Discusses the vital place of proofs in geometry classes. Argues that, although inductive geometry with computer software certainly makes theorems come alive, proofs lead to insight and understanding that allow students to extend the concepts that they see in examples. Presents a theorem, its proof, and a computer exercise. (ASK)

Presents a mathematics activity that illustrates how such adjectives as elegant, surprising, concise, and challenging can be, and in fact are, attributed to proofs by a not very expert audience. (ASK)

Presents a mathematics problem that emphasizes looking for patterns and organizing one's efforts, and a vignette that exhibits classroom efforts while solving the problem. (ASK)

Outlines what is known about mentoring processes and what is unique to mentoring mathematics teachers. Offers some guidance for those wishing to be effective mentors. Contains 27 references. (ASK)

Discusses the mathematical preparation of new teachers in teacher-preparation programs. Outlines three of the many possible emphases that might make the mathematical preparation of secondary teachers more appropriate for a teaching career. (ASK)

Introduces a few examples of Mangbetu designs and examines their underlying structure. Describes Mangbetu design and analyzes its geometric features. (ASK)

Discusses reasons for using spreadsheets in mathematics education. Presents mathematics activities for beginning algebra classes using spreadsheets. (ASK)

Presents a mathematics problem on how a sailor decides the shortest distance between two points by using a calculator. (ASK)

Presents Cevian geometry problems (involving a segment that joins a triangle's vertex to a non-vertex point on opposite side) that illustrate how to implement methods for developing flexible strategies of problem solving, finding multiple representations, and making connections to other areas of mathematics and the real world. (ASK)

Presents a mathematics problem on probability and matrices placed in a context with insects. Provides an overview, prerequisites, materials needed, and worksheets. (ASK)

Examines three scoring methods: (1) item-by-item scoring; (2) holistic scoring; and (3) focused holistic or trait scoring. Emphasizes the advantages and disadvantages of each with particular attention given to the power of trait scoring in supporting teacher development and student learning. Contains 16 references. (ASK)

Presents an activity using dynamic-geometry system software to create an environment in which all students can explore and extend the locus definition of conics. (ASK)

Discusses the effects of mathematical language on the teaching and learning of mathematics. Concludes that educators need to expend far greater effort to bring all students to a fuller understanding of, and appreciation for, the language of mathematics. Contains 18 references. (ASK)

Outlines a course on fractal geometry and chaos theory. Discusses how chaos theory and fractal geometry have begun to appear as separate units in the mathematics curriculum and offers an eight unit course by pulling together units related to chaos theory and fractal geometry. Contains 25 references. (ASK)

Describes the efforts in one large county to provide professional development and encourage dialog among elementary, middle, and high school mathematics teachers about issues related to algebraic thinking. Presents information on the algebra network, sample activities, and participant reactions. (ASK)