Discusses the messages in problem contexts in Standards 2000 from the National Council of Teachers of Mathematics (NCTM). Makes comparisons with the NCTM Standards from 1989. Indicates that the new standards continue to ignore the power that mathematics can have in debate and discussion of issues critical to the elimination of social and economic…

Reflects on activities designed for computer-enhanced in-service training of high school mathematics teachers. Uses a computer-based graphing calculator, a dynamic geometry program, and a spreadsheet program to explore linear algebraic equations that bridge finite and infinite mathematics structures. (ASK)

Reviews the evolution of the educational computer software "Geometer's Sketchpad" and its history. The features of the software invite exploration and play and enable users to sense their own role in shaping and crafting their understanding of mathematics. (ASK)

Reviews the historical development of subtraction algorithms used in the United States. Discusses different algorithms used and developed throughout history that had a major impact on the way subtraction is taught today. (Contains 22 references.) (ASK)

Discusses the development of new mathematics teacher-education programs in Turkey. Presents examples of curricula for elementary and secondary mathematics teachers. (ASK)

Discusses the nature of mathematics, the goals of education, and the political dimension of mathematics. Considers ethnomathematics, the history of mathematics, and advances in ethnomathematics. Proposes a new conception of curriculum. (ASK)

From the perspective of communication of textualized knowledge, problems that concern mathematics education might be amenable to a sharper treatment in which the role of the usual discourse seems important. Contains 14 references. (ASK)

Reviews the nature and application of the skills of reading and writing as they pertain to the learning of mathematics. Argues that students must learn to read mathematically. Contains 22 references. (DDR)

Describes the use of manipulatives for solving simple combinatorial problems which can lead to the discovery of recurrence relations for permutations and combinations. Numerical evidence and visual imagery generated by a computer spreadsheet through modeling these relations can enable students to experience the ease and power of combinatorial…

Discusses the rationale and use of problem fields which are sets of related and/or connected open-ended problem-solving tasks within mathematics instruction. Polygons with matchsticks and the number triangle are two examples of problem fields presented along with variations in conditions that promote other matchstick puzzles. (11 references) (JJK)

Reviews the history of the concept of function, looks at its relationship with other sciences, and discusses its use in the study of real world situations. Discusses the process of constructing mathematical models of function and emphasizes the importance of the roles of the numerical, graphical, and algebraic representational forms. (MDH)

Presents the computer microworlds developed by the Children's Construction of Rational Numbers of Arithmetic (Fractions) Project. Provides an overview of three microworlds: Toys; Sticks; and Candybars. Discusses how children are expected to use the microworlds to construct an understanding of rational numbers. (MDH)

Considers four language arts--speaking, listening, reading, and writing--as activities that enhance the development of mathematical concepts. Suggests ways language arts can be used in learning difficult concepts as missing addends, algorithms, number facts, and problem solving. (39 references) (MDH)

Describes the Microworld Chance, a simulation-oriented computer environment that allows students to explore probability concepts in five subenvironments: coins, dice, spinners, thumbtacks, and marbles. Results of a teaching experiment to examine the effectiveness of the microworld in changing students' misconceptions about probability are…

Describes four activities to develop visualization skills and the concept of dimensionality in which students (1) visualize transforming figures between the second and third dimensions; (2) identify the three-dimensional objects from their two-dimensional projections; (3) conjecture about the vertices, edges, and faces of zero- to four-dimensional…