In this article, Lindsey Fowler describes how an animal rhyme--that she shared with her fifth-grade students with the intention of assisting them with the concept of metric conversions--made fostering the Standards for Mathematical Practice (SMP) more difficult. The addition of animals, which added an extraneous element that students mistakenly…

Gesture is a powerful and frequent means of mathematical communication. It is a rich modality through which we may reach out to students and they may reach out to teachers, and this is particularly true for instances in which spoken language is not necessarily a commonality among classroom participants. Indeed, our movements help us share more…

Children's literature can provide useful contexts for teaching mathematics. In this article, the authors discuss the use of the children's book "Measuring Penny" (Leedy 1997) to support Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) related to length measurement. The authors first describe three types of misconceptions…

The first author's initial attempts at a whole-class mathematics discussion were woefully dysfunctional. Ten second graders showing their answers to a missing addend question about the number of children left riding a school bus did not result in the mathematical epiphany that the textbook promised. She did not give up on using mathematical…

In this article the authors describe a project during which they unpacked fraction standards, created rigorous tasks and lesson plans, and developed formative and summative assessments to analyze students' thinking about fraction multiplication. The purpose of this article is to (1) illustrate a process that can be replicated by educators…

This article describes how a teacher in Mexico City worked with two researchers on an instructional design project to help kindergartners become proficient in participating in whole-class mathematical conversations.

Young children thrive in classrooms that allow them to explore and discover their environment and interests and also support them in this learning. Because children learn best when they are interested and excited, early-childhood educators should offer children play-based, integrated mathematical experiences (NRC 2009). In this article, the…

This article reports on a study in which researchers asked children to "make up as story and a picture about marbles for this number sentence: 3 x 5 = 15." Students in this study came from pre - dominantly low- to average-income families living in three distinct geographical areas within the United States. A similar division task was…

A "tessellation" is a pattern of geometric shapes that fulfills three conditions: (1) No gaps exist between the shapes; (2) The shapes do not overlap; and (3) The pattern can go on forever in all directions. Tilings (such as tiling a floor) are familiar to children and provide a rich resource at all grade levels for learning many…

Many elementary schools across the nation are scaling back or cutting arts curriculum altogether. This article presents classroom teachers with an activity for integrating art with mathematics. Through a three-phase exploration of reasoning with shapes and their attributes, students will get to know a classmate better, work with defining and…

In this article, three instructional situations demonstrate the value of using an "unknown" student's work to allow the advancement of students' mathematical thinking as well as their engagement in the mathematical practice of critiquing the reasoning of others: (1) introducing alternative solution strategies; (2) critiquing inaccuracies…

Mathematics discourse is a teaching approach that encourages student discussion and reveals an understanding of concepts as students engage in mathematical reasoning and debate (Cobb 2006). Grabowski and Ke (2007) posit that students have significantly higher achievement and positive attitudes toward mathematics after participating in gaming…

Skilled instructors observe consistent errors that young children may make in particular situations and seek ways to help children reform their thinking through conceptual understanding. Such teacher observations as those presented at the beginning of this article, combined with similar observations by teachers in other preschool and kindergarten…

Measurement is an important component of K-grade 12 mathematics curricula. The concepts of area and perimeter of polygons are first introduced in third grade and serve as the basis for teaching in the upper grades. Without a strong understanding of measurement, students will struggle to meaningfully grasp three-dimensional measurement concepts…

Geometry is the branch of mathematics that addresses spatial sense and geometric reasoning. Students begin to understand geometry through direct interaction with their physical world. Because it is the study of the physical attributes of the environment, geometry has relevance for every student; the world becomes a big classroom. As students see,…