This work provides a characterization of the learning of graph theory through the lens of the van Hiele model. For this purpose, we perform a theoretical analysis structured through the processes of reasoning that students activate when solving graph theory problems: recognition, use and formulation of definitions, classification, and proof. We…

We report our qualitative study of twenty-four students enrolled in the second-semester of a second-year undergraduate (sophomore-level) organic chemistry course, Organic Two. We asked the research participants to propose the product and electron-pushing mechanism of elementary mechanistic steps in the absence and presence of the corresponding…

This synthesis paper discusses the research exploring analogical reasoning, the role of analogies in the engineering design process, and educational applications for analogical reasoning. Researchers have discovered that analogical reasoning is often a fundamental cognitive tool in design problem solving. Regarding the possible role of analogical…

In an experiment using a conditional logic task, subjects were given a set of cards defining a particular conditional relationship. The subjects were required to determine the rule and predict the outcomes of the rule. Rule structure was varied by providing subjects with either a suggested rule, a partial rule, or no rule for each set of cards.…

Students and instructors may be frustrated with students' lack of understanding of sociological concepts. We suggest that the difficulty of teaching and learning sociology is that sociological concepts and relationships require the use of abstract reasoning patterns. Many students are unaccustomed to using these abstract reasoning patterns. We use…

Proposes that there is a universal method for all realms of knowledge. Reviews Descartes's definition of the universal method, the engineering definition, and the philosophical basis for the universal method. Contends that the engineering method best represents the universal method. (ML)

Children's analogical reasoning has traditionally been measured by classical four-term analogy tasks or problem-solving tasks. Current theories of analogical development and the evidence on which they are based are reviewed. It is concluded that structural views of analogical development are wrong, and knowledge-based accounts of what develops are…

Described is research which sought to prove the hypothesis that mental models tend to preserve their autonomy with regard to the originals they are meant to represent. The results of this investigation involving 200 Israeli students are presented. (CW)

Examines some of the assumptions associated with attempts to define the "engineering method." Critiques a previously stated definition of this method, and offers an alternative definition that attempts to include the ideas put forth in the previous definition. Discusses the use of engineering heuristics in both definitions. (TW)

The mathematical experiences of elementary students often focus on memorizing facts and rules as opposed to making sense of the subject and developing problem solving skills. Students spend large amounts of time processing, memorizing and sorting collections of data which are tasks well performed by computer technology. To correct this situation,…

Students (N=49) enrolled in a physics course for elementary teachers were evaluated for their abilities to use: (1) combinatorial logic; (2) separation and control of variables; (3) proportional reasoning; and (4) reciprocal implications. Performance of four Piagetian tasks during interviews was treated as a measure of the degree to which students…

Examines the problem-solving strategies of experts and novices. Summarizes the overall performance of four experts and eight novices. Examines several protocols in depth in order to show how subjects introduced new terms and relationships during problem solving sessions. Compares the strategies of expert and novice problem solvers. (CW)

Research has revealed distinct differences in the problem-solving approaches of high- and low-aptitude students. As a consequence, content area teachers can focus on thinking skills by having students describe their mental processes and giving them feedback on erroneous or incomplete reasoning. (TE)

A number of studies have reported that there is a strong tendency to ignore base-rate information in favor of individuating information, except when the former can readily be incorporated into a causal schema. In this study, students in eight undergraduate classes were given problems in which the base-rate information was either causal or…

Compared and contrasted are the concepts intuition and logic. The ideas of conceptual thought and algorithmic thought are discussed in terms of the world as a labyrinth, intuition and time, and the structure of knowledge. (KR)