Investigates a way to assist students with learning differences. Considers mathematical connections appropriate in middle grades through college mathematics centered around the words "and" and "or" within the fields of logic, set theory, algebra, number theory, and probability. Teachers and students should be encouraged to investigate mathematical…

Developed are simple recursion formulas for generating the exact distribution of the longest run of heads, both for a fair coin and for a biased coin. Discusses the applications of runs-related phenomena such as molecular biology, Markov chains, geometric variables, and random variables. (YP)

Describes the development of the concept of function including changes of mental images, from the geometric conception versus the algebraic conception and the logical conception versus the algebraic conception. Lists 27 references. (YP)

Describes the mathematics of cycloidal curves. Illustrates how a Spirograph can be used to produce them. Discusses some modifications and applications of the Spirograph. (YP)

Presents an approach to help elementary school teachers understand the difficulties involved in division by zero. Teaching suggestions to help guide students are included. (YP)

Describes a model for geometrical probability. Presents two examples of basic theories of probability using geometrical probability. Provides three problems using the described theorem. (YP)

Describes seven spatial abilities related to mathematics including eye-motor coordination, figure-ground perception, perceptual constancy, position-in-space perception, perception of spatial relationships, visual discrimination, and visual memory. Discusses the relationship of the spatial abilities to the study of geometry. Lists 19 references.…

Offers an approach to the understanding and to the teaching of the fundamental theorem of calculus. Stresses teaching the relation between a function and its derivative and the functions themselves. (YP)

Provides a discussion and an example of a problem which occurs in mathematical contests or entrance examinations and deals with the question of the magnitude of exponentials. Includes additional illustrative examples. (RT)

Presents an example of a mathematical question to illustrate an approach to simultaneous equations. Provides an example with diagrammatic and numerical representations. Suggests some possible developments. (YP)

Proposes elements of a model of knowledge structures used in comprehending and generating graphs. Uses the competence model to attempt to organize and interpret findings on misconceptions in graphing. Discusses two types of common misconceptions; treating the graph as a picture and slope-height confusions. (YP)

Presents an approach to Vieta's formula involving pi and infinite product expansions of the sine and cosine functions. Indicates how the formula could be used in computing approximations of pi. (MVL)

Presents frequently occurring patterns of repeating decimals. Provides a method for completing a repeating decimal with a long period from only a portion of the string. Gives several theorems with proofs. (MVL)

Illustrates how heuristics can provide a psychological narrative of Hippocrates' and Archytas' thinking on the duplication of the cube. Four general heuristic techniques were used. (YP)

Describes the algorithm used to select a simple random sample of certain size without having to list all possible samples and a justification based on Pascal's triangle. Provides testing results by various computers. (YP)