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.…

Suppose a red laser beam (of wavelength ? equal to 0.660 µm) is expanded using an optical telescope into a collimated, approximately plane wave that is 5.68 mm in diameter. Pass that beam through a tall rectangular slit whose width "a" is gradually reduced from 3.30 to 0.100 mm. Look at its image on a screen located at a distance…

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…

This article presents a didactic situation focused on geometric reasoning using 3D GeoGebra, using the concepts Theory of Didactical Situations (TDS). The objective of this work is to bring a didactic proposal for the teaching of Spatial Geometry, working with the students' geometric perception, oriented and elaborated based on the dialectic of…

The paper discusses the perspectives of teaching geometry based on the study The International Commission on Mathematical Instruction ICMI. Bearing in mind the current needs in geometry teaching, we considered that the topics of space and spatial reasoning should be part of it as key issues, as well as teaching approaches, RME, learning through…

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.

The ability to graphically depict objects in two- and three-dimensional space is fundamental to engineering design practice. Historically, engineers have used pencil, paper, and erasers to draft preliminary sketches and to transform initial drafts into precise production drawings. With the proliferation of computer-aided design (CAD) software…

The most recent Kindergarten Common Core Mathematics State Standards include an emphasis on teaching geometry skills, such as recognizing, describing, naming, and composing shapes. This article provides five effective ideas for teachers of young children as they introduce and teach shapes.

This paper outlines the new opportunities that that will be changing the landscape of geometry education at the primary school level. These include: the research on spatial reasoning and its connection to school mathematics in general and school geometry in particular; the function of drawing in the construction of geometric meaning; the role of…

The ability to rotate visual mental images is a complex cognitive skill. It requires the building of graphical libraries of information through short or long term memory systems and the subsequent retrieval and manipulation of these towards a specified goal. The development of mental rotation skill is of critical importance within engineering…

Measurement is an important component of K-grade 12 mathematics curricula. The concepts of area and perimeter of polygons are first introduced in third grade and serve as the basis for teaching in the upper grades. Without a strong understanding of measurement, students will struggle to meaningfully grasp three-dimensional measurement concepts…

This commentary adopts a broad perspective in considering the contributions of papers from cross- and interdisciplinary fields of mathematics education, psychology, child development and neuroscience. The discussion aims to complement the commentary by Dindyal, focused on background research on geometry and implications for pedagogy and curricula.…

In this article, the author features "Flatland," by Edwin Abbott, a fantastic story about a square who lives in a two-dimensional world and who receives a visitor from the third dimension. Written in 1884 by a teacher-theologian who dabbled in mathematics, the novel is full of rich themes, including social class structure, the treatment of people…

In this article, we develop a theoretical model for restructuring mathematical tasks, usually considered advanced, with a network of spatial visual representations designed to support geometric reasoning for learners of disparate ages, stages, strengths, and preparation. Through our geometric reworking of the well-known "open box…