We introduce the concept of the "sequence of the ratios of convex quadrilaterals," identify some properties of these sequences and use them to provide new characterizations for some classic quadrilateral families. The research involves aspects of geometry, arithmetic and mathematical analysis, which converge to produce the results.

Many proofs of the arithmetic mean harmonic mean inequality have been proposed based on the rich connections between mathematics and physics. Sometimes the Arithmetic Mean Harmonic Mean inequality is proved by using electric networks. In this note, we use a simple set of two springs, instead of four springs which would be the equivalent set to…

The integration of technology in entrepreneurship arithmetic that uses realistic mathematic education as the basis into learning processes is instrumental in creating understanding and problem-solving abilities among students. However, until recently only a few technology-based learning media have been developed to accommodate the aforementioned…

The present paper describes beautiful conservation relations between areas formed by different geometrical shapes and area relations formed by algebraic functions. The conservation properties were investigated by students at an academic college of education using a computerized technological tool and were subsequently accompanied by justified…

Instruction geared toward priming the underlying problem structures was suggested as an evidence-based practice for students with a learning disability. Schema-based instruction is one intervention aligned with this principle. We extended prior work by: (1) using a teacher as the implementer; (2) providing teacher flexibility in intervention…

This special issue of the Canadian Mathematics Education Study Group/Groupe Canadien d'Étude en Didactique des Mathématiques (CMESG/GCEDM) Proceedings looks at CMESG/GCEDM's collective history, reflects on where the group has been, and who the members have become as an organization. Through a selection of excerpts from past proceedings, the…

This article explores the notion of collateral learning in the context of classic ideas about the summation of powers of the first "n" counting numbers. Proceeding from the well-known legend about young Gauss, this article demonstrates the value of reflection under the guidance of "the more knowledgeable other" as a pedagogical method of making…

The purpose of this study was to investigate the preservice secondary mathematics teachers' development of pedagogical understanding in the teaching of modular arithmetic problems. Data sources included, written assignments, interview transcripts and filed notes. Using case study and action research approaches cases of three preservice teachers…

The objective of this paper is to explain the need for and defend the sufficiency of the child's-play method of teaching the place value notation concept to preschool and elementary school children. Discussion first illustrates error patterns of school children in the use and interpretation of place value notation, arguing that the errors reflect…

This book re-examines the dichotomy between the everyday and the disciplinary in mathematics and science education, and explores alternatives to this opposition from points of view grounded in the close examination of complex classroom events. It makes the case that students' everyday experience and knowledge in their entire manifold forms matter…

This study compared the acquisition of an initial place value skill when presented in a concrete, semiconcrete, abstract teaching sequence to acquisition of the same skill when presented at the abstract level only. The 24 subjects were elementary and middle school students (ages 8-13) with learning disabilities who were randomly assigned to…

This document contains the second volume of the proceedings of the 30th Annual Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 60 research reports by presenters with last names beginning between Abr…

The first volume of the 29th annual conference of the International Group for the Psychology of Mathematics Education contains plenary lecture and research forum papers as listed below. Short oral communications papers, poster presentations, brief summaries of discussion groups, and working sessions are also included in the volume. The plenary…