Describes a teaching experiment examining the possibility of the redefinition of a multiplication problem from a problem of remembering, to a problem of figuring out why arithmetic rules make sense. (YP)

Presented are five scenarios of how division might be introduced to a class of third graders using experiences with the concept, process, and symbolism of division rather than algorithms. Instruction that makes problem solving the emphasis of students' learning is described. (KR)

Another way to add and subtract, in which the mental regrouping strategy is applied to an original 10-structure, is presented. Pupils use a visual model, called "little person," to move from counting to visualization. Originally designed for use with pupils with learning disabilities, this method has wider applicability. (KR)

Investigates how primary-level pupils can solve word problems more effectively using computational skills in small, cooperative groups. Points out six principles for successful cooperative groups through problem solving protocol analysis: (1) teach strategies; (2) rehearse techniques; (3) involve everyone; (4) cooperate to solve problems; (5) keep…

Presented is a conversation with students that gives an insight into the ways students think about decimals. Students were introduced, with the use of a calculator, to decimal notation and systematic experimentation. What students had learned throughout this conversation is discussed. (KR)

Ways in which the standards of problem solving, communication, reasoning, and connections can be incorporated into the elementary geometry curriculum are identified. Visualization of figures, conservation of area, shape and space, and multicultural study are discussed. (KR)

An activity in which students use manipulative materials to help solve simple algebraic equations using the operations of adding inverses, removing opposites, and sharing equally is presented. Directions, examples, the rationale, and cautions are included. (KR)

Presents 3 examples for setting teacher's aims in Japanese and American mathematics classrooms. Provides 10 guidelines for teachers who would like to include more mathematical dialogue and encourage the expression of conceptual splatter in their classrooms. (YP)

A series of activities involving figurate numbers that allow students at various levels to integrate numerical, geometric, arithmetic, patterning, measuring, and problem-solving skills are presented. A discussion of the geometric and numerical aspects of figurate numbers is included. Appended are IBM Logo procedures that will create pentagonal…

Presents a method for demonstrating addition and subtraction of integers on the number line in a way that distinguishes between subtraction and negative numbers. The model depicts the sign of the number by forward or backward movement on the number line. Subtraction is illustrated by a turning around movement. (MDH)

Contains activities for grades 1 through 8 to develop skills in estimation. Designed to help students deal with numbers sensibly and acquire problem solving competency, the estimation activities involve measurement, telling time, computation, and problem solving. (PK)

Examines whether verbal problem-solving skills in a group of fourth graders would improve if they were specifically taught how to generate their own diagrams when solving word problems. Classifies textbook word problems into three general types and describes them: (1) tabular; (2) geometric; and (3) contingency diagraming. (YP)

Describes two simulations for practicing arithmetic skills: "Calculators," simulating the management of a store with a calculator, and "MECC 'Sell' Series," simulating profit-making with different levels of difficulty from grade two to eight. Provides hints for classroom use. (YP)

Presents an activity for representing a given number in as many ways as possible using short periods of time to develop students' number sense and provide the teacher the opportunity to make informal student assessment and diagnosis. Provides specific dialogue of the activity being used in a third grade class. (MDH)

Describes the benchmark and decomposition-recomposition estimation strategies and presents five techniques to develop students' estimation ability. Suggests situations involving quantities of candy and popcorn in which the teacher can model those strategies for the students. (MDH)