Discusses children's place-value understanding, including initial learning interference, vertical number lines, and planned discourse. Describes a learning activity that can guide children from a concrete to a symbolic understanding of place value. (11 references) (MKR)

Provided are examples from many domains of mathematics that illustrate the Fubini Principle in its discrete version: the value of a summation over a rectangular array is independent of the order of summation. Included are: counting using partitions as in proof by pictures, combinatorial arguments, indirect counting as in the inclusion-exclusion…

Examined the effects of using structurally organized tile patterns or diverse objects in various patterns to represent numbers on kindergartners' learning of number concepts. Found that at the level of numerical operations, structured materials facilitate children's choice of non- finger strategies and speed up response time for finger-strategy…

A problem solving approach to the teaching of the Pythagorean Theorem is described. (SD)

A unit on problems involving large numbers can begin with calculating the amounts of ingredients needed to produce several thousand hamburgers. Other sources of computational problems are described. (SD)

Describes how children can learn fundamental concepts of measurement by using nonstandard measuring devices and simple comparisons. (MLH)

This set of worksheets provides exercises related to making change, spending a fixed amount of money by "buying" items at listed prices, and deciding which of two quantities of coins has greater value. (SD)

The activities presented are all designed to encourage children to learn about the structure of whole numbers by looking at number patterns in various ways. (DT)

A series of activities designed to help primary school children understand the meaning of the term "fraction," the symbolization, and equivalence of fractions are presented. Identification of units and pictorial representation are stressed, as is the uses of concrete materials. (SD)

Several classroom activities using sugar cubes, file cards, and other readily available objects are described. The author argues that use of such games can be used to foster mathematical creativity while strengthening computational skills. (SD)

A framework for organizing instruction on the basic facts is presented. Guidelines are given for blending work with concrete materials, thinking strategies, and drill into a meaningful program. (MN)

A modern adaptation of the historic lattice algorithm which can be used for multiplication and division is discussed. How it works is clearly illustrated. (MNS)

Activities with balance beams were used to motivate students and help them to learn basic mathematical principles. Illustrations are included. (MNS)

Four worksheets are given to enhance the understanding of and facility with numerical concepts and relations for students in grades seven through nine. The focus is on enhancing deductive reasoning abilities with Venn diagrams and arrow diagrams. Teaching ideas are included. (MNS)

An addition "trick," an analysis of why it works, and steps in constructing other problems of the same type from the basis of a discovery learning activity for addition. (DT)