Creates graphs to see how the relative frequency of an event tends to approach the probability of that event as the number of trials increases. Uses a simulation of a poker machine to provide context for this subject. (ASK)

Discusses the mistakes of Kirschner, the German philosopher and mathematician, in calculating factorials of large numbers by hand in the 1600s. Uses computer technology to calculate those numbers now. (ASK)

Responds to the question of how to know whether reforms have an influence on student learning. Discusses the shift in epistemology about the learning of mathematics, systemic notions about schooling, appropriate evidence related to the notion of schooling practices, and assessing mathematics literacy. (Contains 12 references.) (ASK)

Discusses the benefits of new technologies, especially graphing calculators, in the teaching and learning of mathematics. Presents two activities for teaching algebra and regression using graphing calculators. (ASK)

Describes experiences and presents ideas to cope with students of lower ability and improve their self-esteem. (ASK)

Describes the most enduring link between Napoleon and mathematics as the geometric result known as Napoleon's Theorem, which states that if equilateral triangles are drawn on the three sides of any triangle, the line segments joining the centers of these equilateral triangles will themselves form an equilateral triangle. (ASK)

Discusses issues regarding problem solving environments via problem posing. Recognizes the importance of the teacher's questions; language characteristics of problems; problem structure and feature; solution structure; teacher's questions used before, during, or after solving a problem; and introducing problem-posing questions in mathematics…

Discusses problems similar to the Pythagorean Theorem as they were presented in historical mathematical texts from China and Babylon dating back to well before the time of Pythagoras. (ASK)

Examines the role of variation in statistics education. Describes a chance and data unit with a focus on variation that was conducted in three high school mathematics classes. (ASK)

Presents a mathematics learning cycle that can be use in teaching mathematics and gives two examples of how this learning cycle can be utilized in mathematics classrooms. (ASK)

An overview of the history of mathematics and mathematics education is briefly presented, and the impact of learning theories is described. The first-round curriculum projects in the United States, England, and Australia are mentioned; differences between views of mathematics are highlighted. Goals for teaching mathematics are discussed. (DT)

The role of the teacher in discovery teaching is discussed; examples of non-directed and of directed discovery methods are provided. (DT)

Methods of presenting a course on computers for average ability high-school students are outlined briefly. (DT)

The mathematics of cryptology is discussed. Methods for deciphering a code and for ciphering schemes are detailed. (DT)