Jean Piaget (1970) defined "disequilibrium" as a conflict between new ideas and current conceptions. In this article, the author describes how introducing this concept to her first graders improved formative assessment results and the overall classroom climate during mathematics class. Students feel success in mathematics even without mastering a…

Describes a series of learning activities built around number cubes. Sample activities introduce elementary properties of the cube, the magic rule of seven, and basic concepts related to graphs in the plane coordinate system. (PVD)

Describes how students in a third-grade classroom were given opportunities to practice measurement activities on their school playground. Argues that the school buildings and playground can be rich sources of ways to help students make connections and extend their spatial thinking and reasoning beyond the confines of the classroom. (ASK)

Illustrates how many key algebraic concepts can be informally developed within the number and operations strand taught in the primary grades. Discusses expressions and equations, properties and conventions, relationships between operations, and variables from this perspective. (ASK)

Ben, a good mathematics student, participated in a seven-week study. Describes three tasks that reflect impact of textbooks, real-life connections, and mathematical symbols. Shows that Ben's notion of one-half was task-dependent, concrete, and based on physical actions. (NI)

Addresses difficulty levels and the importance of providing experience at all levels. Levels are count and land, at which children do not understand if the number arrived at is reasonable; number sense and relationships, where children are developing a sense of reasonableness; and parts of numbers, when children are able to work flexibly with…

Describes a unit on rain forests in which first graders studied about rain forests, built a classroom rain forest, and created a bulletin board. They also graphed rainfall, estimated body water, and estimated the number of newspapers that could be produced from one canopy tree. (MKR)

Shows how the children's book "How Big Is a Foot?" can motivate measurement explorations with nonstandard units and lead to the development of standard units. (MKR)

Describes situations in which children developed mathematical concepts through processes of sorting and classifying, comparing, measuring, matching with one-to-one correspondence, and enumerating. Data were gathered while observing informal discourse, during sharing sessions, and in a reading session. (MKR)

Demonstrates the use of "Jumping the Broom," a children's book, to integrate mathematics and social studies. Discusses the use of problem solving, finding patterns, and making conjectures by studying the quilt pattern used in the story. (MKR)