Every day, 27,000 trees are used to make bathroom tissue. Americans use an average of 23.6 rolls per person per year, and more than 7 billion rolls of toilet paper are sold yearly in the United States alone. Perhaps the amount of bathroom tissue used can be reduced by changing the dimensions of the paper or the core. This brief article presents…

This article explores three processes involved in attending to evidence of students' thinking, one of the Mathematics Teaching Practices found in "Principles to Actions: Ensuring Mathematical Success for All." These processes, explored during a classroom activity on proportional relationships, are discussed in this article, another…

"Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014) gives teachers access to an insightful, research-informed framework that outlines ways to promote reasoning and sense making. Specifically, as students transition on their mathematical journey through middle school and beyond, their knowledge and use of…

A presentation on the Budapest Seminars in Mathematics Education website, inspired the author to try a new approach while teaching a unit on quadrilaterals in his Geometry for K-8 Teachers course, a class primarily composed of undergraduate students interested in teaching at the elementary or middle school level. The author designed a lesson that…

With the adoption of the Common Core State Standards for Mathematics (CCSSM), many teachers are changing their classroom structure from teacher-directed to student-centered. When the author began designing and using problem-based tasks she saw a drastic improvement in student engagement and problem-solving skills. The author describes the Cake…

Students engage in proportional reasoning when they use covariance and multiple comparisons. Without rich connections to proportional reasoning, students may develop inadequate understandings of linear relationships and the equations that model them. Teachers can improve students' understanding of linear relationships by focusing on realistic…

Emperor penguins, the largest of all the penguin species, attain heights of nearly four feet and weigh up to 99 pounds. Many students are not motivated to learn mathematics when textbook examples contain largely nonexistent contexts or when the math is not used to solve significant problems found in real life. This article's project explores how…

Students often view mathematics as a set of unrelated facts and procedures and fail to make the connections between and among related topics. One role of a teacher is to help students understand that mathematics is an interrelated discipline. Another role is to assist students in the scaffolding of their knowledge so that they can make connections…

Assigning activities based on current or past events allows students to explore mathematics in a social context. Using social justice events in the mathematics classroom is a way for teachers to provide contextual problems that will reach all students and promote equity. Learning mathematics in an environment in which social issues are explored…

Every semester, the authors encounter students who are attracted to the visual and spatial aspects of geometry. They have other students who consider geometry to be challenging for the very same reasons. Students are confounded not only by the fact that geometry relies on visual interpretations but also because it has a language of its own and…

Given the importance of algebra, middle school mathematics teachers have a responsibility to help students transition from understanding arithmetic to understanding the algebra that will be necessary for success in high school. One method of transition involves introducing algebraic concepts in concrete ways using meaningful contexts. The series…

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…

This article describes how to make an origami paper box and explores the algebra, geometry, and other mathematics that unfolds. A set of origami steps that transforms the paper into an open box can hold mathematical surprises for both students and teachers. An origami lesson can engage students in an open-ended exploration of the relationship…

This article addresses the issues of coaching and assessing. A preservice middle school teacher's unique solution to the Pizza problem was not what the professor expected. The student's solution strategy, based on sequences and a reinvention of Pascal's triangle, is explained in detail. (Contains 8 figures.)

Presents a problem-solving activity, the birth order problem, and several solution-seeking strategies. Includes responses of current and prospective teachers and a comparison of various strategies. (YDS)