Intuition in mathematics is essential but it must be based on good knowledge of mathematics. An example related to velocity, time, and area is presented and discussed, with models, visual approaches, and geometric arguments noted. (Author/KM)

The author describes a series of current economic ideas and situations which can be used in the mathematics classroom to illustrate the use of signed numbers, the coordinate system, univariate and multivariate functions, linear programing, and variation. (SD)

By translating inequalities into equations (e.g., x greater than 0 can be written x- absolute value of x = 0) and forming equations for unions and intersections of solution sets, students can develop equations for polygons. The method can be generalized to yield equations in three dimensions. (SD)

Students calculated the potential speed of a 10-speed bicycle when operated in different gears from measured tire circumference and observed number of revolutions per minute. They then tested the bicycle's speed and compared achieved and theoretical speeds. Hypotheses to explain differences are solicited. (SD)

Seven questions concerning the role of computation and the role of electronic calculators in arithmetic were posed to a sample of teachers, mathematicians, and laymen. Responses are given in percentage form and typical comments are included. (LS)

The possibility of non-transitivity of preference choices is discussed. One example each from voting and from sports demonstrate some conditions where transitivity does not hold. Suggestions are made for using this type of problem in the classroom. (LS)

An interpretation of the transformation formulas for rotations in a plane in terms of the exponential function is given. Addition of two rotations is shown to correspond to the multiplication of the two corresponding matrices. (Author/LS)

A problem is posed concerning the area of certain parts of a plane geometric figure. The problem was used in a student contest with 71 of 270 mathletes answering correctly. An outline of the general proof is given. (LS)