Reasons for using manipulative materials in mathematics instruction are discussed: motivation, stimulation to think mathematically, and introduction of big ideas in mathematics. (MNS)

Activities that provide opportunities for students to investigate solving linear equations using both a physical and a pictorial model are given. Students should discover a method that will permit them to solve such equations at the symbolic level. (MNS)

Geometric constructions are viewed as providing an opportunity both for use of tangible materials and for problem solving, as well as being useful and interesting experiences. A brief history is provided, followed by seven constructions using a hinged mirror. (MNS)

Following background information on Rubik's Cube, a bibliography of print materials and computer software useful in using the cube in mathematics and science instruction is presented. (MNS)

Research on object exploration by infants addresses milestones in the process by normally developing infants, including spontaneous manipulation strategies. Implications for developmentalists working with high-risk preterm infants are noted, including the need for direct assistance in manipulation and for selection of materials. (CL)

A new model of geoboard based on an axis, the "Gyratory Geoboard," is described. Some activities for teaching plane rotations and central symmetry are included. (MNS)

Presents pedagogical and physical criteria for selecting manipulative materials. Pedagogical criteria include clear representation of mathematical ideas, appropriateness for students' developmental level, interest, and versatility. Physical criteria include durability, simplicity, attractiveness, manageability and ease of storage, and reasonable…

Discusses: (1) different types of learning (concepts, properties, facts, procedures, algorithms, skills, and problem solving); (2) types of learning behaviors; and (3) types of representational models, considering concreteness, meaningfulness, and manipulation (active manipulation, passive manipulation, and nonmanipulation). (JN)

Describes an exploratory study in which alternative dramatic play areas are compared among older preschoolers. Twelve children, grouped into same-sex pairs (55 to 67 months old), were observed in various playroom environments. Results indicate that theme specific settings stimulated dramatic play while neutral areas encouraged personal fantasy…

Descriptions are given of how groups aged 7, 10, and 13 tackled the problem of how many squares are on a chessboard. Teachers noted that often the less able children were the ones with ideas, whereas the able ones became impatient and were unwilling to go on trying. (MNS)

Methods of constructing polyhedra models are described. (DT)

A method for using a geoboard to calculate the area of a polygon is described and explained. (DT)

Saxon's primary mathematics series is a "hands-on," success-oriented program which emphasizes manipulatives and mental math. The series addresses the multisensory approach to teaching. Its use enables all children to develop a solid foundation in the language and basic concepts of mathematics. Concepts are presented in carefully…

Innovations in technology, along with the growing prevalence of the Internet and its increasing availability in classrooms and homes throughout the world, have created a new class of manipulatives, virtual manipulatives. These "virtual manipulatives" offer a new, enhanced approach for teaching and learning mathematics using manipulatives and…

Student scores on the Woodcock-Johnson Achievement Test showed four years of declining scores. Data collected from a teacher pre-questionnaire indicated problems in the areas: elementary mathematics curriculum, the curriculum adoption process, training of teachers in using purchased texts and manipulatives, confidence of teachers in utilizing…