This paper reviews the literature concerning the development of deductive reasoning, emphasizing the verbal form of the arguments involved in the reasoning. Empirical research is grouped under the heading: assessment studies, critical thinking, instructional studies, and logic and proof. A conceptual framework is developed and a section on errors…

Investigated proportional reasoning of a select group of older, college-bound adolescents on a task set in a geometric/spatial context with a multiple-proportion, multiplicative structure. Sex-related differences and the influence of course experience in mathematics and science were also investigated. (JN)

Article describes an experiment to deterimine how to promote cognitive growth in terms of classroom mathematics learning. (MM)

Reported is a study involving six group administered tasks concerning proportional, probablistic, and correlational reasoning with 505 students aged 11.5 to 20.0 years. Investigated were the effectiveness of the tasks for assessing formal reasoning; categories of classification for students' responses and implications for teaching are suggested by…

Quantitative literacy for students with deafness is addressed, noting work by the National Council of Teachers of Mathematics to establish curriculum standards for grades K-12. The standards stress problem solving, communication, reasoning, making mathematical connections, and the need for educators of the deaf to pursue mathematics literacy with…

Examines U.S. and Chinese 6th grade students' mathematical thinking and reasoning involved in solving six process-constrained and six process-open problems. Concludes that the Chinese sample had a significantly higher mean score than the U.S. sample on the process-constrained tasks, but the sample of U.S. students had a significantly higher mean…

This is the first of the NCTM yearbooks to be written by a single author. He traces the history of the terms "variable" and "function" and discusses the meaning of functionality. The logical and psychological bases are examined followed by a general discussion of the psychology of reasoning. Two chapters outline the history of…

Four experiments are presented to support the theory that the rule system governing the law of large numbers is not tied to a content domain, and that it can be improved by formal teaching techniques. The experiments showed that statistical training enhanced everyday reasoning. Test problems and objective example problems are appended. (LMO)

Discusses geometrical reasoning in the framework of the theory of Figural Concepts to highlight the interaction between the figural and conceptual components of geometrical concepts. Examples of students' difficulties and errors in geometrical reasoning are interpreted according to the internal tension that appears in figural concepts resulting…

Six fifth-grade children participated in a four-day teaching experiment on complex additively structured problems to investigate difficulties in concurrently holding in mind situations in which items play multiple roles. Difficulties included distinguishing take-away difference from comparison difference and indirect evaluation of an additive…

Math historian Morris Kline suggests that math instruction should be made concrete and that teachers should not turn kids off by making intuitively understood concepts complex through the use of fancy language. He advocates using pictorial representations and examples of actual physical occurrences. The dyslexic student has special difficulties in…

The papers contained in this document were originally presented at the May 1978 conference on Modeling Mathematical Cognitive Development sponsored by the Models of Learning Mathematics Working Group of the Georgia Center for the Study of Learning and Teaching Mathematics. Most have been revised to reflect comments and suggestions made at the…

Seventh-grade students enrolled in two average classes were pretested, randomly assigned to two training groups--an active group in which physical materials were employed and a verbal group in which standard textbook procedures were employed--immediately posttested and posttested one month later. The active group showed greater achievement and…

The author reviews pertinent studies conducted between 1917 and 1973 in which the introspective-retrospective technique of data gathering was employed in determining the mental processes of children in arithmetical reasoning and the difficulties encountered. (MN)

Relational thinking is suggested as a major goal of elementary mathematics education and some problems purporting to induce relational thinking are suggested. (CS)