Used are test and interview data to extract evidence as to what level tenth graders have coordinated the worlds of arithmetic and algebra and can move freely between them. More dissociation is shown than was expected. (Author/MVL)

Two incidents involving novice teachers with classes in grades 7 and 10 are presented. Then considered are the nature of intuitive mathematics and contributions computers can make to such intuitive mathematics, particularly in Algebra. (MNS)

This article discusses the classroom use of discovery of number pattern. Provided are examples of a table of squares, multiplications of numbers, and algebraic expressions. (YP)

Describes the Interactive Mathematics Program (IMP), a four-year program of problem-based mathematics that integrates algebra, geometry, and trigonometry with additional topics, such as probability and statistics, and uses calculator and computer technology to enhance student understanding. (MKR)

This article provides pedagogical techniques that require active student participation in the use of computer spreadsheets while determining recursive numerical solutions to equations. Included are several computer screen displays which illustrate the various advantages in using spreadsheets specific to synthetic division, the bisection method,…

Presents activities to visually explore the algebraic concepts of variable, constant, the distributive property, and combining like terms. Presents four transparencies that use visual models to understand exercises in students perform the same mental calculations on a number of their choice and obtain the same result. (MDH)

New developments in the use of automatically scorable constructed response item types for large-scale assessment are reviewed for five domains: (1) mathematical reasoning; (2) algebra problem solving; (3) computer science; (4) architecture; and (5) natural language. Ways in which these technologies are likely to shape testing are considered. (SLD)

An incident light ray parallel to the optical axis of a parabolic mirror will be reflected at the focal point and vice versa. Presents a mathematical proof that uses calculus, algebra, and geometry to prove this reflective property. (MDH)

Presents an alternative method to teaching percent problems which uses a 10x10 grid to help students visualize percents. Offers a means of representing information and suggests different approaches for finding solutions. Includes reproducible student worksheet. (MKR)

Discussed are properties possessed by polygons inscribed in the lattice parabola y=x, including the area of a triangle, triangles of minimum area, conditions for right triangles, triangles whose area is the cube of an integer, and implications of Pick's Theorem. Further directions to pursue are suggested. (MDH)

Presented is a scheduling algorithm that uses all the busses at each step for any rectangular array. Included are two lemmas, proofs, a theorem, the solution, and variations on this problem. (KR)

The harmonic mean, neglected in favor of arithmetic and geometric means in modern mathematics, is defined and its historical relationship to music as presented by Pythagoras is described. Two geometric constructions present a picture of harmony, and an application in calculating the square root of a number is given. (MDH)

Presented are three methods to enrich the mathematics classroom. The first introduces an activity allowing students to discover the law of sines. The second gives eight distance-rate-time problems of value for their counterintuitive or elegant solutions. The third poses multiple answer questions that promote student interaction and communication.…

Presented is a teacher's guide for a hands-on activity challenging students to develop problem-solving behaviors by exploring the construction of a right-cylinder of maximum volume from an m x n sheet of metal. Reproducible worksheets leading students through the activity are provided. (MDH)

Discussed are the philosophy and procedures behind the introduction of algebra to students in grade 7 in Australia. Included are the importance of concrete experiences, language development, and the consequences involved in this procedure. (CW)