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.

This report presents results of the 2011 National Assessment of Educational Progress (NAEP) in mathematics at grades 4 and 8. Nationally representative samples of 209,000 fourth-graders and 175,200 eighth-graders participated in the 2011 National Assessment of Educational Progress (NAEP) in mathematics. At each grade, students responded to…

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…

How can teachers learn what they need to know? Every community of educators, regardless of field or specialization, can benefit from being well informed about current research findings. A considerable amount of mathematics education research exists to inform teachers and administrators about teaching and learning mathematics. Research can show…

This paper profiles the student subgroup achievement and gap trends in Utah for 2010. Utah implemented new standards and cut scores in math so trend data that include 2009 are not available. In grade 8 (the only grade in which subgroup trends were analyzed by achievement level), Utah showed across-the-board gains in reading at the basic,…

Learning about mathematics begins in the early years. Through their everyday activities, young children build important foundational knowledge and understanding of mathematics, especially when adults provide specific opportunities to learn and practice concepts and skills. Young children develop early on an informal understanding of important…

In this article we describe a hands-on activity for a liberal arts mathematics course that focuses on the beauty and unity of mathematics. The purpose of the activity is to tie together several topics in the context of a "real-world" situation. These topics include: fractals, non-Euclidean geometry, symmetry, and Platonic solids. This activity…

Jean Louis Nicolet is a Swiss teacher of mathematics who found his subject so fascinating that he was puzzled as to why so many pupils could not share this enjoyment in their studies. He came to a conclusion which is now supported by the results of psychological research into the learning process: he suggested that the mind does not spontaneously…

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-…

In this article, the author investigates effective teaching and learning of geometrical concepts using dynamic geometry software (DGS). Based from her students' reactions to her project, the author found that her students' understanding of the concepts was better than if they had learned geometry through paper-based tasks. However, mixing computer…

This paper sits within the research on the affordances of new technologies in the mathematics classroom and focuses on a specific feature that is available in dynamic geometry environments, i.e. measuring tools, within the context of conjecturing and proving in open geometry problems. We develop a classification of different modalities of…

To help classroom teachers construct mathematics tests, thirty-seven general objectives, corresponding sub-objectives, sample test items, and answers are presented. In general, sub-objectives are arranged in increasing order of difficulty. The objectives were written to comprehensively cover two categories: measurement and geometry. Measurement…

In this article, the author describes two Powerpoint presentations designed to help visual learners calculate the circumference and the area of a circle. In particular, the author describes how these presentations can be used to establish mental images that can help pupils to understand, and so recall, the principles that underlie the formulae for…

This paper discusses the use of geometry and proportional reasoning techniques used at the United States Department of Agriculture by two of its branches: the Farm Service Agency and the Natural Resources Conservation Service. This paper discusses the agricultural agency and two branches involved, details a seven-lesson geometry module for high…

This note considers the four classes of orthogonal polynomials--Chebyshev, Hermite, Laguerre, Legendre--and investigates the Gibbs phenomenon at a jump discontinuity for the corresponding orthogonal polynomial series expansions. The perhaps unexpected thing is that the Gibbs constant that arises for each class of polynomials appears to be the same…