Using science experiments in life science, chemistry, and physics, helps ground students' understanding of abstract algebra concepts in real-world applications. Hands-on activities connect mathematics with science in a way that is accessible to teachers and students alike. Each activity explores a scientific phenomenon, connecting it to algebra…

The cognitive processes in a widely used, non-verbal test of analytic intelligence--the Raven Progressive Matrices Test (J. C. Raven, 1962)--were analyzed. The analysis determined which processes distinguished between higher-scoring and lower-scoring subjects and which processes were common to all subjects and all items on the test. The analysis…

This report summarizes research on experienced programmers' comprehension of computer programs that was carried out over a three-year contract period (1982-85). Following an extensive review of the programming skill literature, an analysis of programs based on the multiple abstractions (points-of-view) that characterize program text and design was…

The reflective judgment (RJ) model is described, along with research findings based on the model and contributions to understanding student intellectual development in higher education. The RJ model (Kitchener & King, 1981) describes a series of changes that occur in the ways adults/young adults understand the process of knowing, and…

An inquiry attempted to build an agenda for research that would result in a cognitive theory of instruction capable of informing educational practice and extending the limits of knowledge about how people learn and develop. What would such a theory look like, how close are we to having one, and what directions must be followed to further its…

Teacher questions have been the subject of a substantial amount of research and analysis in recent years. Debate has centered around the appropriate use of this instructional and evaluative tool. A study examined the impact on student achievement of manipulating abstractness-concreteness, independent of cognitive level, in achievement test items.…

The Inductive Reasoning and Analytical Reasoning tests of the Johnson O'Connor Research Foundation have been analyzed in a factorial study including marker tests for two commonly recognized reasoning factors, induction (three tests) and logical reasoning (two tests). The primary purpose of the study was to determine the extent to which the Johnson…

Over the past several years, one study after another has uncovered a positive relationship between interpersonal interaction and individual achievement. According to a handful of these studies, interaction is more effective than are individually-based strategies for promoting reasoning. We give our attention here to the link that possibly exists…

The difficulties that younger students experience in understanding concepts related to the use of variables in computer programming are examined through descriptions of two studies: (1) detailed case studies of six highly intelligent children--three fourth graders and three sixth graders--who learned to program in BASIC during 60 hours of…

The purpose of this study was to describe and compare kindergarten and first-grade children's performance on addition and subtraction problems presented in two contexts: verbal (in which problem data were linked to physical referents such as objects or people and their actions), and abstract (in which no such links to physical situations…

Students in grades three and four are introduced to the concepts of abstract reasoning, ambiguity, and interpersonal relationships in this philosophic reader. The story involves mystery and myth and works with literary techniques of similie and metaphor. Pixie is introduced as a precocious character who is impatient with other people, a tease, and…

Designed to accompany "Pixie," a philosophy reader for students in grades three and four, this instructional manual presents discussion plans, games, philosophical activities, and reasoning exercises so that the concepts in the reader can be readily operationalized in the classroom. The "Pixie" program focuses on abstract reasoning, ambiguity, and…

Tautologies in student essays, arguments that most commonly assume the truth or self-evidence of themselves without relationship to something other than themselves, can be identified whenever an essay contains a series of nonsuccessive, noncumulative discourse units. Three kinds of tautologies in student papers are tautologies of redundancy,…

Semiotics is the science of signs and the structures of signs within which meanings emerge. The process through which these sign structures are built up is called semiosis. Courses commonly taught as foundational to teacher trainers should be imbued with a specific semiotic emphasis. At a general level, teachers may be introduced to the notion of…

Preservice elementary teachers' use of examples in recognizing and disproving invalid deductive arguments related to topics in elementary school mathematics was examined. Two forms of the Classroom Logic Test were developed, one multiple choice and one free response. Subjects were asked to judge the correctness of arguments and, if incorrect,…