Geometry and spatial reasoning form the foundations of learning in mathematics. However, geometry is a subject often ignored by curriculum writers and teachers until high school, leading to students lacking in critical skills in geometric reasoning. As the United States moves into a new curriculum epoch, heralding the commencement of the national…

This research study focuses on preservice teachers' (n=66) inspection of pedagogical connections between geography and geometrical reasoning. The aim of this study was to empirically investigate the use of mathematical analysis to enrich the social studies topics of the distortion of country sizes on the world map. The analysis of data collected…

The purpose of this research is to examine preservice elementary school teachers' geometry learning as investigated by both qualitative and quantitative methods. For the qualitative investigation, narrative analysis and thematic analysis methods were used. The findings of narrative analysis indicated two main kinds of stories: as a learner and as…

Current research and policy statements regarding mathematics teacher preparation support shifting the focus of content courses for prospective elementary teachers (PTs) towards the mathematics that elementary teachers are expected to teach, or "content knowledge for teaching mathematics" (CKTM). This paper describes a research-based…

In high school geometry courses, students are often given a prepackaged statement that they are asked to prove. In these situations, the process of writing proofs is being abridged, if not misrepresented. To provide her students with a more authentic experience in writing a proof, the author provided them with a summative project for which they…

Twenty-three female elementary pre-service teachers were assessed on their ability to answer questions involving geometry concepts. Despite being given the definitions of the altitude of a triangle and the diagonal of a polygon on the pretest, limited understanding of these concepts was evident. A treatment using both graphic organizer and concept…

This study examines the mediating role of homework in the daily practice of a middle-school mathematics teacher and her colleagues in Shanghai. It aims to explore how a system of homework activities mediates and engenders a cultural pedagogy characterized by transforming errors into resources for teaching and learning. The transformation itself…

Sometimes a picture is worth a thousand numbers. Use geometric representations to teach and reinforce the multiplication tables. (Editor)

Explores how constructing mazes to race two mice, Thunderbolt and Sweetie Pie, leads to an investigation of geometry and measurement concepts. (KHR)

A solid understanding of equivalent fractions is considered a steppingstone towards a better understanding of operations with fractions. In this article, 55 rural Australian students' conceptions of equivalent fractions are presented. Data collected included students' responses to a short written test and follow-up interviews with three students…

The method of Teaching for Abstraction was applied in grades 2 and 4 to individual teaching interviews focusing on the angle concept. Responses of three students who successfully matched different physical angle situations are compared to responses of three that did not. The teaching method was generally supported, but it appears that more…

Arrays are seen as excellent models for beginning multiplication examples, but that they are often put aside by teachers when they become unwieldly for greater factors, possibly depriving learners just when they need the help. The use of grids made on paper marked in squares is suggested. (MP)

Some reasons why simple ideas in projective geometry should have a place in the elementary school curriculum are suggested. Then, seven lessons on projective geometry that were taught to a class of 10-year-olds are described. (MNS)

Trademark designs provide a familiar yet innovative way for students to look at a number of mathematical concepts. How line and rotational symmetry can be presented using trademarks is the focus of this article. The emphasis is on the design of bulletin boards. (MNS)

Identifies common misconceptions about polygons. Discusses current practices used to teach geometry to search for the source of misconceptions, and describes ways to help students avoid these misconceptions. (ASK)