Structure of mathematical concept of multiplication and its integration into conceptual system, with respect to formal and informal aspects of understanding for 10 university students, are investigated through linear scale assessment of examples for prototypical effects and through follow-up interview which included direct explanations of…

Presented is the ancient Egyptian algorithm for the operations of multiplication and division of integers and fractions. Theorems involving unit fractions, proved by Fibonacci, justifying and extending the Egyptian or Ahmes' methods into the Hindu-Arabic numeric representational system are given. (MDH)

The effect of equations in scientific proofs on readers' comprehension was studied. Forty college undergraduates solved unfamiliar physics problems with or without a traditional series of related equations. Verbal proofs produced better responses than did equation-based proofs. Equations in proofs cause readers to shift attention away from…

Illustrates one seven-year-old boy's understanding of mathematical relationships through drawings of his favorite "superheroes." Also illustrates how he conveyed the qualities of his heroes by weaving together the three symbol systems of language, art, and mathematics. (BB)

Reviews research indicating that students' cognitive models hold random events to be equiprobable Examined 87 students between the ages of 15 and 17 to determine whether masking a random event using geometric figures would affect the students' view of the event as equiprobable. Results indicated that masking overcame the equiprobable bias of the…

KeyMath Revised was devised as a power test for use with students from kindergarten through grade 9. The test is divided into three dimensions: basic concepts, operations, and applications. This paper describes the test's administration, summation of data, standardization, reliability, and validity. (JDD)

Presented is an exploration of a number of ways these quantities can be demonstrated and some interconnections between them. Discussed are triangular numbers, sums of squares, sums of cubes, table squares, and counting rectangles. (CW)

Illustrated is the use of computer algebra software to assist in both a computational and theoretical way to develop the underlying theory of polynomials and the partial fraction decomposition of a rational function. Background information and a discussion of theoretical considerations are provided. (KR)

Discusses the contributions in each chapter of the book, highlighting the textbook analyses for each arithmetic topic presented. (MDH)

Presents a mathematics activity involving a function box for students to develop an understanding of patterns, relationships, and functions. Uses the function box as an aid in teaching about squares, cubes, and circles. (ASK)

Many Native Americans struggle with mathematics because they cannot see its relevance. Comments from three Native Americans reveal how art, culture, and math can be taught in an integrated fashion through beadwork. Elementary school children can experience nearly all mathematical concepts presented in school through beadwork, which also teaches…

Discusses key areas in science that require students to have a well-developed sense of numeracy for full understanding. Suggests that some of the difficulties students have with numeracy arise from not distinguishing between the teaching of facts and skills and teaching through conceptual understanding. Makes some recommendations for correcting…

The Monte Carlo method provides approximate solutions to a variety of mathematical problems by performing random sampling simulations with a computer. Presents a program written in Quick BASIC simulating the steps of the Monte Carlo method. (ASK)

Discusses the extent of students' difficulties with spatial structuring in volume and packing problems. Explains how to help students develop more powerful ways of thinking about such problems. (ASK)

Presents small group activities and materials to emphasize geometric properties and definitions. Activities are designed to encourage student reasoning, communication, and measurement. (ASK)