Proposed is a gradual transition from arithmetic to the idea of an equation with variables in the elementary grades. Vertical and horizontal formats of open sentences, the instructional sequence, vocabulary, and levels of understanding are discussed in this article. (KR)

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 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)

Investigates different approaches of students from different cultures to problems and problem-solving strategies. Suggests ways to encourage students to use algebraic strategies. Provides some action research ideas for teachers to try in their classrooms. Contains 11 references. (ASK)

Lists questions and answers for mathematical investigations that teachers should ask when they consider using alternative approaches to teach new content. Presents an example of a mathematical investigation on concepts of area, symmetry, pattern, function, algebraic rules, and Pythagorean theorem. Argues that investigations offer opportunities for…

Although research has confirmed block scheduling's nonacademic benefits, effects on academic achievement are mixed. Teachers do not always replace lecturing with more effective participatory teaching methods. To work best under an intensive or alternating block schedule, schools should adapt the math curriculum to reduce course redundancy and…

Presents activities which highlight major concepts of linear programming. Demonstrates how technology allows students to solve linear programming problems using exploration prior to learning algorithmic methods. (DDR)

This aptitude-treatment interaction (ATI) study was designed to clarify the relationship between the aptitude variable spatial visualization and two modes of presentation of linear absolute-value inequalities. The modes of presentation include computer-enhanced instruction (CEI) and traditional. (Author/KR)

Discusses research findings related to students' ability to make connections between analytical (symbolic) and graphical representations of functions in calculus. Describes graphing tasks and typical student interpretations. Implications for teaching are suggested. (Contains 17 references.) (MKR)

Presents a series of 5 reproducible worksheets for grade levels 5-10 that provide hands-on activities to help develop the concept of slope. (MDH)