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…

Measurement concepts such as volume and surface area provide rich contexts for real-world applications of number processes. Despite their importance, many students and prospective teachers show superficial understanding of measurement concepts. A lack of spatial reasoning and integration of geometric knowledge in problem solving situations may be…

The three-dimensional design and production technologies are today widely used in many fields. Automotive, health, art and education, and especially architecture and engineering are among the prominent examples. The three-dimensional design technology can be categorized into two dimensions: design and production. The first of these dimensions,…

Spatial ability is a form of intelligence where a person demonstrates the capacity to mentally generate, transform, and rotate a visual image and thus understand and recall spatial relationships between real and imagined objects. The aim of this paper is three-fold: (1) to review related empirical studies on spatial abilities for young children…

This paper initiates a discussion around the potential of Dynamic Measurement, an alternative approach to geometric measurement that focuses on how space is generated, and thus measured by the lower-dimensional objects that define it. I use data from a series of design experiments with fourth-grade students to illustrate some forms of reasoning…

This paper explores three multilingual students' (9 to 11-years-old) conceptual understanding of three-dimensional (3D) shapes as displayed through peer and classroom interactions in two New Zealand primary classes. Bakhtin's dialogic theory and Garfinkel's ethnomethodology inform the theoretical framework. The paper presents two excerpts from…

As algebra teachers, the authors explore the following question in this article: "How can algebra 1, algebra 2, and precalculus teachers support students to develop algebraic reasoning and understanding of structure that can serve them in day-to-day algebraic computation?" The article shows how the algebraic identity "(a +…

The visualization of chemical compounds in three-dimensions is a foundational skill in the study and practice of chemistry and related fields, and one which has the potential to be supported by interaction with virtual models. Here, we present a collaborative learning activity piloted in first-year chemistry which investigates if inquiry-driven…

Admittedly, the study of Complex Analysis (CA) requires of the student considerable mental effort characterized by the mobilization of a related thought to the complex mathematical concepts. Thus, with the aid of the dynamic system Geogebra, we discuss in this paper a particular concept in CA. In fact, the notion of winding number v[f(gamma),P] =…

This paper argues that rationality and belief are mutually formative dimensions of school mathematics, where each term is more politically embedded than often depicted in the field of mathematics education research. School mathematics then presents not so much rational mathematical thought distorted by irrational beliefs but rather a particular…

Spatial language constitutes part of the basic fabric of language. Although languages may have the same number of terms to cover a set of spatial relations, they do not always do so in the same way. Spatial languages differ across languages quite radically, thus providing a real semantic challenge for second language learners. The essay first…

As the traditional toys of the past are quickly being replaced with electronically "enhanced" toys, it is important to understand how these changes impact parent--child interactions, especially in light of the evidence that the richness and variety of these interactions have long-term effects on diverse areas of cognition (Hart &…

Geometry is one of the highest achievements of our species, but its foundations are obscure. Consistent with longstanding suggestions that geometrical knowledge is rooted in processes guiding navigation, the present study examines potential sources of geometrical knowledge in the navigation processes by which young children establish their sense…

A question posed by a teacher can often serve as an effective and engaging way to start a class. Sometimes, however, interesting questions arise from comments made by students. The investigation presented in this article arose from a student's very simple question: "Is there a perfect rectangle for folding origami?" The initial investigation was…

Geometrical concepts are critical to a host of human cognitive achievements, from maps to measurement to mathematics, and both the development of these concepts, and their variation by gender, have long been studied. Most studies of geometrical reasoning, however, present children with materials containing both geometric and non-geometric…