Technology permeates every aspect of daily life, from the sensors that control the traffic signals to the cameras that allow real-time video chats with family around the world. At times, technology may make life easier, faster, and more productive. However, does technology do the same in schools and classrooms? Will the benefits of technology…

Telling children that they can learn from their mistakes is common practice. Yet research indicates that many teachers in the United States limit public attention to errors during mathematics lessons (Bray 2011; Santagata 2005). Some believe that drawing attention to errors publicly may embarrass error makers or may be confusing to struggling…

Do manufacturers' claims about water projectile toys measure up? It is one thing to assert that a Super Soaker[R] shoots thirty linear feet, but can it really shoot that far? This lesson gives students an opportunity to test the claims, experience measurement in a meaningful context, and analyze data within that context. Although measurement can…

As teachers work to ensure that their students meet and exceed standards set by state and national governing bodies, the need for teacher support becomes greater and greater. Teachers, who play the most important role in a student's education, are faced with a classroom full of children who understand concepts on many different levels. To gain…

Cognitively demanding tasks are at the heart of the implementation of the Common Core State Standards in Mathematics (CCSSI 2010). As with all the grades, teachers of grades 5 and 6 are challenged to use tasks that simultaneously address the grade-level Standards as well as the Standards for Mathematical Practice (SMP). Cognitively demanding tasks…

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…

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…

"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…

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…

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…

Regular education teachers may have received inadequate preparation to work with the variety of student disabilities encountered in the classroom, or they may have received limited training regarding the full range of learning disabilities and their effects on classroom performance. Along with problems in the area of math, students may also have…

In a 1981 diagnostic test, the Ministry of Education in Singapore found its country facing a challenge: Only 46 percent of students in grades 2-4 could solve word problems that were presented without such key words as "altogether" or "left." Yet today, according to results from the Trends in International Mathematics and Science Study (TIMSS…

The authors observed preschoolers engaged at the sand and water table to determine if math could be found within their play. Wanting to understand how children interact with provided materials and what kinds of math ideas they explore during these interactions, the authors offer practical examples of how such play can promote mathematical…

During a two-week summer professional development workshop, teams of intermediate-level school teachers and college methods instructors crafted mathematics learning modules--activities, lesson plans, work sheets, and technology-oriented tasks--with the primary goal of strengthening students' understanding of various geometric concepts. They recast…

To prepare to teach in mathematics classrooms where children learn to justify their thinking, the teachers themselves must have experienced an environment of inquiry, communication, collaboration, and reasoning. Teacher educators strive to establish such environments for preservice teachers (PSTs) and to support their transition from rules-based…