Seventy fifth-grade students in Australia were observed as each solved a jigsaw puzzle. Boys obtained higher scores on a measure of cognitive style and took less time to complete the jigsaw task; the two measures were significantly correlated. Uses of tangrams are also discussed. (MNS)

A test of whether metacognition is a separate factor from cognition was conducted by measuring the effects of metacognitive factors in problem solving, while attempting to hold relevant cognitive factors constant. Learning disabled subjects were less skilled in metacognition with respect to knowledge about cognition and regulation of cognition.…

A class survey is suggested as a way to stimulate students' interest in applying mathematics to a real-life problem that will require them to collect, organize, and interpret data. How to proceed from selection of topic to using the data to estimate and predict is discussed. (MNS)

Example of magic tricks that can be used as an integral part of various lessons in arithmetic and algebra are given. Their mathematical basis is also discussed. (MNS)

A mathematics problem is presented and solved which concerns determining the approximate speed of an automobile involved in an accident. Extensions of the problem are suggested. (DT)

This paper discusses problems many tenth grade students have when asked to apply a familiar formula in an unfamiliar context: specifically factoring a compound expression. Some of their attempts at solution are presented and discussed in terms of structure sense. (Contains 1 table.) [For complete proceedings, see ED496848.]

This book is designed to help adults gain the range of math skills they need to succeed in life and work and on standardized tests including the GED. It is expected to help students overcome math anxiety, discover math as interesting and purposeful, and develop good number sense. Lessons are organized around four strands: (1) skill lessons…

Problem solving and justification of a diversified group of two-year college students was compared with approaches of younger pre-college students working on the same task. The students in this study were engaged in thoughtful mathematics. Both groups found patterns, justified that their patterns were reasonable and, utilized similar strategies…

This paper adds to the research studies on prospective elementary school teachers' mathematics knowledge with findings on proportional reasoning. In addition to analyzing prospective elementary school teachers' solution strategies for solving a missing value proportion task, it also examines the nature of the drawings and writing they used to…

In this paper we report on a case study of a university student (third year of Mathematics course). She was engaged in proving a statement of elementary number theory. We asked her to write the thoughts that accompanied her solving process. She was collaborative and her protocol is suitable to study the interrelation between affect and cognition.…

The materials and ideas in this document are intended to be used by teachers in schools in order to bring adults and children together to experience good mathematics. It features an evening of hands-on mathematics scheduled for one night a week for four weeks. Students and adults come together to share mathematics activities, solve problems, and…

The materials and ideas in this document are intended to be used by teachers in schools in order to bring adults and children together to experience good mathematics. It features an evening of hands-on mathematics scheduled for one night a week for four weeks. Students and adults come together to share mathematics activities, solve problems, and…

This report analyzes the discursive interactions of four students to understand what heuristic methods they develop as well as how and why they build isomorphisms to resolve a combinatorial problem set in a non-Euclidian context. The findings suggest that results of their heuristic actions lead them to build isomorphisms that in turn allow them to…

To examine how conceptual knowledge about fraction magnitudes changes as students' learning progresses, 5th and 7th-grade students were asked to solve fraction magnitude problems that entailed finding a fraction between two given fractions and then to evaluate solutions for similar problems that were modeled for them. When the given fractions…

The logical mysteries in this book are designed to develop critical thinking and deductive reasoning skills, motivate children to read carefully, and develop memory skills. The mystery solutions are explained at the end of the book. The first nine mysteries are intended for third grade students to work on with their teacher or parents. The second…