A mult tile is a set of polygons each of which can be dissected into smaller polygons similar to the original set of polygons. Using a recursive LOGO method that requires solutions to various geometry and trigonometry problems, dissections of mult tiles are carried out repeatedly to produce tile patterns. (MDH)

In polar coordinates, the intersection of the graphs of two functions, f(x) and g(x), does not always correspond to the solutions of the equation f(x) = g(x). Presented are examples to illustrate this concept, proofs demonstrating why this is true, and a computer program to simultaneously plot polar coordinate graphs. (MDH)

Reported are the results of the Second International Mathematics Study describing U.S. eighth (n=235) and twelfth grade (n=156) teachers' reasons for deciding what teaching methods to employ and topics to cover in the classroom. Teacher knowledge and textbook inclusion or exclusion are the most frequently cited reasons. Implications for curricular…

Defines the mathematical concept of proportionality. Uses graphs of linear relationships to explore and make generalizations about the characteristics of proportional situations to help students critically evaluate problems involving proportions. (MDH)

Discusses the surprising result that the expected number of marbles of one color drawn from a set of marbles of two colors after two draws without replacement is the same as the expected number of that color marble after two draws with replacement. Presents mathematical models to help explain this phenomenon. (MDH)

Reviews chapters of this book on probability in mathematics education. Topics discussed in the chapters include a historical perspective of probability, an epistemological perspective of probability, an overview of the psychological research on probability learning, computers in probability education, and an analysis of the probability curriculum.…

Cryptography is the science that renders data unintelligible to prevent its unauthorized disclosure or modification. Presents an application of matrices used in linear transformations to illustrate a cryptographic system. An example is provided. (17 references) (MDH)

The Monte Carlo procedure of generating random points that lie within the unit square is used to approximate pi, as the ratio of points within the first quadrant of the unit circle to the total number of randomly generated points. A BASIC computer program for this method is included. (JJK)

Several examples of solid figures that calculus students can use to exercise their skills at estimating volume are presented. Although these figures are bounded by surfaces that are portions of regular cylinders, it is interesting to note that their volumes can be expressed as rational numbers. (JJK)

Examined is the extent to which the current trend favoring full integration of LOGO into the mathematics curriculum responds to the current extensions of the LOGO environment, beyond its original applications within the authentic mathematics curriculum, proceeding into the domains of visual arts, physics, and composition, for example. (JJK)

Described is a recursive LOGO method for dissecting polygons into congruent parts (rep tiles) similar to the original polygon, thereby producing unexpected patterns. A list of descriptions for such dissections is included along with suggestions for modifications that allow extended student explorations into tile patterns. (JJK)

Study identified types of software applications and computer-assisted instruction (CAI) software chosen over three years by secondary mathematics teachers enrolled in a graduate level computers-in-education course. Subjects learned four relevant general computer applications and various CAI programs. They unanimously rejected drill and practice…

Children's responses to an alternative model over three lessons were described and their learning assessed in a posttest. Their responses and performances were compared to that of a similar group of children learning through a conventional number line model. The two models were compared from practical and theoretical viewpoints. (Author/CW)

An application of critical cultural and ideological technology is reported in the field of mathematics education. A step-by-step method is set out and applied to a particular classroom problem. (CW)

Described is a theorem which is generally not present in most high school geometry textbooks. Presented are two proofs and two cases which illustrate the use of the SSA theorem. (CW)