Starting a math club as early as kindergarten and having a range of grade levels in attendance can be successful. With the help of the older students, the varied age groups are entertained and excited about attending math club. The purpose of the club is to enrich the classroom mathematics curriculum with hands-on activities and to have members…

Students' use of technology allows them to generate and manipulate multiple representations of a concept, compute numbers with relative ease, and focus more on mathematical concepts and higher-order thinking skills. In elementary school mathematics classrooms, students develop higher-order thinking skills by completing complex tasks that require…

How can a teacher use the practice of reflection to create rich mathematical learning environments that are engaging to students? In such environments, one can hear and see a seamless integration of Problem Solving, Reasoning and Proof, Communication, making mathematical Connections, and Representation (the NCTM Process Standards) through Number…

A storied math context helps students engage both emotionally and cognitively with mathematics and helps show that mathematics develops out of human experience. Children's literature also models mathematical storytelling for students, and creates opportunities for them to retell and extend stories. This article describes mathematics investigations…

Considerable evidence shows that the number line is a powerful learning tool for children in elementary school. Diezmann and Lowrie (2006) noted several cognitive advantages for users, including opportunities to demonstrate the continuity aspect of numbers as well as the provision of a useful tool for representing and solving problems. However,…

In the third century, Diophantus, the "Father of Algebra" no less, described equations of the form x + 20 = 4 as "absurd." The absurdity stemmed from the fact that the result of four is obviously less than the addend of twenty. And more than 1300 years later, Pascal argued that subtracting four from zero leaves zero because of the impossibility of…

As mathematics becomes more complex and abstract in the higher grades, helping students find purpose and meaning for doing it becomes more important. Juvenile literature can serve as a powerfully motivating force for students in intermediate elementary school grades to learn mathematics, often providing an intrinsically interesting, real-world…

What is the role of patterns in developing algebraic reasoning? This important question deserves thoughtful attention. In response, this article examines some differing views of algebraic reasoning, discusses a controversy regarding patterns, and describes how three types of patterns--in contextual problems, in growing geometric figures, and in…

During the past five years, the authors have collaborated to provide elementary school teachers with professional development that focuses on both mathematical content and pedagogy. All the professional development was created in keeping with the best practices. Many conversations evolved around the role of a coach and the most effective ways to…

The widely adopted Common Core State Standards for Mathematics (CCSSM) are designed to deepen instruction of number sense and will demand that elementary school teachers have a strong understanding of number. These changes arrive at a time when it is still understood that teachers and the curriculum in the United States have not been fundamentally…

In this article, the authors discuss their approach to column addition and subtraction algorithms. Adapting an original idea of Paul Cobb and Erna Yackel's from "A Contextual Investigation of Three-Digit Addition and Subtraction" related to packing and unpacking candy in a candy factory, the authors provided an analogous context by…

Tasks that ask students to label rational number points on a number line are common not only in curricula in the upper elementary school grades but also on state assessments. Such tasks target foundational rational number concepts: A fraction (or a decimal) is more than a shaded part of an area, a part of a pizza, or a representation using…

Beginning in third grade, Pennsylvania students are required to take the Pennsylvania State Standardized Assessment (PSSA), which presents multiple-choice mathematics questions and open-ended mathematics problems. Consistent with the Communication Standard of the National Council of Teachers of Mathematics, while solving the open-ended problems,…

The concrete, pictorial, and abstract methods of this lesson give students access to investigate, isolate, define, and use prime numbers. In this article, the authors describe an enrichment lesson that offers opportunities to investigate prime numbers in concrete, pictorial, and abstract ways. Originally introduced by Jerome Bruner in 1960, the…

The topic of fractions is an important concept in elementary school mathematics. The study of fractions not only enables students to perform computations but also provides a foundation for later work with rates, percents, slope, and other topics in secondary school mathematics. However, research has long reported that many students and even adults…