Describes examples of rational representation as a guide for translating terminology and information encountered in manuals for computers. Discusses four limitations of the representation. (YP)

Discusses arithmetic during long-multiplications and long-division. Provides examples in decimal reciprocals for the numbers 1 through 20; connection with divisibility tests; repeating patterns; and a common fallacy on repeating decimals. (YP)

Describes a model for geometrical probability. Presents two examples of basic theories of probability using geometrical probability. Provides three problems using the described theorem. (YP)

Discusses the planning, organizing, and implementing of a week of mathematics activities at an elementary school. Describes five activity stations, including activities for mental mathematics, calculator mathematics, estimation, geoboards and tengrams, and graphing and estimation exercises. (YP)

Provides a discussion and an example of a problem which occurs in mathematical contests or entrance examinations and deals with the question of the magnitude of exponentials. Includes additional illustrative examples. (RT)

Students have the opportunity to verbalize relationships that demonstrate the acquisition of good number sense. They are to develop clues about the answer to a problem without computing or telling the answer, and to state or write several things they know about the answer to each problem. (MNS)

Describes the algorithm used to select a simple random sample of certain size without having to list all possible samples and a justification based on Pascal's triangle. Provides testing results by various computers. (YP)

Studies of young children's sequence of development from counting to the beginnings of formal arithmetic are reviewed. Four essential basic skills are identified: use of counting words, enumeration, the cardinality rule, and quantitative comparison. The contribution of counting to the development of arithmetical proficiency is stressed. (JDD)

Demonstrates how spreadsheets can be used to implement linear system solving algorithms in college mathematics classes. Lotus 1-2-3 is described, a linear system of equations is illustrated using spreadsheets, and the interplay between applications, computations, and theory is discussed. (four references) (LRW)

Proposes a simple procedure based on an expansion of the exponential terms of Raoult's law by applying it to the case of the benzene-toluene mixture. The results with experimental values are presented as a table. (YP)

Describes how five-year-old children responded to the investigation of looking for patterns in a multiplication square. Provides a 10 x 10 multiplication square for the investigation. (YP)

Describes a method of teaching the order of mathematical operations based upon the psychological theory of conceptual generalization. (MDH)

Discusses rationale for use of children's counting books and guidelines for selection and use. Provides suggestions for writing individual or class counting books. Includes an annotated booklist. (HTH)

Notes the importance of students' understanding measurement concepts to enable solving real world problems. Suggests classroom activities to sharpen students' measurement skills. Emphasizes active participation of students in groups or individually. (BAC)

Reviews research on computational estimation and curricular and instructional issues, characterizes computational estimation and distinguishes it from other types of estimation, summarizes the generally low levels of student performance on estimation across several cultures, and identifies difficulties inherent in assessing computational…