Differentiation is one way to make the success of all students in mathematics a reality. However, many teachers continue to wonder how to make differentiation work in everyday classroom instruction, practice, and assessment. One approach that allows educators to deliver differentiated practice and assessment opportunities to effectively reach all…

In this article, the author shares how his fourth-grade students' creative thinking concerning a long-standing research problem stimulated changes in his instructional strategies. He begins by providing an example which illustrates that the standard tool of democracy, the plurality vote, suffers serious deficiencies: "The winner can be the voters'…

Over the past two decades, mathematical patterns have been acknowledged as important early components of children's development of algebraic reasoning (NCTM 2000). In particular, growing patterns have attracted significant attention as a context that helps students develop an understanding of functional relationships (Lee and Freiman 2006; Moss et…

Given the recent release and widespread state adoption of the Common Core State Standards for Mathematics (CCSSM), teachers across the country now have common goals related to what their students should understand about particular mathematical topics. The authors of CCSSM explain, "Asking a student to understand something means asking a teacher to…

In this article, the authors begin with a description of an algebraic dance--the translation of composite linear growing patterns into choreographed movement--which was the last component of a research-based instructional unit that focused on fostering an understanding of linear functional rules through geometric growing patterns and…

With the introduction of the Common Core State Standards (CCSS), teachers must now teach math with an eye on simultaneously meeting the Standards for Mathematical Practice (CCSSI 2010). These Standards "describe varieties of expertise that math educators at all levels should seek to develop in their students" (p. 6). The first Standard, that…

The importance of a literacy-based approach to content learning, especially within elementary school grades, is not a new idea. During the past quarter-century, the use of children's literature as an effective teaching tool has gained popularity across all content areas (Thiessen 2004). The definition of literacy has expanded not only to include…

Current mathematical standards expect students in the upper elementary grades to learn and use three-dimensional models and represent them in two dimensions using isometric and orthogonal representations. In this article, the authors address the challenges of teaching students and teachers alike, including those who have little or no experience…

Parents as Literacy Supporters (PALS) is an interactive, culturally responsive, family literacy program that brings parents of kindergartners into the classroom as partners in their children's education. Co-developed by Jim Anderson of the University of British Columbia and Fiona Morrison, Director of Family Literacy and Early Learning at 2010…

The concepts of angle and angle measure have been acknowledged as difficult for elementary school students to grasp (Strutchens, Martin, and Kenney 2003). The Wedge activity (Browning and Garza-Kling 2009; Van de Walle 2004; Wilson 1990) can provide an opportunity for students to examine their understanding of angle measurement and to rethink what…

When the author asked her preservice elementary teachers what "order of operations" is and why it is important for children to learn, they recited "PEMDAS" or "Please Excuse My Dear Aunt Sally" but typically became silent when questioned about the importance of the order of operations. Reys and Fennell once suggested that the mathematics component…

The Common Core State Standards for Mathematics (CCSSM) were "designed to be robust and relevant to the real world, reflecting the knowledge and skills that young people need for success in college and careers" (CCSSI 2010). For the first time in U.S. history, a set of standards is established that will be taught in nearly every state. Forty-four…

By following learned rules rather than reasoning, students often fall into common error patterns, something every experienced teacher has observed in the classroom. In their effort to circumvent the developing common error patterns of their students, the authors decided to supplement their math text with two weeklong investigations. The first was…

The author is a strong proponent of incorporating the Content and Process Standards (NCTM 2000) into the teaching of mathematics. For candidates in her methods course, she models research-based best practices anchored in the Standards. Her students use manipulatives, engage in problem-solving activities, listen to children's literature, and use…

"What do you do with the remainder when you divide?" Mrs. Thompson asked her third-grade students. They replied with such comments as, "You can't share that, because they won't be equal!" and "It's not going to come out even because you can't do that!" These answers were consistent with third- and fourth-grade student performance in a pretest and…