Reasoning is handled as a basic process skill in mathematics teaching. When the literature was examined, it was seen that many types of reasoning related to mathematics education were mentioned. In the present study, it was focused on visual reasoning, which is one of the types of reasoning and also used in different research areas. The purpose of…

Aiming to enhance understanding of visual obstacles inherent in two-dimensional (2-D) sketches used in high school spatial geometry instruction, we propose a measure of visual difficulty based on two attributes of the sketches: potentially misleading geometrical information (PMI) and potentially helpful geometrical information (PHI). The…

There is a consensus that certain cognitive abilities and mathematics performance are related. This link also extends to geometry. Surprisingly, however, little research has examined specific aspects of cognition that may contribute to successful performance in geometry, particularly at the secondary level. In this study, we explored in what ways,…

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…

This paper attempted to make explicit some of the underlying characteristics of spatial visualisation using the concept of area of composite shapes. By engaging students with metric-free tasks, we identify the type of perceptual and visual/spatial manoeuvres that they deploy in such situations. Interview data collected from three students in Grade…

A well-documented experience of students of elementary Euclidean geometry is "seeing" a geometric result and being sure about its truth; this sort of experience gives rise to the notion of geometrical visualisation that is developed here. In this essay a philosophical argument for the epistemic potential of geometrical visualisation is reviewed,…

In the summer of 2009, a professional development partnership was established between the Peoria Public School District (PPSD), a local education agency (LEA), and Illinois State University (ISU) to improve geometric and trigonometric knowledge and skill for high school mathematics teachers as part of the Illinois Mathematics and Science…

High-ability Jamaican students in grades one, three, five, seven, and nine were asked to draw five three-dimensional objects (cuboid, pyramid, cylinder, cone, cube) from memory, and with the object visible; later they were asked to select the best sketch of each solid from among several presented. Drawings and selections were scored for…

Examines the role of visualization within the process of geometrical concept attainment for students in grades five through eight, preservice elementary teachers, and inservice senior elementary teachers. Investigates the "bitrian" and "biquad" examples, numbers of critical attributes, elements in triangles, judgment in quadrilateral examples, and…

Describes two instructional activities to develop spatial imagery and the pupil's responses to these activities. Discusses how the classroom atmosphere contributed to the success of the activities. (YP)