"Modeling Mathematical Ideas" combining current research and practical strategies to build teachers and students strategic competence in problem solving.This must-have book supports teachers in understanding learning progressions that addresses conceptual guiding posts as well as students' common misconceptions in investigating and…

How do children learn math--and why do some children struggle with it? The answers are in "Number Sense and Number Nonsense," a straightforward, reader-friendly book for education professionals and an invaluable multidisciplinary resource for researchers. More than a first-ever research synthesis, this highly accessible book brings math…

The manual on problem solving was culled from a set of newspaper articles in the Philadelphia Inquirer. Each brief article typically suggests problem solving strategies and offers sample problems on which to test one's skill. Articles are organized into the categories of input, process, and output. The input section offers ideas about analysis,…

Generally, reading is perceived as consisting of identifying words and increasing comprehension skills, but there are a plethora of additional symbols which students need to read and comprehend meaningfully. This paper first discusses reading across the curriculum, emphasizing abstract words, and then considers symbols peculiar to diverse academic…

Following a brief discussion of two facets of written material readability--reading ease and human interest--two reasons why written instructional material may be so difficult to read are considered: use of technical vocabulary and abstract language. Suggestions to make written instructional materials more readable are provided. (MBR)

Describes the use of chess instruction to develop abstract thinking skills and problem solving among gifted students. Offers suggestions for starting school chess programs, teaching and evaluating chess skills, and measuring the success of both student-players and the program in general. (PB)

This guide describes, from the perspecitve of J. Piaget's theories, the nature of intellectual handicaps and their significance for cognitive development, personality development, and interaction with the environment. A description of intellectual capacity and intellectual development is followed by an analysis of the role of intellectual capacity…

Possible legal justifications for "reasons"--statements that justify conclusions--are discussed. It is suggested that justification is a concept that should be taken seriously and is one that is guided by objective standards, authority, tautology, tradition, consequences, comparison, intuitive moral sense, internal consistency, determinism, or…

The "word problem" is stated for a given collection. Facts regarding Dehn's Algorithm, definition of Thue systems, a rewriting system, lemmas and corollaries are provided. The situation is examined where the monoid presented by a finite Thue system is a group. (DC)

An important task for literature teachers is to develop students' capacity for abstract thinking so that it can be employed on problems at will and by choice. The first process of abstract thinking is one which enables a person to see a connection between A and B, including processes of cause/effect, making analogies, or making comparisons.…

"In Brief" focuses on K-12 mathematics and science research and implications for policymakers, educators, and researchers seeking to improve student learning and achievement This brief highlights the learning gains of 240 elementary students involved in a long-term study in Madison, Wisconsin and their remarkable ability to reason with arithmetic…

Many science curriculum development projects have the goal of increasing students' ability to employ scientific or formal reasoning strategies. Argues that longitudinal data of students who acquired formal reasoning strategies as a consequence of specific instruction are needed to provide evidence that these skills will help in other academic…

Discusses the tutorial process in problem-based learning (PBL) and how it can be used to cultivate higher order thinking skills. Considers the role of the problem, collaboration among peers, the facilitator role, and the importance of student reflection. PBL principles are applied to instruction of gifted students. (DB)

Considers Richard Ohmann's argument that composition texts which instruct students to emphasize concrete details over abstract concepts encourage conformity with the dominant order. Suggests that Ohmann failed to consider the effects of teachers' and students' viewpoints. Cites methods that encourage students to use detail as a device of broader…

The origins of the emphasis on formal proof are discussed as well as more recent views. Factors in acceptance of a proof and the social process of acceptance by mathematicians are included. The impact of formal proof on the curriculum and implications for teaching are given. (DC)