Following a short introduction on the rationale and purpose for using algorithmic structures in the teaching of algebra, two topics from elementary algebra are presented in relation to control structures from computer programing, specifically: the multiplication of polynomials defined in terms of nested loops, and the distributive property…

Presents an algorithm to estimate pi by approximating a unit circle with a sequence of inscribed regular polygons. Demonstrates the application of the algorithm with a hand-held calculator and an Apple computer. Provides a program to calculate pi in Pascal programing language. (12 references) (MDH)

Various researchers have associated meaningful problem solving with methods guided directly by a conceptual knowledge base. By contast, a meaningless solving course, or sequence of operations, is essentially independent of the solver's conceptual understanding of the problem under consideration. This paper is the first to document a meaningless,…

This SMSG study guide is designed to aid the teacher in acquiring familiarity with digital computer concepts or to further his/her knowledge of the field. Suitable references for important topics are categorized as central, peripheral, or advanced. Topics covered include: (1) nature and organization of computers; (2) problem analysis; (3)…

The sixteen chapters of this book provide the core material for the Elements of Mathematics Program, a secondary sequence developed for highly motivated students with strong verbal abilities. The sequence is based on a functional-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is…

Activities are given to assist students in seeing a rationale for the difficult algorithms we teach for fractions. Both interpretations of fractions and operations with fractions are discussed. (MNS)

Algorithmic and investigative approaches to mathematics are compared and discussed. Their mutually contradictory spirit is explored. Examples of the application of each method to a mathematics problem are presented. (CW)

Prior studies indicate that, given time to develop their own algorithms, primary students will process multidigit addition or subtraction problems from left to right. Gives evidence to support that idea, describes methods of getting students to invent their own algorithms, and discusses advantages of child-invented procedures. (21 references) (MDH)

Presents a study that analyzed errors made by randomly chosen fourth grade students (25 of 57) while using the division algorithm and investigated the effect of remediation on identified systematic errors. Results affirm that error pattern diagnosis and directed remediation lead to new learning and long-term retention. (MDH)

This article, which is organized around a single, well-known algorithm for root extraction, presents a way of incorporating dynamical systems into the teaching of mathematics. Included are sample exercises using complex numbers and the computer where students have the opportunity to do some analysis on this algorithm. (KR)

Fourteen research reports related to mathematics education are abstracted and analyzed. Two of the reports deal with teacher education, two with problem solving, three with basic operations, and one each with learning disabled students, rational numbers, proportional reasoning, counting, teacher effectiveness, group cooperation on mathematical…

Parts one and two of a one-year computer-oriented calculus course (without analytic geometry) are presented. The ideas of calculus are introduced and motivated through computer (i.e., algorithmic) concepts. An introduction to computing via algorithms and a simple flow chart language allows the book to be self-contained, except that material on…

The article considers the problem of how to plot on the computer screen a circle with center (A,B) and radius R. Several different procedures are discussed and compared. (PK)

Argues that the type of calculator that is used in mathematics instruction is very important. Suggests that four-function calculators fail to give correct values of mathematical expressions far more often than do scientific calculators. (PK)

Describes the nature and use of computer algebra and its applications to various physical sciences. Includes diagrams illustrating, among others, a computer algebra system and flow chart of operation of the Euclidean algorithm. (SK)