Interprets the philosophical concept of warrant in a mathematics education context and applies it to two central questions: (1) in what sense does mathematical proof warrant?; and (2) can there be warrants for mathematical knowledge other then deductive proofs? (Contains 36 references.) (Author/ASK)

Persistence of Vision Raytracer (POV-Ray), a free computer program for creating photo-realistic, three-dimensional scenes and a link for Mathematica users interested in generating POV-Ray files from within Mathematica, is discussed. POV-Ray has great potential in secondary mathematics classrooms and helps in strengthening students' visualization…

According to the National Council of Teachers of Mathematics (NCTM) (1989, 2000), students at all levels should be exposed to geometry and measurement topics. Standards documents have identified the importance of primary school students selecting appropriate units for measurements in one- and two-dimensional space (NCTM 1989, 2000). This paper…

Concludes that the significant difference found between responses made to displayed drawings and those made to models suggests that, independently of the complexity of stimulus, encoding will not influence responses if the very economical process of simple coding can be used. (Author/AM)

Describes an activity for children of any age to develop spatial sense and explore the effects of transforming, combining, subdividing, and changing geometric figures. Students analyze empty cereal boxes opened flat to determine the specific shape, how it opens and closes, to check maps or sketches against the actual geometry of the box, and write…

Spatial tests involving the comparison of diagrams of interlaced ropes or knots at varying orientations were given to (n=21) subjects, mostly English college undergraduates, to determine an ordering in terms of complexity of tasks involving the mental manipulation of the knots. Certain knot shapes were processed faster than others and greater…

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…

Presents the Shape Search problem to develop student visualization. Focuses attention on the National Council of Teachers of Mathematics (NCTM) Geometry Standard. (Author/NB)

This investigation is part of a combined research/curriculum development project in which children's learning is being examined in the context of developing and testing instructional units on 3-D geometry in grades 3, 4, and 5. There are two components to the article. First, the strategies and cognitive constructions that students utilize to…

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…

Defines spatial structuring as the mental operation of constructing an organization or form for an object/set of objects. Examines in detail students' structuring and enumeration of two-dimensional rectangular arrays of squares. Concludes that many students do not see row-by-column structure. Describes various levels of sophistication in students'…

With both "Cabri" and "Autograph" now venturing into 3D, the dimension that previously was only demonstrated in the classroom with a lot of arm waving and crude wire cages can now be explored dynamically on screen. "Cabri 3D" concentrates on constructions, using the principles of Euclidian geometry, whereas "Autograph" creates objects using a…

The author recounts experiences introducing a first grade class to the concept of symmetry. The lesson includes activities for developing recognition of objects that have symmetry as well as visualization of both horizontal and vertical lines of symmetry.

The theme of the 38th meeting of the International Group for the Psychology of Mathematics Education (PME 38) and the 36th meeting of the North American Chapter of the Psychology of Mathematics Education (PME-NA 36) was "Mathematics Education at the Edge." Academically, the theme provides opportunities to highlight and examine…

In this study of deaf high school students, imagery and familiarity were found to be the best predictors of geometry word recall, whereas neither concreteness nor signability of the terms was a significant predictor variable. Recall of high imagery terms was significantly better than for low imagery terms, and the same result was found for high-…