Activities are presented that permit students to gain firsthand experiences with ideas about two-dimensional and three-dimensional shapes and volume that textbook exercises rarely provide. (MP)

Some practical, hands-on ways in which ideas about geodesic domes can be used in secondary school mathematics are described. Instructions for constructing a one-frequency geodesic sphere are given. (MP)

Three instructional settings were compared to determine which was most effective: no aids, two-dimensional aids, or three-dimensional aids. Results favored the three-dimensional aids. (MP)

The use of two different colored beans or chips to represent positive and negative charges is discussed as a method of demonstrating operations with integers. (MP)

Angle measurement activities utilizing tinker-toys, geoboards, and paper-and-pencil constructions are given which could be used with children prior to the development of the degree concept. (MN)

An instructional sequence in which number lines and beads are used to illustrate addition and subtraction of directed numbers is described. (SD)

The construction of geodesic domes of four different sizes is explained. (JT)

The author illustrates a method for the construction of the eight deltahedra, using cardboard and rubber bands. (MN)

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…