Members of a third-grade class were involved in a heated discussion. They were using a fixed number of links to create fences for toy cows. The children could change the shape of the field produced by the links, but they could not add any links or take any away. Understanding the relationship between perimeter and area is a difficult concept for…

When presented with a problem in mathematics class, students often function as problem performers rather than problem solvers (Rigelman 2007). That is, rather than understanding the problem, students focus on using an operation to complete it. Students' tendencies to act as problem performers can prevent them from suggesting problem-solving…

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…

Children are naturally curious and want to make sense of their world. To implement mathematical tasks that nurture children's desire to reason, it is valuable for teachers to have experienced for themselves comparable tasks and learning environments (Ball and Bass 2000). In this article, the author describes three strategies to facilitate…

"Strategy sharing" is a certain type of discussion that centers on students' ideas and occurs when children present different approaches to problems and provide information about how they solved the problem (Wood, Williams, and McNeal 2004). A teacher may orchestrate a strategy-sharing discussion to achieve one or more of the…

Elapsed-time problems are notoriously difficult for children. Instruction on techniques for teaching and learning elapsed time is not emphasized in current mathematics education literature. Nor is it addressed in "Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence" (NCTM 2006). This absence of…

Each year, more teachers learn about the successful intervention program known as Math Recovery (USMRC 2008; Wright 2003). The program uses Steffe's whole-number schemes to model, understand, and support children's development of whole-number reasoning. Readers are probably less familiar with Steffe's fraction schemes, which have proven similarly…

Problem solving lies at the heart of mathematical learning. Children need opportunities to write, discuss, and solve problems on a regular basis. The problems must incorporate grade-appropriate content and be "accessible and engaging to the students, building on what they know and can do." Teachers also play a key role in establishing a classroom…

This article describes how the promotion of purposeful mathematical discussions can enhance young mathematicians' construction of knowledge and their explanation of strategy use.

Describes the characteristics of young children as they develop problem-solving skills and strategies. (Author/NB)

Presents responses to the Stair Skipping problem that appeared in the April, 2000 issue of this journal. (KHR)

Presents student responses to the "The Darts, Anyone?" problem that appeared in the May, 1999 issue of this journal. The problem concerned finding possible scores on dart rings. (KHR)

This article describes the results of a year-long exploration of first graders' tool use. It also showcases instructional activities designed to link tool use with quantitative understanding. (Contains 3 figures.)

Can a rich problem-solving task challenge a diverse range of students? How would students across various grade levels, from elementary school to secondary school, respond to the same task? These were the questions five different teachers in different schools wanted to explore in their respective classes, ranging from first grade through ninth…

Features responses to a problem that appeared in the January, 2001 issue of this journal. The problem concerned finding all of the shape combinations of two colors of blocks in four-block combinations. (KHR)