The teacher displayed counting cards that included both dots and numerals in order from one to five, as she counted them with her students. She then turned the cards facedown, keeping them in order, and began an identify-a-hidden-card activity with the class. This class was engaged in the third of three card activities that develop number sense…

Multiplicative thinking is a critical stage in mathematical learning and underpins much of the mathematics learned beyond middle primary years. Its components are complex and an inability to understand them conceptually is likely to undermine students' capacity to develop beyond additive thinking. Of particular importance are the ten times…

Recognizing and using mathematical structure are key components of mathematical reasoning. The authors believe that one productive way to support students' use of structure is by identifying opportunities to address structure in the context of what teachers are already doing, rather than developing additional tasks or new curriculum materials. The…

Despite the growing attention being paid to teaching mathematics for students with disabilities, the existing research tends to focus on mathematical skill acquisition, but not on skill maintenance. Maintenance of mathematical skills is especially important as mathematics has applications in daily life and is directly related to important life…

"Mathematical Thinking: From Assessment Items to Challenging Tasks" is a compilation of 36 problem-based lessons that encourage students to engage in productive struggle and deep thinking. Its 36 full-length lessons for grades 2-8 are each inspired by an actual test item from the National Assessment of Educational Progress (NAEP).…

Research indicates that parental involvement in children's education is positively related to academic achievement in mathematics; however, there are few studies on the role of parental involvement in the context of developing countries. The purpose of this paper is to document the iterative development using design-based research (DBR) of a…

Not all children are made the same. Learning disabilities like dyslexia, dysgraphia or dyscalculia are either not understood or ignored in schools. As a result, the schoolchildren suffer for no fault of theirs and they lag behind in their course of learning. They may find it difficult to achieve the basic skills of learning such as reading,…

How can teachers learn what they need to know? Every community of educators, regardless of field or specialization, can benefit from being well informed about current research findings. A considerable amount of mathematics education research exists to inform teachers and administrators about teaching and learning mathematics. Research can show…

These materials were designed to help remedial students increase mathematics proficiency on topics found in the Regents Competency Testing Program. The activities developed come complete with questions, "cards," and/or sample gameboards. Included in each activity is a list of materials needed. Several different activities often use the…

In a series of exercises students develop designs in which nodes are labelled according to the isolation rules defined. Strategies for creating new designs from known ones, finding the maximum number of isolation designs on a given configuration, and developing larger isolation designs are encouraged. Sample worksheets are included. (SD)

Presents activities that focus on number sense. (KHR)

Describes a problem that appeared in the April, 1999 issue of this journal and analyzes student responses and misconceptions. The problem concerns exponential progressions. (KHR)

This unit is 1 of 12 developed for the university classroom portion of the Mathematics-Methods Program (MMP), created by the Indiana University Mathematics Education Development Center (MEDC) as an innovative program for the mathematics training of prospective elementary school teachers (PSTs). Each unit is written in an activity format that…

Provided is an introduction to the properties of continued fractions for the intellectually curious high school student. Among the topics included are (1) Expansion of Rational Numbers into Simple Continued Fractions, (2) Convergents, (3) Continued Fractions and Linear Diophantine Equations of the Type am + bn = c, (4) Continued Fractions and…

This paper summarizes our analysis of the complexity of ratio problems at Grades 6 and 7, and reports a two-year experiment related to the teaching and learning of rational numbers and proportionality in these grades. Two classes were followed and observed. Part of the teaching material was common to both classes, mainly the objectives and the…