A sixth-grade teacher reports an incident in which an average student discovered a complex relationship between equivalent fractions. (SD)

Developing numerical relationships with calculators is emphasized. Calculators furnish some needed support for students as they investigate the value of fractions as the numerators or denominators change. An example with Logo programing for computers is also included. (MNS)

The number concepts of greatest common divisor and least common multiple are related to star patterns created through line designs. (JT)

Three examples are given in which students create their own Logo software to explore the topics of number patterns and operations, fractions, and decimal parts in measurement. (MNS)

The goal of this book is to help students make sense of mathematics and become confident in their ability to do so. Section 1: "Foundations of Teaching Mathematics," includes chapters entitled: (1) "Teaching Mathematics: Reflections and Directions"; (2) "Exploring What It Means to Do Mathematics"; (3) "Developing Understanding in Mathematics"; (4)…