"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,…

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)

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…

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)

The papers contained in this document were originally presented at the May 1978 conference on Modeling Mathematical Cognitive Development sponsored by the Models of Learning Mathematics Working Group of the Georgia Center for the Study of Learning and Teaching Mathematics. Most have been revised to reflect comments and suggestions made at the…

This article presents specific instructional approaches and examples to develop the algebraic reasoning skills of middle and secondary students with mild disabilities. Discussion of the National Council of Teachers of Mathematics standards identifies general principles, content standards, and process standards. Discussion of effective instruction…

Concepts from cognitive psychology are presented as an alternative framework to arithmetic instruction for students with disabilities. The approach, which emphasizes reasoning, communication, and problem solving, is applied to addition, division, multiplication, subtraction, and word problems. The purpose of arithmetic instruction is asserted to…

This article describes a problem-solving strategy unit to be used as a supplement to the regular mathematics curriculum at the primary level. Specific teaching steps and examples are given for three developmental stages of thinking: (1) concrete, (2) representational, and (3) abstract. (DB)

A mapping procedure based on the SOLO Taxonomy developmental model was used to classify the problem-solving strategies of students (n=34) in grades K-2. Only one multiplication problem was used to isolate three components of the problem-solving procedure. (MDH)

Effective intervention strategies for learning disabled students should recognize such cognitive deficiencies as weaknesses in attention, memory deficits, and problems in generalizing and abstracting information. Approaches which emphasize enhanced learning processes include: self-monitoring; repetition and deliberate instruction in control…

This article describes methods for teaching higher level thinking skills to children. A four-step teaching plan utilizing Beyer's Taxonomy of thinking skills provides a sequential technique for teaching these skills as do increased verbal interaction, skillful questioning, and use of knowledge organizers. The I PLAN strategy can aid decision…

The use of microcomputer-assisted therapy as part of the total rehabilitation plan for brain-injured individuals with cognitive-communicative impairments is addressed. Design of effective computer-assisted remediation requires a careful decision-making process. Specific types of software are suggested for dealing with deficits in organization,…