Integrates the sum, difference, and multiple angle identities into an examination of Ptolemy's Theorem, which states that the sum of the products of the lengths of the opposite sides of a quadrilateral inscribed in a circle is equal to the product of the lengths of the diagonals. (MDH)

Presents ideas for using a spreadsheet to reinforce teaching of enumerative combinatories in the secondary mathematics classroom. (PR)

A computer microworld called Triple Representation Model uses graphical, tabular, and algebraic representations to influence conceptions of function. A majority of students were able to cope with partial data, recognize invariants while coordinating actions among representations, and recognize invariants while creating and comparing different…

Describes situations in which children developed mathematical concepts through processes of sorting and classifying, comparing, measuring, matching with one-to-one correspondence, and enumerating. Data were gathered while observing informal discourse, during sharing sessions, and in a reading session. (MKR)

Low ability sixth graders (n=19) participated in a teaching experiment involving fraction concepts. Results showed students were able to acquire and use semantic processes and transfer these processes to novel tasks. Semantic processing was positively associated with performance. (MKR)

This article offers teaching strategies for developing number sense for children who are blind and braille users. Suggestions focus on developing number meanings, exploring number relationships with manipulatives, understanding the relative magnitude of numbers, developing intuitions about the relative effect of operating on numbers, and…

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)

Discusses a differential equations course emphasizing conceptual understanding, linear and nonlinear systems, and technology. Presents sample exercises illustrating the difference between this approach and the traditional approach. (MKR)

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…

Offers suggestions for presenting multiplication to elementary students at the primary and intermediate levels. At the primary level, the emphasis is on introducing the concept of multiplication; at the intermediate level, the focus is on numeration and place value (using grids and a place value game). (SM)

Reviews the mathematics utilized in the design and construction of suspension bridges, in general, then illustrates these mathematical concepts by examining data associated with the Mackinac Bridge, which connects the two peninsulas of Michigan. Emphasizes the strong interest factor these gigantic structures have for students by attaching a sense…

Provides a brief summary of current research in mathematics education at the college level. Explores the current needs of college-level faculty. Suggests ways of coping with the apparent perception that some of the best contemporary research is useless or irrelevant from the practitioner's point of view. (22 references) (JJK)

Using a graphical analysis of the linear best fit for a set of Cartesian data points, the drawbacks of the least-squares method for determining this best fit are discussed. The Wald Line, which utilizes a variation of the geometric mean, is proposed as the best alternative to the least-squares regression line particularly when the data contain…

Early childhood teachers need to integrate math education into the daily routine of the classroom by using counting books and physical props and also by emphasizing the mathematical aspects of play and other components of the curriculum. (MDM)

Discussed is the method of substitution of variables within the framework of precalculus level extremum problems, both maximum and minimum. Many examples with graphical representations are provided. (JJK)