Geometry learning has a long history with the connection to human cognitive development. The ability to mentally or physically orient 2D shapes or 3D objects in space is believed to support achievement in science, technology, engineering, and mathematics (STEM) disciplines. Thus, geometry by its description is characterised by space; hence its…

This article discusses the advanced characteristics of a mathematical and geometrical system explained and published in the course of several preceding journal articles (Teia, 2015, 2016, 2018a and 2018b). The reading of the preceding articles is encouraged for a clearer understanding of the discussion that follows.

Generalizing, conjecturing, representing, justifying, and refuting are integral parts of algebraic thinking and mathematical thinking in general (Lannin et al., 2011). The activity described in this article makes a case for generalizing as an overall mindset for any introductory algebra or geometry class by illustrating how generalization problems…

Video game use is widespread among all age groups, from young children to older adults. The wide variety of video game genres, which are adapted to all tastes and needs, is one of the factors that makes them so attractive. In many cases, video games function as an outlet for stress associated with everyday life by providing an escape from reality.…

Unprecedented investments are being made in mathematics tutoring interventions for K-12 students, but results from these interventions are not always promising. Traditional online or distance math tutoring can treat learning as disembodied, and not give learners access to embodied resources like gestures, movements, and actions. Virtual Reality…

Access to body-based resources has been shown to augment cognitive processes, but not all movements equally aid reasoning. Interactive technologies, like dynamic geometry systems (DGS), potentially amplify the link between movement and geometric representation, thereby deepening students' understanding of geometric properties. This study…

The research this report belongs to aims at exploring the functional reasoning of high-school students from a covariation approach and proposing a framework to describe and predict the student's responses to modeling tasks in Dynamic Geometrical Situations. Items were designed for the students to build/construct the corresponding function guided…

Twenty students who earned A or B course-grades in the proof unit(s) of a secondary course that addressed proof in geometry were asked to work on two proof tasks while sharing their thinking aloud and using smartpens. Students were classified into two categories: those who were successful with both proofs and those who were unsuccessful with both…

Spatial reasoning is critical across the STEM disciplines. Examining deaf and hard of hearing (DHH) children's spatial reasoning in mathematics, particularly geometry, as an embodied phenomenon opens new possibilities for deaf education. The authors inquire into the embodied processes and forms of DHH learners' spatial reasoning, considering how…

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…

Spatial reasoning, recognised as playing a critical role across STEM disciplines, is gaining prominence in mathematics education, not only as fundamental to mathematics, but also as embodied mathematical activity. In this paper, we discuss spatial reasoning and its embodiment in mathematics. We then present a systematic review of the topics as…

Although spatial thinking and reasoning is recognised as a key component for promoting STEM discipline, very little research has been done on its promotion in middle years in Australia. How do students perceive three dimensional geometrical objects? Are they able to recognise the objects from different perspectives and explain their reasoning for…

In this study, we designed geometry learning activities so that students could apply newly learned knowledge to solve real-life problems, such as estimating the distance to real objects they find in their local community, measuring objects' length, width, and height, and calculating objects' surface area. Our participating students were divided…

Grounded and embodied cognition (GEC) serves as a framework to investigate mathematical reasoning for proof (reasoning that is logical, operative, and general), insight (gist), and intuition (snap judgment). Geometry is the branch of mathematics concerned with generalizable properties of shape and space. Mathematics experts (N = 46) and nonexperts…

As a component of a course on geometry for preservice elementary teachers (PSTs), we derive area formulas for a variety of polygons including triangles, quadrilaterals, and both regular and irregular shapes whose areas can be measured empirically using decomposition. Decomposing a circle to justify why its area can be measured using the standard…