Patterning, or the ability to understand patterns, is a skill commonly taught to young children as part of school mathematics curricula. While a number of studies have demonstrated that patterning is beneficial for young children acquiring mathematical skills, little research exists that examines the cognitive components of the skill. It seems…

Basic brain function is not a mystery. Given that neuroscientists understand the brain's basic functioning processes, one wonders what their research suggests to teachers of developmental algebra. What if we knew how to teach so as to improve understanding of the algebra taught to developmental algebra students? What if we knew how the brain…

"The power of two" is a Royal Institution (Ri) mathematics "master-class". It is a two-and-a half-hour interactive learning session, which, with varying degree of coverage and depth, has been run with students from Year 5 to Year 11, and for teachers. The master class focuses on an historical episode--the Josephus…

The Euclidean algorithm for finding the greatest common divisor is presented. (MNS)

Four answers to a probability problem involving a perceived coincidence are discussed. (MNS)

A familiar Christmas song described as a second-year algebra problem is presented in "The Twelve Days of Christmas". Five strategies for solving inequalities are discussed in "Solving Algebraic Inequalities". (JT)

Advocated is developing intuitive ideas of limits whenever the opportunity arises in elementary mathematics. Examples are given for geometry, fractions, sequences and series, areas, probability, graphing, and the golden section. (MNS)

Deriving all Pythagorean triples from simple patterns within an addition table is presented, with formulas included. (MNS)

A student noticed an interesting fact about the base two numerals for perfect numbers. Mathematical explanations for some questions are given. (MNS)

Presented are the mathematical explanation of the algorithm for representing rational numbers in base two, paper-and-pencil methods for producing the representation, some patterns in these representations, and pseudocode for computer programs to explore these patterns. (MNS)

Patterns resulting from polygonal numbers are explored, with examples of triangular, square, pentagonal, rectangular, and other numbers. Tables and formulas to be developed are included. (MNS)

Discusses the importance of identifying and describing the pattern by students in algebra class. Provides some examples showing the usefulness of the method seeing the pattern from mathematical materials. (YP)

An investigation of patterns in magic triangles leads to a number of discoveries concerning the sums of sides and corners. (MP)

Activities and problems are interspersed with commentary in this book on the learning and teaching of mathematics. The emphasis is on helping students to enjoy mathematics through an awareness of structure and patterns. The chapter titles are as follows: (1) "My Three Sons--A Game"; (2) "The Tower Game"; (3) "Mathematical Games on a Different…