We examined the codevelopment of mathematical concepts and the mathematical practice of defining within a sixth-grade class investigating space and geometry. Drawing upon existing literature, we present a framework for describing forms of participation in defining, what we term aspects of definitional practice. Analysis of classroom interactions…

This article examines the bodies of knowledge that influence and inform the teaching of mathematics methods courses for preservice early childhood teachers, focusing on the U.S. context. In particular, the article reports on an analysis of scholarship published over the last 20 years in four journals (two focused on early childhood education and…

The role of information and communication technologies (ICT) in education is well recognised--learning environments where the ICT features included are being proposed for many years now. The Web Geometry Laboratory (WGL) innovates in proposing a blended learning, collaborative and adaptive learning Web-environment for geometry. It integrates a…

These Proceedings are a written record of the research presented at the 40th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) held in Greenville, South Carolina, November 15-18, 2018. The theme of the conference is "Looking Back, Looking Ahead: Celebrating 40…

In this note, an approach combining dynamic geometry and automated deduction techniques is used to study the bisectors between points and curves. Usual teacher constructions for bisectors are discussed, showing that inherent limitations in dynamic geometry software impede their thorough study. We show that the interactive sketching of bisectors…

With GeoGebra introduced into mathematics instruction the teaching/learning process is not improved in terms of speed and quality only. Mathematical concepts, rules and procedures must be adjusted to the new environment. On the other hand, characteristics of the computer and the educational software in use must be thoroughly examined and a…

This module examines Rigor, the third of the three shifts required for implementation of the Common Core State Standards for Mathematics (CCSSM). This module is based on the premise that the information from Modules 1 and 2 is well understood. Course Objectives: By the end of the module, the learner will be able to: (1) identify the components of…

How many rods does it take to brace a square in the plane? Once Martin Gardner's network of readers got their hands on it, it turned out to be fewer than Raphael Robinson, who originally posed the problem, thought. And who could have predicted the stunning solutions found subsequently for various generalizations of the problem?

The focus of a parabola rolling without sliding along a straight line traces a catenary. We give some historical notes on this classical kinematical construction, observe that it was rediscovered in a recent article, and give a simpler and more geometric alternative derivation.

When a plane figure is photographed from different viewpoints, lengths and angles appear distorted. Hence it is often assumed that lengths, angles, protractors, and compasses have no place in projective geometry. Here we describe a sense in which certain angles are preserved by projective transformations. These angles can be constructed with…

Statistical graphs, measures of central tendency and measures of spread are key concepts in the statistics curriculum, so we present here a dynamic method (software) that may be used in the classroom. In this work we begin with an introductory approach. This is done to emphasize the importance of stimulating the visualization of statistical…

One of the most common household polyhedra is a cereal box. For over 100 years, American companies like Kellogg's™ have packaged cereal in containers shaped like rectangular prisms. Why is a rectangular prism the most commonly used solid for holding cereal? Would another design work equally or more efficient? This article describes an…

An influential theory of spatial navigation states that the boundary shape of an environment is preferentially encoded over and above other spatial cues, such that it is impervious to interference from alternative sources of information. We explored this claim with 3 intradimensional--extradimensional shift experiments, designed to examine the…

Geometry is one of the most important branches of mathematics education, because the aim of the geometry teaching is to provide students with the ability of critical thinking, problem solving and a better understanding of the other subjects in mathematics by making the students have a high level of geometric thinking skills (Sahin, O., 2008).…

An eighth-grade English teacher and a math teacher work together to improve student writing, engagement, and communication in English and geometry classes.