The teacher displayed counting cards that included both dots and numerals in order from one to five, as she counted them with her students. She then turned the cards facedown, keeping them in order, and began an identify-a-hidden-card activity with the class. This class was engaged in the third of three card activities that develop number sense…

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…

Building physical models is a natural activity for children and provides a context for lessons on two-dimensional (2D) and three-dimensional (3D) shapes. However, children do not think of their models as prisms, cylinders, and pyramids. Their creations are spaceships, tunnels, castles, and nets on the floor. Creating these types of shapes with…

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…

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…

The Math Promise is a contract that family members make with one another. They commit to spending mathematical time together; getting to know each other's mathematical thinking and understanding; and finding time to play math games, solve problems, and notice mathematics in their daily lives. Whether parents and children are cooking in the…

The study of functions has traditionally received the most attention at the secondary level, both in curricula and in standards documents--for example, the Common Core State Standards for Mathematics (CCSSI 2010) and "Principles and Standards for School Mathematics" (National Council of Teachers of Mathematics [NCTM] 2000). However, the…

Suggests that issues surrounding the teaching of algorithms focus not on whether to teach them but rather on balancing and connecting the development of algorithmic thinking. Presents an approach to help students develop their algorithmic thinking. Contains 18 references. (ASK)

Invites students to try magic-number tricks and discover how and why they work. (Author)

Discusses various tools to further understanding of measurement. (Author)

Presents activities providing a cultural journey through history that allow children to understand that many mathematicians have contributed mathematical thoughts and ideas. (KHR)

Presents responses to the Marbles problem, which explores the many ways to arrange a given number of square tiles. (Author/YDS)

Examines activities and children's thinking in four main areas of the Geometry Standard in the National Council of Teachers of Mathematics' (NCTM) "Principles and Standards for School Mathematics": (1) properties of shapes; (2) locations and spatial relationships; (3) transformations and symmetry; and (4) visualization. (Author)

Examines the nature of mathematically rich tasks and varied ways in which students respond to these tasks. Explores approaches for using such tasks to foster inquiry that engages children in mathematical practice. (Contains 16 references.) (ASK)

Describes a method for helping children become powerful thinkers who explore mathematical ideas deeply and creatively as they develop their mathematical promise, and approach mathematics in a manner similar to that of mathematicians in the field. Discusses ways of assessing this kind of learning. (ASK)