There may be a social and an intellectual aspect to the process of development of mathematical knowledge. This paper describes quadratic equations as intellectual mathematics and as colloquial mathematics. Provides some historical data. (YP)

Discusses the needs and the content of a philosophy of mathematics course. Provided are sample term paper topics, sample final exam items, and an annotated bibliography. (YP)

Provides several problems and their solutions for a descriptive statistics course. Included are problems related to measurement, data collection, sample construction, applications, and computation. Discusses the misleading nature of statistics. (YP)

Provides a BASIC program to compute the number of shuffles required for packs containing even numbers of cards up to 100. Lists 4 further questions on the shuffling program. (YP)

Shows a series of Euclidean equations using the Euclidean algorithm to get the greatest common divisor of two integers. Describes the use of the equations to generate a series of circles. Discusses computer generation of Euclidean circles and provides a BASIC program. (YP)

We review the processes of goal identification employed in teacher planning. A new type of graphical organizer (Fact-Action-Schema-Transcript or FAST) is introduced and its applications to teacher planning discussed. We describe a pair of algorithms for (a) creating FASTs for undergraduate mathematics and (b) using FASTs to create sets of student…

This paper reports a study in which eighteen structural and linguistic variables were identified, defined and used in an attempt to determine which variables accounted for a significant amount of the observed variance in the difficulty level of items on two different conditional reasoning tests administered to high school and college students. The…

Reported are the results of an eighteen-month study of junior college students using programmed algebra materials. Of the 118 students tested at the beginning of the study, only 77 completed the course. When the students were divided into three subgroups based on either their entering mathematics ability or reading ability, the highest group…

This pamphlet provides a comprehensive listing of mathematics tests available in the United States classified under eight headings: Arithmetic; Junior High; Batteries and General Listings, K-14; High School; General; Algebra; Geometry; Trigonometry; and College-related. Information given for each test includes title, authorship, grade levels and…

The author argues that statistics is no more a branch of mathematics than it is of economics. It is suggested that because statistics is a distinct discipline, it is unprofessional for mathematicians who lack training and experience in working with data to teach statistics. (PK)

Eleven responses are given regarding whether mathematicians should teach statistics. In general statistics is seen as a separate discipline not appropriately subsumed in the mathematics department. Some general discussion of statistics instruction is given. (PK)

This essay paper discusses the decline in the numbers of students studying mathematics at German universities. Sections on mathematics in German secondary schools, reasons for the decline in numbers, and issues related to reversing the trend are included. The article also highlights the German "Diplom" and mathematics departments in…

Describes Newton's method to locate roots of an equation using the Newton-Raphson iteration formula. Develops an adaptive method overcoming limitations of the iteration method. Provides the algorithm and computer program of the adaptive Newton-Raphson method. (YP)

Determines which chessboards contain a chromatic rectangle having all four corners the same color for any black-white coloring. Expands the problem to a three color problem. (YP)

Illustrates how to draw a regular pentagon. Shows the sequence of a succession of regular pentagons formed by extending the sides. Calculates the general formula of the Lucas and Fibonacci sequences. Presents a regular icosahedron as an example of the golden ratio. (YP)