This essay argues for the importance of quantitative reasoning skills as part of a liberal education and describes the successful introduction of a mathematics-based quantitative skills course at a small Canadian university. Today's students need quantitative problem-solving skills, to function as adults, professionals, consumers, and citizens in…

Discusses the history of different methods of representing numbers and how these representations facilitated counting and computing devices such as the abacus. (MDH)

Until recently the testing of a 100-digit number to determine whether it is prime or composite could have taken a century. However, in the past two years a method has been developed enabling a computer to determine the primality of an arbitrary number in about 40 seconds of running time. (Author/JN)

Representation of integers in various bases is explored, with a proof. (MNS)

The archaeology of mathematics is discussed by tracing a portion of the research of Otto Neugebauer and Abraham Sacks. Patterns found on an ancient cuneiform tablet are explored. (MK)

Why a computer error occurred is considered by analyzing the binary system and decimal fractions. How the computer stores numbers is then described. Knowledge of the mathematics behind computer operation is important if one wishes to understand and have confidence in the results of computer calculations. (MNS)

Describes properties of Fibonacci numbers, including the law of recurrence and relationship with the Golden Ratio. Discussed are some applications of the numbers to sewage of towns on a river bank, resistances in electric circuits, and leafy stems in botany. Lists four references. (YP)

A student noticed an interesting fact about the base two numerals for perfect numbers. Mathematical explanations for some questions are given. (MNS)

Presents examples of 3-by-3 and 4-by-4 magic squares. Proves that the numbers 1 to 10 can not be fitted to the intersections of a pentagram and that the sum of the 4 numbers on each line is always 22. (YP)

The hypothesis was tested that students with a field-independent cognitive style would learn most about numeration systems if they had minimum guidance and maximum opportunity for discovery through the use of manipulative materials. Data were gathered on 46 prospective elementary school teachers. The hypothesis was supported. (Author/MH)

Discusses two mathematical ideas that come from the Incan and Mayan cultures: (1) the quipus, an Incan recordkeeping tool that encoded data via a logical-numerical system on spatial arrays of colored, knotted cords; and (2) the link between recording time and counting in the Mayan culture. (MDH)

Presented are the mathematical explanation of the algorithm for representing rational numbers in base two, paper-and-pencil methods for producing the representation, some patterns in these representations, and pseudocode for computer programs to explore these patterns. (MNS)

Difficulties that entering college freshmen showed on a mathematics assessment test are discussed. More students can perform decimal computation than can order decimals. The concept of equivalent decimals should be taught more carefully at every level. (MNS)

Investigated (n=124) preservice school teachers' reasoning and concepts of invariance of fractional numbers under numeration systems in different bases. The majority of students believed that fractions change their numerical value under different symbolic representations. (Author/MKR)

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)