The opening lines of "How the Grinch Stole Christmas!" (Geisel 1957) set the tone for an inspiring change-of-heart story about a grumpy creature that comes to value humanity and the Christmas spirit. Although the book is often considered inspirational for other reasons, the authors were particularly moved by Dr. Seuss's interesting conjecture…

Research has proved that American students, as well as some adults, struggle with understanding fraction concepts and operations (Behr et al. 1992; NCES 2011). Having a solid understanding of this topic is important because fraction concepts are a foundation for many areas in secondary school mathematics, such as rate of change, rational…

March 14 is special because it is Pi Day. Mathematics is celebrated on that day because the date, 3-14, replicates the first three digits of pi. Pi-related songs, websites, trivia facts, and more are at the fingertips of interested teachers and students. Less celebrated, but still fairly well known, is National Metric Day, which falls on October…

Proportional reasoning is an important aspect of formal thinking that is acquired during the developmental years that approximate the middle years of schooling. Students who fail to acquire sound proportional reasoning often experience difficulties in subjects that require quantitative thinking, such as science, technology, engineering, and…

The merging of the fields of special education and mathematics was never meant to be a recent phenomenon. The true intention of the Individuals with Disabilities in Education Act (1975) was for students with disabilities to remain in the least restrictive environment. However, because mathematics is a content area with the greatest dependency on…

Data analysis plays an important role in people's lives. Citizens need to be able to conduct critical analyses of statistical information in the work place, in their personal lives, and when portrayed by the media. However, becoming a conscientious consumer of statistics is a gradual process. The experiences that students have with data in the…

Mathematics lessons can take a variety of formats. In this article, the authors discuss lessons organized around complex mathematical tasks. These lessons usually unfold in three phases. First, the task is introduced to students. Second, students work on solving the task. Third, the teacher "orchestrates" a concluding whole-class discussion in…

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…

In education, it is common to set aside older curriculum documents when newer ones are released. In fact, some instructional leaders have encouraged the "out with the old, in with the new" process by asking teachers to turn in all copies of the older document. Doing so makes sense when the old curriculum document is incompatible with the new.…

Just as students need plenty of time to practice skills such as solving fraction problems, they also need time to practice the skills of discourse to become better communicators and stronger mathematicians. Embedded within discourse strategies are specific ways to maximize communication. When repeatedly practiced, students learn to listen to one…

Students are often encouraged to work on problems "like mathematicians"--to be persistent, to investigate different approaches, and to evaluate solutions. This behavior, regarded as problem solving, is an essential component of mathematical practice. Some crucial aspects of problem solving include defining and interpreting problems, working with…

The process of developing definitions is underemphasized in most mathematics instruction. Investing time in constructing meaning is well worth the return in terms of the knowledge it imparts. In this article, the authors present a third approach to "defining," called "constructive." It involves modifying students' previous understanding of a term…

How better to promote a healthy lifestyle than to get an entire middle school involved in analyzing dietary information? This article describes a series of activities that was part of an interdisciplinary schoolwide effort to discuss healthy food choices. Mathematics teachers chose to focus on students' dietary habits and, over several days,…

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…

No person, place, or thing can capture the attention of a class of sixth graders like "man's best friend." To prompt students' interest in a series of lessons on proportional relationships, the authors brought in a unique teaching aid--a dog. A family dog was used to supply the measurements for scatter plots and variables so that students could…