Even after many decades of productive research, problem solving instruction is still considered ineffective. In this study we address some limitations of extant problem solving models related to the phenomenon of insight during problem solving. Currently, there are two main views on the source of insight during problem solving. Proponents of the…

According to the intuitive rules theory, students are affected by a small number of intuitive rules when solving a wide variety of science and mathematics tasks. The current study considers the relationship between students' Piagetian cognitive levels and their tendency to answer in line with intuitive rules when solving comparison tasks. The…

Students react similarly to a wide variety of conceptually unrelated situations. Describes a rule that is manifested when two systems are equal with respect to certain quantity A, but differ in another quantity B. Indicates that in such situations students often argue that the same amount of A implies the same amount of B. (Contains 30…

Analyzes the relationship between intuitions and structural schemata. Indicates that intuitions are generally based on structural schemata and the transition from schemata to intuitions is achieved by a particular process of compression. (Contains 38 references.) (Author/ASK)

Abstracts of 12 mathematics education research reports and critical comments (by the abstractors) about the reports are provided in this issue of Investigations in Mathematics Education. The reports are: "More Precisely Defining and Measuring the Order-Irrelevance Principle" (Arthur Baroody); "Children's Relative Number Judgments:…

Counterintuitive moments in the classroom challenge common sense and practice and can be used to help mathematics students appreciate the need to explore, reflect, and reason. Proposed are four examples involving geometry, systems of equations, and matrices as counterintuitive instances. (MDH)

Mathematical creativity ensures the growth of mathematics as a whole. However, the source of this growth, the creativity of the mathematician, is a relatively unexplored area in mathematics and mathematics education. In order to investigate how mathematicians create mathematics, a qualitative study involving five creative mathematicians was…

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)

Divided into two parts, this article analyzes why some pupils feel reserve about instantaneous velocities and instantaneous flows. The second part relates reactions of pupils facing a problem that implicates the instantaneous rate of change. Describes some characteristics of this problem that enables the authors to explain its instructional…

Presents 13 examples in which the intuitive approach to solve the problem is often misleading. Presents analysis of these problems for five different sources of misleading intuitive generators: lack of analysis, unbalanced perception, improper analogy, improper generalization, and misuse of symmetry. (MDH)

With respect to the innovative roles of technology within the educational realm, an important task of educational research is the investigation of how school children accommodate themselves to innovative computer-based learning environments. This paper describes the strategies and techniques employed and extended by above-average second- through…