Application of the integral calculus to predicting supplies of oil in future years is described. (SD)

A method of approximating areas under curves in precalculus courses is described. (SD)

The inequality involving the arithmetic and geometric means is a powerful tool in dealing with applications of mathematics. It is very important in geometric programming. The article discusses this inequality and demonstrates two real world applications accessible to secondary teachers and students. (Author/KM)

This bulletin focuses on three developments related to evaluation. First, the plans and initial work of the Mathematical Sciences Education Board, formed in 1985, are described. The Board's goals, its view of the major challenges in mathematics education facing the nation's schools, and its plans are discussed. The development of a design for…

Students in adult basic education/general educational development classes need skills in analyzing and solving programs, extending beyond those learned through word problems in the mathematics curriculum. The following strategies can help students broaden their problem-solving skills: (1) act it out, (2) construct a table, (3) draw a picture, (4)…

Reported are early results of a research program that aims to improve children's mathematics learning by developing attitudes and strategies that support processes of interpretation and meaning construction in mathematics. Considerable research shows that many children learn mathematics as symbol manipulation rules, without meaning. Collaborative…

Mathematics is generally regarded as a well-structured discipline by educators and cognitive scientists. This leads to the analysis of the suggestion that practitioners begin investigating possibilities for teaching mathematics as if it were an ill-structured discipline, with more than one interpretation for mathematical statements. The paper is…

This chapter from a longer work concerns the ability of children to solve arithmetic word problems. The studies reviewed suggest that, with age, children's improved ability to solve word problems primarily involves an increase in the complexity of conceptual knowledge required to understand the situations described in those problems. Considered in…

This monograph provides teachers with a wide range of articles on the teaching of problem solving in the mathematics classroom. The first section, on Understanding the Problem, includes articles which provide a sense of the "problem" of teaching problem solving. The second section, on Devising a Plan, provides suggested plans for…

Prior research on problem solving is discussed, followed by a review of research on mental processes, intellectual development, information processing, mental images, and conceptual imagery. Then four intact fourth grade classes of 23 pupils each were assigned to a 2 x 2 factorial design. One factor was the type of instruction (Method A and Method…

Five steps common to different problem solving models are listed. Next, seven specific abilities related to solving problems are discussed and examples given. Sample activities, appropriate to help in developing these specific abilities, are suggested. (LS)

Nine problem situations involving the use of random numbers are given. Topics include cooking, hunting, bacteria contamination, waiting lines, ransom walks, and branching. In addition to the problem situation, questions are suggested which can be used to extend the investigations. (LS)

The focus of this study was on the processes students used in making mathematical conjectures for five divergent problem situations. The relationship of the processes to creativity factors across the problems was also examined. The results of various cluster analyses and correlational measures indicated that students use different sequences of…

This study investigated the effect of initial instruction on the processes children use to solve basic addition and subtraction verbal problems. Prior to instruction and following a 2-month introductory unit on addition and subtraction, 43 first-grade children were individually tested on verbal problems representing different models of addition…