Seventeen research reports are arranged under several broad topics of mathematics education. Section 1 concerns language and mathematics learning, with one paper on word problems and one on concept formation. Papers on university level mathematics in Section 2 explore problem solving, characteristics of school leavers, some mathematical aspects of…

Teaching students to think mathematically or to apply mathematics to the solution of real-world problems has become a national priority. This paper explores a method of developing the basic problem-solving skills in a remedial mathematics course at the college freshman level. The first part of this paper describes some basic problem-solving skills…

During the past decade, problem solving has become a major focus of the mathematics curriculum. Many feel that in this era of increasing technology, it is important for students to learn how to approach a problem situation. This book was designed to help teachers teach problem solving. Chapter 1, "An Introduction to Problem Solving," deals with…

The nature of "A Programing Language" (APL) is viewed as unambiguous, consistent, and powerful. It is based on the notion of functions as imperative verbs, and is used by a small but growing number of mathematicians and computer programers. Three areas of mathematical activity are addressed: calculation of arithmetic expressions,…

Suggests that good number sense is fundamental for success in estimation, approximation, and problem solving. Further, large-number concepts are appropriate for development in upper elementary school, high school, and beyond. Presents examples to enhance a sense of large numbers in middle and high school students. (PK)

Presented are six problems from diverse areas of mathematics that are appropriate for students of differing age and ability levels. (PK)

Twenty secondary mathematics teachers described their thinking as they solved four proportion problems, explained how they would teach two of the problems, and solved four similar problems after having been asked to use proportional strategies. Findings indicate that less formal strategies were not often used by these teachers. (PK)

Presents several kinds of mathematical problems or activities which are suggested by a clock face. (PK)

That the principal axis theorem does not extend to any finite field is demonstrated. Presented are four examples that illustrate the difficulty in extending the principal axis theorem to fields other than the field of real numbers. Included are a theorem and proof that uses only a simple counting argument. (KR)

Presents an instructional strategy for teaching how to solve word problems and understand the operations involved. Describes the acquisition method of the part-whole relationships of problem situations. Provides some samples of the instructional strategy used and classroom test results. Lists nine references. (YP)

Emphasizes the importance of problem-solving attitudes when the problem solver is waiting for a breakthrough. Discusses the classroom use of five components of "mathematical disposition" from the chapter on "Evaluation" in the "Curriculum and Evaluation Standards for School Mathematics." Nine references are listed.…

Investigates the relationship between the strategies used by preservice elementary teachers in geometric problem solving and two primary mental abilities--spatial visualization and formal reasoning. Reports that the two abilities were related to problem-solving performance, and the strategies used were related to achievement in the geometry…

Discusses an activity which models the building of a tunnel by ants using the definitions of derivative and indefinite integral from calculus. Includes a discussion of reasonableness and interpretation of the problem. (MKR)

Presents activities on problem solving, mathematical induction, proof by induction, and use of the phrase "without loss of generality." Provides a computer application illustrating recursive and iterative functions using C language. (ASK)

This article describes activities that promote students' understanding of equation solving through analyzing and correcting student work. (Contains 5 figures.)