Open-ended individually administered questions can ascertain whether students can reason about arithmetic problems. Free response test items are useful in assessing students' thought processes as they solve mathematics story problems. Since story problems do not state explicitly which arithmetic operations are required for solution, students must…

An overview is first given of some main theoretical frameworks underlying current European research in mathematical thinking, learning, and teaching. Together with the information-processing and the (neo)-Piagetian approaches, both well known in the United States, two other research paradigms can be distinguished: the action-oriented approach to…

This handbook, and the VITAL Mathematics Series videotapes, contain 12 lessons that model effective use of active learning strategies in elementary mathematics instruction. The lessons are designed for preservice and inservice teacher development programs through courses or individual study. The videotapes that are available separately demonstrate…

The model of instruction proposed by Good and Grouws as an outcome of their research is the focus of this report prepared for teachers in Wisconsin. In chapter 1, the topic discussed is "Effective Mathematics Teaching in the Elementary Grades." Sections are devoted to key instructional behaviors, development, seatwork, homework, special…

This book shows how to increase one's power to analyze and comprehend problems. First, it outlines and illustrates the methods that good problem solvers use in attacking complex ideas. Then it gives some practice in applying these methods to a variety of questions in comprehension and reasoning. Chapters include: (1) "Test Your Mind--See How…

These materials are intended to provide meaningful mathematical experiences for pre-algebra students. These experiences emphasize the development of computational skills, mathematical concepts, and problem-solving techniques. This bulletin may be used as the basis for the first term of a one-year course. The complete course is divided into 12…

This study investigated the relationships between the mathematical problem-solving performance of fourth-grade children, their attitudes toward problem solving, their teachers' attitudes, and related sex and program-type differences. Three instruments were used to gather data. Data were gathered for the first part of the study from 30 classes in…

Recent research on solving addition and subtraction word problems has resulted in the construction of theoretical models of children's problem-solving processes. Some of these models have been translated into computer programs. Characteristics and predictions of the theoretical analysis developed by Riley, Greeno, and Heller (1983) are discussed…

Presented is a discussion of the nature of individual differences in the learning of mathematics, which leads to a review of field-dependent and field-independent cognitive styles. Field-dependence-independence is noted as an important variable in school learning and a study is cited that investigated the relationship between pupil success at…

Sixty-four fifth and sixth-grade pupils were taught number series extrapolation by either an algorithm, fully prescribed problem-solving method or a heuristic, less prescribed method. The trained problems were within categories of two degrees of complexity. There were 16 subjects in each cell of the 2 by 2 design used. Aptitude Treatment…

Applied mathematics is seen often to involve the solution of single equations or systems of equations. A particular technique for solving equations in the context of functions on the real line is examined. This technique includes an iterative process, which is viewed as an algorithm that can be implemented readily on inexpensive and widely…

This study explored the variance in mathematical problem-solving achievement accounted for by sex and ethnicity. Each of 316 adolescents in a rural school district in southeast Texas was administered the California Achievement Test and a set of five affective scales. Reading scores accounted for 49.5% of the variance; computation, 14.6%; affective…

This study addressed: (1) what difference, if any, would calculators make on a typical mathematics assessment instrument; (2) what might occur if students were allowed to use, but were not furnished with, calculators for testing; and (3) what implications do answers to these questions have for future statewide assessment. Eighth-grade students…

This collection of material is designed to illustrate the nature and variety of the idea of proof in mathematics. It is intended to be a "background book" for the use of teachers, particularly those in initial training courses. Individual chapter titles are: (1) The Role of Proof in Mathematics; (2) Logical Reasoning: The Idea of Implication; (3)…

Presented are 13 articles which contain abstracts and analyses of research reports related to mathematics education. The first article considers six working papers, on a variety of topics, from E. G. Begle and the Stanford Mathematics Education Study Group. Of the remaining reports, two deal with problem solving, five with some aspect of learning…