Compared and contrasted are the concepts intuition and logic. The ideas of conceptual thought and algorithmic thought are discussed in terms of the world as a labyrinth, intuition and time, and the structure of knowledge. (KR)

Described is a learning activity that requires students to write a manual to explain how to apply procedures and algorithms used in mathematics. A list of possible precalculus and calculus topics that can be used in this activity is included. (KR)

Discussed is the effectiveness of using analogies in chemistry instruction. Students' mathematics anxiety, spatial visualization skill, and proportional reasoning ability were found to be important aptitudes for determining chemistry achievement. The relationship between analogs and algorithms is described. (KR)

Described are ideas for the development of problem solving in the context of chemistry. Strategies for improving students' problem solving abilities are included. (KR)

Presents an example using a computer to illustrate concepts graphically in an introductory course on differential equations. Discusses the algorithms of the computer program displaying the solutions to an equation and the inclination field of the equation. (YP)

Studies whether students' stated preferences for flowcharts or pseudocodes match their actual behaviors. Provides a review of the literature on flowchart utility. Reports that students preferred flowcharts to pseudocodes. Lists an example of both a flowchart and pseudocode. (MVL)

P-adic or g-adic sets are sets of elements formed by linear combinations of powers of p, a prime number, or g, a counting number, where the coefficients are whole numbers less than p or g. Discusses exercises illustrating basic numerical operations for p-adic and g-adic sets. Provides BASIC computer programs to verify the solutions. (MDH)

Studies the simple dynamical system of the pendulum and the chaotic behavior that occurs when the pendulum is both damped and driven. Provides an algorithm and BASIC program for the numerical solution to the differential equations encountered in the discussion. (MDH)

An algorithm is described for generating smooth curves of first-order continuity. The algorithm is composed of several cubic Bezier curves joined together at the user defined control points. Introduced is a tension control parameter which can be set thus providing additional flexibility in the design of free-form curves. (KR)

Among 1,453 male and 1,133 female academically talented 7- to 11-year-old students, boys performed better overall than girls on mathematical reasoning. Gender differences appeared as early as second grade, varying according to mathematics subskills. Male performance was better on tasks requiring application of algebraic rules and understanding of…

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…