In high school, students extend understanding of linear and exponential functions and explore trigonometric functions. This includes using the unit circle to connect trigonometric functions to their geometric foundation, modeling periodic phenomena, and applying (and proving) trigonometric identities. These ideas are fundamental for trigonometric…

Spatial ability was defined by Lohman (1996) as the ability to create, maintain, retrieve, and change visual pictures. Linn and Peterson (1985) distinguished among spatial perception, mental rotation, and spatial visualization. Spatial perception is the determination of spatial connections with respect to the orientation of the learners' body;…

Critical to constructing and interpreting graphs is an individual's understanding of the underlying coordinate systems, yet coordinate systems are often overlooked or taken-for-granted in both mathematics education research and curricula. In this paper, we foreground coordinate systems and present a distinction between two uses of coordinate…

This paper provides historical insights and educational background of Froebel's Gifts, hands-on materials developed in the early 19th century. Based on an explorative study with 54 German children (aged 5 to 10) in 2016, we first took steps to explore how these materials meet the demands for early mathematics learning of primary children. Starting…

Geometry is the branch of mathematics that addresses spatial sense and geometric reasoning. Students begin to understand geometry through direct interaction with their physical world. Because it is the study of the physical attributes of the environment, geometry has relevance for every student; the world becomes a big classroom. As students see,…

While maps and globes continue to be an important part of the geography and social studies curricula, there has been some debate about the ability of young children to engage in maps in a meaningful way. Some researchers have argued that children younger than seven do not have the spatial-cognitive abilities to truly understand the perspective and…

This conference presentation examines concept development for congenitally blind students. It presents current research on best-practice for teaching this population. Examples of strategies to reinforce understanding of body concepts, spatial awareness, and positional language, while promoting mirroring, self regulation, and purposeful movement to…

Most students love to play games. Ernest (1986) believed that games could be used to teach mathematics effectively in four areas: motivation, concept development, reinforcement of skills, and practice of problem-solving strategies. Fifteen is an interesting and thought-provoking game that helps students learn mathematics at the same time. Playing…

While Shulman argues that an important component of pedagogical content knowledge (PCK) is teachers' understanding of the alternative conceptions commonly held by students, relatively little is known about what students believe about many topics in the school curriculum. This paper focuses on a content area typically featured in Geography…

Open-ended tasks focused on content specific features are regarded as an effective way to promote particular concept development and to elicit higher-order thinking. Such tasks may vary widely in their focus and approach and they can be formulated without unnecessary complexity. When mathematics tasks are designed in an open-ended fashion they can…

Invented by English mathematician and pedagogist, Caleb Gattegno (1911-1988), the geoboard was designed as a manipulative tool for teaching primary geometry in schools (Williams, 1999). Traditionally made out of plywood and nails, geoboards today are usually made out of plastic and come in a variety of different sizes and colours. Rubber bands are…

The article describes a project in which blind and partially sighted children used a computer-guided floor turtle to develop spatial concepts such as right and left and accurate facing movements. (Author/DB)

Reviews the formation of space, time, and measurement concepts in children with respect to Piagetian developmental levels and presents some teaching methods to help promote these concepts. (SK)

Discusses the role of computer assisted instruction in helping children develop such basic skills as handwriting, reading, and understanding elementary numerical and spatial concepts. Indicates that techniques based on computer assisted instruction will aid children in academic and social development. (Author/JN)

The computer packages of PLOTALL, SYMAP, SURFACE II, QUSMO, QUSMO2, QUCRS, and QUTAB are commercially available plotting programs that provide aids for visualizing spatial distributed data and concepts. The incremental drum and line printer plots communicate often vast and difficult-to-interpret tabular data with or without geographic coordinates.…