Presented is a problem involving a real-life situation involving simple ideas, computation, and a proof. A variety of other situations in which this type of problem may be applied are discussed. (CW)

Investigates the ways children used their schemes of fractions to interpret fraction situations. Records clinical interviews with nine children (grades three through five). Reports that children do not establish relationships among different schemes when giving meaning to a given situation. (Author/YP)

Investigated whether children who reflected the structure of word problems with their concrete models were successful in learning to symbolically represent problems with structure-based open number sentences. Forty-five first graders were taught to write canonical and noncanonical open number sentences. (Author/YP)

Presents five small group tasks for upper elementary students to find arithmetic averages. Provides worksheets for each task. (YP)

Discusses the geometrical array of the keys on a calculator that can be turned into a problem-solving, problem-posing situation for the upper elementary or middle school classroom. Provides figures showing the arrays, including rows, diagonals, crosses, rhombi, angles, and squares. Lists seven references. (YP)

Provided are four activities focusing on the application of mathematics to real-world situations: (1) Baby Weight; (2) High Temperature; (3) Skin Weight; and (4) Whale Weight. Each activity contains the objective, directions, extensions, and answers with worksheet. The activities required include the skills of making charts and graphs. (YP)

Presents games for practicing and reinforcing the basic facts of addition, subtraction, multiplication, and division in spite of differences in age and ability. Describes the materials and rules for the games. (YP)

Compares two methods of approaching problem solving in quantitative disciplines. The danger of looking at answers too quickly is discussed. (YP)

Learning at a distance from the source of instruction through textbooks and other media is distance learning. Robert Record wrote mathematics textbooks for the home learner of the sixteenth century. He used dialogue between Master and Scholar to present concepts and correct possible mistakes and misconceptions. (DC)

A description of De Morgan's life and work is followed with quotations of his thoughts and insights on the teaching and learning of mathematics. The purpose is to illustrate the sharpness of his ideas, his creative insights, and his wit for the enjoyment of the reader. (DC)

Coordinates anthropological and cognitive perspectives on one child's learning of the standard addition algorithm in second and third grade. Analysis showed that the student abandoned his self-generated computational algorithms in favor of less understood conventional procedures. (25 references) (Author/MKR)

Elementary education students (n=141) were asked to estimate answers to 25 arithmetic problems. Half were presented the problems in an application (word problem) format, and the other half received the same problems in a computational format. Results indicated higher success levels with the applied format which is contradictory to previous results…

Eye-fixation analysis of 38 undergraduates allowed identification of phases in solution of arithmetic word problems and location of students' difficulties with inconsistent problems within the phases. Results indicate that the locus of the inconsistency effect lies outside the execution phase of problem solving. (SLD)

Presents a model of rational number using pairs of line segments which can embody ratios of numbers. Actions upon these segments can embody arithmetical operations. Discusses tasks in a computer environment for bringing out diverse algebraic and geometric meanings of rational numbers. (Contains 23 references.) (MKR/Author)

Attempted to establish the incidence of using taught algorithms versus invented methods of subtraction in (n=1,370) male secondary school students and to relate the use of invented methods to age, mathematical achievement, and lateral thinking ability. Use of invented algorithms increased with age. (23 references) (MKR)