Presents a series of solution methods to the Eight Queens Problem of placing eight queens on a chess board so that no one queen can capture another. Solution methods progress from empirical approaches to the use of computer algorithms. Geometric transformations are used to find other solutions. (MDH)

Effects of previous training and experience in peer tutoring on student interactions were studied for 16 elementary school classes. Student dyads with experience and training in peer tutoring provided more interactional explanations and incorporated sounder instructional principles. In both situations, student explanations tended to be algorithmic…

Reform efforts in mathematics aim to increase conceptual understanding, an aim that can be supported through concept maps. This study compared the conceptual knowledge of function held by college students in reform and traditional calculus sections at a large state university. Fourteen students from reform sections and 14 from traditional sections…

A paradigm for the recalibration of teacher-made assessment that assesses and evaluates in one operation is formulated. The effort to make the classroom the primary source of educational research activity is contingent on redefining educational research as empirical and not experimental. This emphasizes that the empirical analysis of instructional…

This paper describes an approach to instruction and learning processes in professional training schools using microcomputers and computer assisted instruction (CAI). It is argued that the use of computers in education changes existing approaches to teaching and learning by focusing on the structure of the information being taught, the organization…

The reliability of four branching algorithms commonly used in computer adaptive testing (CAT) was examined. These algorithms were: (1) maximum likelihood (MLE); (2) Bayesian; (3) modal Bayesian; and (4) crossover. Sixty-eight undergraduate college students were randomly assigned to one of the four conditions using the HyperCard-based CAT program,…

This textbook was designed for a first course in differential and integral calculus, and is directed toward students in engineering, the sciences, mathematics, and computer science. Its major goal is to bring students to a level of technical competence and intuitive understanding of calculus that is adequate for applying the subject to real world…

The problem of determining optimal test lengths with fixed total testing time has proved to be a difficult one for criterion-referenced test developers. An algorithm is needed which can be used by test developers to allocate available testing time to maximize the validity of their total criterion-referenced tests or testing programs. To be…

The central objective of this study was to determine the effects of formal training in the use and types of questions and in the nature and use of algorithms on middle school students' achievement in economic geography. Subjects were 190 eighth grade students in a large metropolitan school district. Three experimental groups received either: (1)…

This is one of a series of monographs developed by teachers in schools near Leeds, England. This volume focuses on recommended methods for teaching operations with whole numbers, fractions, decimals, and percentages. For children to attain confidence in dealing with arithmetical processes, it is considered important that they not be confused by…

Bilingual mathematics competencies and competency-coordinated activities are provided in the four sections of this curriculum guide for kindergarten (pre-operational) and grades 1-3 (concrete-operational) children. Topic areas for kindergarten include: classification (logic); comparing/ordering/graphing; quantitative; measurement; geometry;…

This issue contains abstracts and critical comments for 11 articles. Three articles focus on problem solving; the remainder concern understanding of the equals sign, mathematical structure, mathematical abilities, the role of language in tasks involving sets, sex differences in mathematical errors, subtraction, algorithms as schemes, and…

The concept of multiplication is described and illustrated using several different representational systems. A conceptual approach to teaching mathematics is compared with the procedural approach commonly found in the school curriculum. Four different methods of representing the multiplication process with numbers larger than ten are presented:…

The uses of programable calculators in the mathematics classroom are presented. A discussion of the "microelectronics revolution" that has brought programable calculators into our society is also included. Pointed out is that the logical or mental processes used to program the programable calculator are identical to those used to program…

The minicomputer-based Computerized Diagnostic and Decision Training (CDDT) system described combines the principles of artificial intelligence, decision theory, and adaptive computer assisted instruction for training in electronic troubleshooting. The system incorporates an adaptive computer program which learns the student's diagnostic and…