This practitioner article describes a lesson carried out in a high school classroom at the conclusion of a unit on exponential growth. Two teachers use a series of music-related activities to engage students in using and connecting multiple representations of exponential growth while exploring musical frequencies on a piano.

Purpose: Although children with hearing loss (HL) can benefit from cochlear implants (CIs) and hearing aids (HAs), they often show language delays. Moreover, little is known about the mechanisms by which children with HL learn words. One mechanism by which typically hearing (TH) children learn words is by acquiring word learning biases such as the…

In this paper, we focus on two particularly problematic concepts in teaching mathematics: the complex unit i and angles. These concepts are naturally linked via De Moivre's theorem but are independently misused in numerous contexts. We present definitions, notations, and ways of speaking about these terms from mathematics education that are not…

Although geometric transformations are functions, few studies have examined students' reasoning about these two important concepts. The purpose of this study was to examine the various ways students reasoned about functions in the context of pre-constructed, dynamic sketches of geometric transformations. We found that, regardless of prior…

This work shows how playing chess creates capacities in the student such as increasing visual memory. This helps to classify information in an orderly manner in the mind and contributes to a better understanding of geometric transformations such as displacements, turns and similarities. This was done with a mixed technique (Quantitative and…

As children progress through the elementary grades, they are expected to begin to use attributes of shapes to name and classify them. When listening to children talk about shapes, it becomes clear that the process of learning to reason geometrically is complex. Recognizing the complex nature of students' geometric reasoning, the authors present in…

In this article, we examine spatial inscriptions marked in real or rendered spaces, rather than on two-dimensional surfaces, conceptualize spatial inscriptions from an inclusive materialist perspective and consider realizations of spatial inscriptions that are possible with emerging technologies (e.g. 3D pens, immersive virtual reality). We then…

Spatial reasoning is seen as increasingly important in STEM fields. Within mathematics, geometry is a potential site to study and support young children's spatial reasoning. In this paper we revisit Piaget and his colleagues' theoretical perspective on children's development of geometry concepts and take note of projective geometry in that theory.…

A large and growing body of work has documented robust illusions of area perception in adults. To date, however, there has been surprisingly little in-depth investigation into children's area perception, despite the importance of this topic to the study of quantity perception more broadly (and to the many studies that have been devoted to studying…

Variance and invariance are two powerful mathematical ideas to support geometrical and spatial thinking, yet there is limited research about teachers' knowledge of variance and invariance. In this paper, we examined how high school teachers deal with the task of looking for invariant properties in a dynamic geometry environment (DGE) setting.…

This study aims to examine the situational flow experiences of students creating 3D designs in 3D multi-user virtual environments. This time series quasi-experimental study included 40 volunteer junior students who studied at the Computer Education and Instructional Technology department and had taken the elective course of "Instructional…

This paper contains information on a study which investigated the use of GeoGebra software in teaching and learning circle geometry enhancing Grade 11 learners' academic achievement in South Africa. The study employed a quantitative methodological research design that included non-equivalent (pre-test and post-test) quasi-experimental research.…

Along with emerging literacy and numeracy, spatial skills and reasoning set the foundation for young children's school readiness and early education. This study explored introducing an innovative curriculum for promoting young children's spatial learning in Morogoro, Tanzania. Four hundred twenty-eight children from 21 schools participated; 11…

The results of an assessment taken at the start and end of the Reception Year by children in state schools in England over three years were analysed. Over 70,000 children were assessed during this time. The results of the analysis provided evidence of what the average child could do when they started school, and how much progress they made in that…

In this paper a class of regular surfaces, generated by rotation and twist of a rigid line segment, is considered. Firstly a complete description of those surfaces by means of local charts is obtained and then its orientability is characterized in terms of the number of half-twists, taking into account their direction (clockwise or…