In 1943 Jacques Hadamard gave a series of lectures on mathematical invention at the Ecole Libre des Hautes Etudes in New York City. These talks were subsequently published as The Psychology of Mathematical Invention in the Mathematical Field (Hadamard, 1945). In this article I present a study that mirrors the work of Hadamard. Results both…

The Magic Mathworks Travelling Circus is a touring maths lab--in and of itself, a good thing. When children enter it, they find particular pieces of apparatus captioned with particular challenges--which is perhaps not such a good thing. Students are faced with an apparatus that can do only one thing, and so are not encouraged to look again at…

BECAUSE OF THE EVER INCREASING EXPANSION OF KNOWLEDGE AND CULTURAL CHANGES, TEACHING CHILDREN TO DISCOVER (DEFINED HERE AS THE ACQUISITION OF AN ABILITY TO FORMULATE AND SOLVE PROBLEMS) SHOULD BE GIVEN CONSIDERABLE SIGNIFICANCE AS AN EDUCATIONAL GOAL. THE PURPOSE OF THIS REPORT IS (1) TO CLARIFY CERTAIN ASPECTS OF TEACHING CHILDREN TO DISCOVER,…

Meanings of "surprise" are wide and include uplifting and engaging facets like wonder and amazement on the one hand as well as ones that may be of the opposite nature like interruption and disrupt on the other. Pedagogically, educators who use surprise in class activities are focusing on students being "taken aback" by a situation, hopefully…

Human expert problem-solving in science is defined and used to account for scientific discovery. These ideas are used to describe BACON.5, a machine expert problem solver that discovers scientific laws using data-driver heuristics and "expectations" such as symmetry. Implications of BACON.5 type research for traditional science education…

Analyzed were the relationships between and among mathematical ability, verbal ability, mathematical achievement, general scholastic intelligence, number of years of high school training in mathematics, plans to specialize in mathematics education in college, sex, and the student's performance in solving mathematical problems by the discovery…

Discusses the proposition that rarely does an investigation follow the orderly and systematic course suggested by the scientific method. The most vital elements are not the experimental and theoretical tools of science, but human ingenuity and intuition. (BT)

Three models have been proposed to account for the relationship between the principle of commutativity and the development of more economical addition strategies, which disregard addend order. In the first and second models, it has been proposed that either discovery or assumption of commutativity is a necessary condition for the invention of…

A TWO DAY RESEARCH CONFERENCE ON "LEARNING BY DISCOVERY" WAS HELD TO--(1) CLARIFY SOME OF THE ISSUES INVOLVED IN LEARNING BY DISCOVERY, (2) REVIEW WHAT IS KNOWN OF THE SUBJECT, AND (3) SUGGEST WAYS OF EXTENDING KNOWLEDGE ABOUT IT. THE 25 PARTICIPANTS WERE REPRESENTATIVES FROM MANY AREAS IN PSYCHOLOGY AND EDUCATION. OBSERVERS FROM GOVERNMENT…

This research was based on the assumption that the teaching of broadly generalizable cognitive skills should be a primary goal of education--that students can be taught to be better insight problem solvers outside of school by training in school and that they can be given the skills necessary for efficient discovery learning. The subjects were 116…

Explains a discovery activity using the possible positions of the faces of a cube when represented in two dimensions. Suggests rules which would determine which of the edges would connect if the drawing were folded to form the cube. (RS)