbooks with those in U.S. high school geometry textbooks. This work…

Chemistry is a highly abstract discipline that is taught and learned with the aid of various models. Among the most challenging, yet a fundamental topic in general chemistry at the high school level, is molecular geometry. This study focused on developing exemplary educative curriculum materials pertaining to the topic of molecular geometry. The…

Understanding spatial reasoning is important to success in mathematics. This article shows how the proficiency strands in the "Australian Curriculum: Mathematics" provide the tools needed for effective teaching and learning of spatial thinking.

This study aims to explore a phenomenon of a one-off manifestation of mathematical creativity on the part of a student, against the background of her normative and not especially creative behavior--a flash of creativity. We seek to elaborate on this phenomenon in terms of the 4P (person, press, process and product) model of creativity. Namely,…

This article aims to describe the mathematical identity of elementary school students during studying mathematics. When studying mathematics, the students often face difficulties in understanding the concepts which results the decrease in their learning motivation. It will lead to the lack of development of their mathematical identity. The…

The objective of this study is to produce a vignette in measuring mathematical knowledge for teaching based conceptual (MKT-C). The method of this research is a development research conducted by synthesizing the expert reviews on MKT-C in the knowledge domain of material content which was divided into sub domains: common content knowledge based…

Preschool education is fundamental to shape children's aptitudes and skills in early life. Ecuador is following a global education trend for starting-up mathematical thinking at earlier development ages, but this is only reflected in vehement curricular changes that are not supported properly. As a result, the safeguarding of a good children's…