Research studies are abundant in pointing at how the transition from additive to multiplicative thinking acts as a core challenge for students' understanding of proportionality. This said, we have yet to understand how this transition can be supported, and there remains significant questions to address about how students experience it. Recent work…

Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…

This article presents a sequence of learning activities that lead to using the area model of multiplication to understand the distributive property (DP). The connection between area and multiplication is an important one, both for algebraic thinking and for geometry, as indicated in two of the critical areas for the third grade in the Common Core…

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…

In the September 2010 issue of "Mathematics Teaching," Tom O'Brien offered practical advice about how to teach addition, subtraction, multiplication, and division and contrasted his point of view with that of H.H. Wu. In this article, the author revisits Tom's examples, drawing on his methodology while, hopefully, simplifying it and giving it…

This submission contains the Proceedings of the 2015 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at the Université de Moncton in Moncton, New Brunswick. 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…

High academic standards are an important first step in ensuring that all Alaska's students have the tools they need for success. These standards reflect the collaborative work of Alaskan educators and national experts from the nonprofit National Center for the Improvement of Educational Assessment. Further, they are informed by public comments.…

For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards…

Provides domino geometry problems, problems with arithmetic progressions, and magic pentagram sums. (JM)

This is a first-grade manual for teachers using SMSG elementary school text materials. For each chapter background information is given; for each section, objectives, vocabulary, materials, suggested procedures, and further activities are listed. Chapter topics include: (1) pre-number experiences; (2) recognizing geometric shapes; (3) building…

This booklet, one of a series, has been developed for the project, A Program for Mathematically Underdeveloped Pupils. A project team, including inservice teachers, is being used to write and develop the materials for this program. The materials developed in this booklet include (1) number patterns, (2) measuring the interior and exterior angles…

Introduces a toy, the Educated Monkey, developed to help students learn multiplication tables and associated division, factoring, and addition tables and associated subtraction. Explains why the monkey works and reviews geometric, algebraic, and arithmetic concepts. (KHR)

This book is one in a series of teacher resource books developed to: (1) rescue students from the clutches of computers that drill and control; and (2) supply teachers with computer activities compatible with a mathematics program that emphasizes investigation, problem solving, creativity, and hypothesis making and testing. This is not a book…

Research Ideas for the Classroom is a three-volume series of research interpretations for early childhood, middle grades, and high school mathematics classrooms. Each volume looks at research from the perspective of the learner, the content, and the teacher, and chapters are co-authored by a researcher and a teacher. Chapter titles in the early…

By using word problems relevant to agricultural occupations, this workbook presents a concept-oriented approach to competency development in seven areas of basic mathematics: (1) the expression of numbers as figures and words; (2) the addition, subtraction, multiplication, and division of whole numbers, fractions, and decimals; (3) ratios and…