The authors introduce an educational video game (application, or "app"), "CandyFactory Educational Game," designed to promote students' development of partitive understanding of fractions while demonstrating the critical need to promote that development. The app includes essential game features of immediate feedback,…

As the sole math teacher in his middle school, the first author has always worked hard to provide quality mathematical experiences for his students. In an era of accountability defined by standardized test scores, he has also closely monitored his students' performance on such tests. After a few years of hoping that scores would improve, he…

Developmentally, middle school students progress from being concrete thinkers and learners to abstract thinkers. Traditional middle school mathematics instruction introduces a curriculum that is intuitive and taught within a natural trajectory of the content. However, with this traditional approach, students may miss out on being exposed to…

John Dewey discussed the dry school curriculum a century ago. One of the "evils" was a simplified curriculum having an outward appearance of mathematics. Dewey posited that such a simplified curriculum deprived students of opportunities to experience the thought-provoking character of the accumulated wisdom found in human knowledge. Dewey's…

The change in size from a smaller shape to a larger similar shape (or vice versa) is created through continuous proportional stretching or shrinking in every direction. Students cannot solve similarity tasks simply by iterating or partitioning a composed unit, strategies typically used on numerical proportional tasks. The transition to thinking…

Reasoning and sense making are at the heart of mathematics teaching and learning throughout the K-12 mathematics curriculum. Focusing on these skills gives students the opportunity to analyze, interpret, and critically think about the mathematics they learn. The terms "reasoning" and "sense making" are frequently used to describe the wide range of…

Implementing Universal Design for Learning (UDL) principles can provide solutions for general educators in inclusive mathematics environments. Any lesson can be planned to provide learning experiences appropriate for meeting diverse learning needs. This article explores an example of both how to approach a topic in middle school mathematics and…

The current state of the economy elevates the need to build awareness of financial markets and personal finance among the nation's young people through implementing a financial literacy curriculum in schools. A limited amount of time spent on financial literacy can have a positive effect on students' budgeting skills. This knowledge will only add…

This article describes a particular activity, the Motorized Toy unit, which supports science, technology, engineering, and mathematics (STEM) goals and teaches students the basic concept of ratio. The unit addresses both mathematics and science standards and is part of a team-teaching activity. The unit comes from a curriculum titled A World In…

Taiwanese students consistently rank near the top on international exams on mathematics and science. In 2007, Taiwan recorded the highest TIMSS math score for eighth grade. The central education agency in Taiwan publishes detailed mathematics curriculum guidelines, which textbooks and national exams follow closely. In May each year, all ninth…

To help fifth- through eighth-grade students develop their deductive reasoning skills, the author used a ten-week supplementary curriculum so that students could answer logic questions. The curriculum, a series of lessons built around language-independent logic puzzles, has been used in classrooms of fifth through eighth grades. In most cases,…

Presents an overview of Chester Finn's and Zalman Usiskin's criticisms of the National Council of Teachers of Mathematics (NCTM) Standards and suggestions for improvement to the Standards. (AIM)

Describes a professional development program for upper elementary and middle school teachers that includes a sequence of four activities designed to foster improved understanding of the connections among measurement, ratio, scale, and proportion. (YDS)

Discusses experiences using a new mathematics curriculum with sixth grade students for nine weeks. Presents a student's discovery of her power in mathematics through this problem-centered curriculum. (ASK)

Describes a professional development project to increase teachers' understanding of proportional reasoning, the thinking patterns associated with proportional reasoning, and the applications of proportional reasoning across the middle-grades curriculum. (YDS)