In this short note, by using one of Li and Liu's theorems [K.-H. Li, "The solution of CIQ. 39," "Commun. Stud. Inequal." 11(1) (2004), p. 162 (in Chinese)], "s-R-r" method, Cauchy's inequality and the theory of convex function, we solve some geometric inequalities conjectures relating to an interior point in triangle. (Contains 1 figure.)

Effective competition in a rapidly growing global economy places demands on a society to produce individuals capable of higher-order critical thinking, creative problem solving, connection making, and innovation. We must look to our teacher education programs to help prospective middle grades teachers build the mathematical habits of mind that…

Introduction: For decades, prior to the inception of the Common Core State Standards (CCSS), the National Assessment of Educational Progress (NAEP) was the only vehicle through which states could assess the progress of their students using a common metric. Now, 45 states, 4 U.S. territories, and the District of Columbia have adopted the CCSS to…

This case is part of a teaching experiment that sought to provide insight into how the use of mathematics technology affects the internal mathematical representations possessed by adult developmental mathematics students. Sequences of dot patterns were examined and analyzed by the participant. He then used the algebraic features of a dynamic,…

A three-step active-learning approach is described to enhance the spatial abilities of general chemistry students with respect to three-dimensional molecular drawing and visualization. These activities are used in a medium-sized lecture hall with approximately 150 students in the first semester of the general chemistry course. The first activity…

In mathematics, engaging in reasoning-and-proving (RP) includes investigating mathematical relationships, formulating conjectures, evaluating others' conjectures or arguments, generating arguments, and communicating mathematical knowledge. These mathematical processes are key habits of mind that help learners think critically within and…

Engineering Graphics curricula have changed dramatically in the past three decades. In the past, students in nearly all engineering disciplines were instructed in manual drafting and descriptive geometry. Students spent many hours "on the board", and this training enhanced the students' graphics communication, design and visualization…

The present study tries to identify the "picture in mind" that students' have about defining, proving and modelling. We access to it through external representations of their mental representations; in particular, from the way in which these representations are expressed in written form (sentences and situations). In the study we have…

There has been increased attention to the development of assessment measures for evaluating mathematical skills in young children in order to inform instruction and intervention. However, existing tools have focused primarily on number sense with little attention to other areas of mathematical thinking such as geometry and algebra. The purpose of…

In this article an application of conformal mapping to aerofoil theory is studied from a geometric and calculus point of view. The problem is suitable for undergraduate teaching in terms of a project or extended piece of work, and brings together the concepts of geometric mapping, parametric equations, complex numbers and calculus. The Joukowski…

NCTM (2000) described geometry as "a means of describing, analyzing, and understanding the world and seeing beauty in its structures" (p. 309). Dossey et al. (2002) captured the essence of this aspect of visualization by stating that geometry fosters in students an ability to "visualize and mentally manipulate geometric objects." (p. 200).…

Much of the evidence provided in support of the argument that mathematical knowing is embodied/enacted is based on the analysis of gestures and bodily configurations, and, to a lesser extent, on certain vocal features (e.g., prosody). However, there are dimensions involved in the emergence of mathematical knowing and the production of mathematical…

This submission contains the Proceedings of the 2017 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at McGill University in Montreal, Quebec June 2-6. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the…

The main goal of the Learning and Teaching Geometry project is to build professional development materials that provide opportunities for teachers to learn about mathematical similarity through the use of videocases, in which specific and increasingly complex mathematical ideas are presented within the dynamics of classroom practice. The central…

Self-efficacy beliefs in mathematics, as a dimension of the affective domain, are related with students' performance on solving tasks and mainly on overcoming cognitive obstacles. The present study investigated the interrelations of cognitive performance on geometry and young students' self-efficacy beliefs about using representations for solving…