Describes a study of the estimation skills of mathematicians (N=44), accountants (N=44), psychology students (N=44), and English students (N=44). Explores their methods of estimating the products and quotients of 20 problems. Contains 49 references. (DDR)

Considers educational aspects of the development of ratio and proportion focusing on the arithmetization undergone by these concepts in light of the relationship between mathematics and music. Investigates the instructional aspects of compounding ratios. Points out features of the differences between identity and proportion which can be…

Discussed are the background and implementation of a method of teaching fractions to primary children referred to as "The Visual Concept of Fractions." The advantages and criticisms of the use of this method are stressed. (CW)

Explored is young children's ability to estimate set sizes and use reference points such as 10. Results indicated that many children could accurately place sets somewhat smaller than a reference point but had difficulty placing sets somewhat larger than a reference point. (CW)

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)