The aim of this study was to determine preservice mathematics teachers' personal figural concepts and hierarchical classifications about quadrilaterals and to investigate the relationships between them. The participants were 57 preservice primary mathematics teachers in their senior year at a state university in Turkey. The preservice…

To encourage students to do geometry, the art of Islamic geometric ornamentation was chosen as the central theme of a lesson strand which was developed using the newly presented didactical tool called "Learning by Acting". The Dutch students who took these lessons in 2010 to 2013 were challenged to act as if they themselves were Persian…

One aspect of professional development of mathematics teachers relates to the development of assessment skills. The aim of this study is to examine the effects of engaging prospective mathematics teachers in peer assessment, both as assessors and assessees, on the development of their assessment skills in general and assessment of geometrical…

People mentally represent the shapes of objects. For instance, the mental representation of an eagle is different when one thinks about a flying or resting eagle. This study examined the role of shape in mental representations of "similes" (i.e., metaphoric comparisons). We tested the prediction that when people process a simile they…

Biochemistry is a visual discipline that requires students to develop an understanding of numerous representations. However, there is very little known about what students actually understand about the representations that are used to communicate ideas in biochemistry. This study investigated biochemistry students' understanding of multiple…

A 3D printer is used to prepare a variety of models representing potential energy as a function of two geometric coordinates. These models facilitate the teaching of structure-energy relationships in molecular conformations and in chemical reactions.

Tangible models help students and researchers visualize chemical structures in three dimensions (3D). 3D printing offers a unique and straightforward approach to fabricate plastic 3D models of molecules and extended solids. In this article, we prepared a series of digital 3D design files of molecular structures that will be useful for teaching…

Young children frequently tell visual stories, drawing pictures to record and share their thoughts, feelings and understanding. How and what young children describe through art, especially when written language is not an option, is the focus of this interpretive analysis. A series of pictures by John, a 6-year-old boy, were drawn across the…

The main goal of the Learning and Teaching Geometry project is to build professional development materials that provide opportunities for teachers to learn about mathematical similarity through the use of videocases, in which specific and increasingly complex mathematical ideas are presented within the dynamics of classroom practice. The central…

Geometry students need challenges. They need to apply what they already know to new contexts. As a result, high school teacher Wayne Nirode is always looking for groups of related problems of theorems to challenge his geometry students. He came across one such group or problems when reading Jun's (2012) one-page abstract posted online for the…

Constructing viable arguments and reasoning abstractly is an essential part of the Common Core State Standards for Mathematics (CCSSI 2010). This article discusses the scenarios in which a mathematical task is impossible to accomplish, as well as how to approach impossible scenarios in the classroom. The concept of proof is introduced as the…

Pattern blocks are inexpensive wooden, foam, or plastic manipulatives developed in the 1960s to help students build an understanding of shapes, proportions, equivalence, and fractions (EDC 1968). The colorful collection of basic shapes in classic pattern block kits affords opportunities for amazing puzzle-like problem-solving tasks and for…

In this article we discuss the findings of our research on students' understanding of vector concepts in problems without physical context. First, we develop a complete taxonomy of the most frequent errors made by university students when learning vector concepts. This study is based on the results of several test administrations of…

We investigated whether low-functioning children with autism generalise labels from colour photographs based on sameness of shape, colour, or both. Children with autism and language-matched controls were taught novel words paired with photographs of unfamiliar objects, and then sorted pictures and objects into two buckets according to whether or…

Preschool children can navigate by simple geometric maps of the environment, but the nature of the geometric relations they use in map reading remains unclear. Here, children were tested specifically on their sensitivity to angle. Forty-eight children (age 47:15-53:30 months) were presented with fragments of geometric maps, in which angle sections…