Mathematics education often grapples with the challenge of teaching abstract mathematical concepts, particularly those existing in 3D space. Visualizing, manipulating, and comprehending these abstract objects can be a formidable task for learners. While 3D printing technology has found applications in various fields, its utilization in mathematics…

Twenty years ago when the author was student teaching, he quickly learned what geometry teachers and researchers (e.g., Senk 1985) have long known: High school geometry students struggle with proof. Throughout his career, he has tried to create instructional materials to make proof more accessible to his students. From field-testing materials with…

This article describes a part of a large scale study which helped to gain understanding of the high school mathematics teachers' belief about proof. There is obvious disconnect between general beliefs and high school teachers' conceptions about proof as central element of mathematics and mathematics education. A total of 374 mathematics teachers…

Many "if p, then q" conditionals have decision-theoretic features, such as antecedents or consequents that relate to the utility functions of various agents. These decision-theoretic features leak into reasoning processes, resulting in various paralogical conclusions. The theory of utility conditionals offers a unified account of the various forms…

Bethpage Union Free School District in New York is a high-performing district by almost any current accountability measure. Yet administrators and teachers worried that they were not doing enough to prepare their students as critical thinkers for the 21st century. Inspired by the curriculum framework of the Partnership for 21st Century Skills, the…

A logical thinking test containing logical fallacies was administered to groups of 16-year-old and 17-year-old students (N=437) in Austria, Israel, and the Philippines. Students considered very able performed satisfactorily when required to choose a logically sound option, but exhibited weak performance when test items required a logically…

Discusses students' progress through distinct levels in the development of their thinking as described by van Hiele levels. Focuses on the quadrilaterals and suggests some level 3 tasks and construction problems. (ASK)

Suggests having students write short summaries using the principles of the journalistic news "lead" to help them sharpen their abstraction skills. Includes samples of data blocks from which students would compose their summaries, kernel sentences from the samples, "kernel" kernel sentences, first draft summaries, and 30-word…

To investigate the role expectation based rules governing formal reasoning performance, a battery of group and individual aptitude measures and formal reasoning tests were administered to 17-year-olds. Individual differences in usage of these rules were clarified by establishing an overlap between an aptitude model and formal reasoning.…

Using Raven Progressive Matrices Test items, this study developed an empirical measure of subjects' ability to create new problems. The relationship between this ability and problem solving skills was examined. A very low correlation was found between inventing and solving problems. Problem creation was more difficult than problem solving. (BS)

Lawson's test was used with 66 ninth grade and 63 tenth grade students. Results show: that boys outperformed girls; a small correlation between achievement in science and mathematics and the Lawson test; and that Israeli students achieved significantly higher than United States students on the Piagetian skills measured by the test. (Author/JN)

This study examined whether postprimary education enhances informal reasoning skills, operationalized as skill in constructing arguments about everyday issues. Eight subject groups, balanced for six, ranged over high school, college, graduate school, and nonstudents with or without bachelor's degrees. (Author/BS)

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)

This study examined the problem-solving protocols of 21 students in a grade 11 enriched physics course as well as 3 adult "experts" in physics. Experts and high performing students made more correct metastatements and more references to prior knowledge than did average performing students. (DB)

Thirteen learning disabled and 15 remedial high school students were taught reasoning skills using computer-assisted instruction and were given basic or elaborated corrections. Criterion-referenced test scores were significantly higher for the elaborated-corrections treatment on the post- and maintenance tests and on a transfer test assessing…