Anti-evolutionists are fond of presenting their audiences with numbers of dizzying magnitude that they use to represent incredibly low probabilities for such events as the chance formation of a protein molecule or the origin of life by invoking beloved mathematical law by Borel. Presents an illustration to reveal what Borel really meant. (ASK)

Some of the most impressive-sounding criticisms of the conventional theory of biological evolution involve probability. Presents a few examples of how probability should and should not be used in discussing evolution. (ASK)

It is very well known that the Cauchy-Schwarz inequality is an important property shared by all inner product spaces and the inner product induces a norm on the space. A proof of the Cauchy-Schwarz inequality for real inner product spaces exists, which does not employ the homogeneous property of the inner product. However, it is shown that a real…

This article describes a classroom learning experience at a Head Start program in Boston, Massachusetts. In this classroom, children were taught how to integrate mathematics and science skills--from exploring shape, pattern, measurement, and spatial relationships to developing an understanding of stability, balance, and properties of materials--by…

Four activities consisting of puzzles are introduced, which help students to recognize the strength of algebraic generalizations. They also assist them to comprehend algebraic concepts, and enable them to develop their individual puzzles and games.

Two technology-oriented activities are used successfully with entry-level geometry students during their study of symmetry. Reflection symmetry gives students opportunities to deepen their understanding of fundamental mathematical concepts like slope and symmetry, in a flexible and self-paced way.

Mathematical problems when solved with different approaches deepen the understanding of topics learned. It is reported that weighted average is commonly used in applications and the relationship between all the ratios involved in the problem emphasized could be learned from Farey sum of two fractions.

For many years I have been advocating the use of hands-on materials to assist students in the understanding and application of mathematical concepts. Some of the methods have been introduced as small parts of earlier Discovery articles, (de Mestre, 1994, 1996, 1998, 1999a, 1999b, 1999c, 2000a, 2000b, 2001), but here I propose to devote the whole…

The kaleidoscope is a toy that turns chips of colored glass into endlessly varied patterns through the use of mirrors. There's something satisfying about patterns--we need them to create meaning, and we find beauty in their symmetry. Yet complex systems defy simple formulas. For example, it is impossible to describe something as mundane as the…

Teachers should not assume a problem is difficult for the students just because it appears difficult. A teacher solves one such difficult mathematical problem, an egg dilemma problem.

Using MAPLE enables students to consider many examples which would be very tedious to work out by hand. This applies to graph plotting as well as to algebraic manipulation. The challenge is to use these observations to develop the students' understanding of mathematical concepts. In this note an interesting relationship arising from inverse…

Faced with the achievement demands of the No Child Left Behind Act and high-stakes testing, principals are being called on to provide leadership that ensures that their students demonstrate mathematical proficiency. To accomplish this goal, it is important for principals to understand what mathematical proficiency is and how they can promote it in…

This article introduces the concept of a prediction interval in a gambling context.

Rolling dice and tossing coins can still be used to teach probability even if students know (or think they know) what happens in these experiments. This article considers many simple variations of these experiments which are interesting, potentially enjoyable and challenging. Using these variations can cause students (and teachers) to think again…

The traditional approach to expressing cumulants in terms of moments is by expansion of the cumulant generating function which is represented as an embedded power series of the moments. The moments are then obtained in terms of cumulants through successive reverse substitutions. In this note we demonstrate how cumulant-moment relations are…