Consider that colorful photographs, eye-catching illustrations, and captivating images intended to make textbooks more appealing may actually distract students from the lesson at hand. Or that asking students to simply solve math problems might not be as effective as having them explain the steps of solutions that are already worked out--even some…

Describes seven number-sense skills for elementary and middle school grades. Provides eight short stories for grades three through eight designed to develop students' number-sense skills in which students replace missing data so that the story makes sense. (MDH)

This paper identifies five types of learning experiences which are relevant to understanding students' grasp of concepts and principles. These include exploring existing concepts, honing and clustering concepts, developing analytical and reasoning skills, developing problem solving skills, and structuring knowledge in memory. Each of these…

Asserts that metacognition is one of the most important developments in the contemporary study of learning. Proposes a theoretical analysis of a number of interrelated issues with regard to their importance for metacognition. Focuses on strategy selection in light of the impasse-based theories of problem solving. (CFR)

Presents teaching methods to rectify the tendency of students and even teachers to divide the smaller number into the larger in problem situations requiring division, while recognizing the impossibility of the answer in the situation. (MDH)

This collection of activities demonstrates how the study of elementary mathematics can be extended beyond the school and involve teachers and students in investigative, problem-based experiences. The activities include topics in geometry, concept of number, algebra, measurement, graphing, statistics, and probability, and are organized into five…

Based on suggestions of participants at the second annual Instructional Methods Forum held in June 1989, the monograph considers cognitive-based approaches to teaching mathematics to students with learning problems. It addresses identification of characteristics of successful cognitive approaches and the role of media and materials. An…

Discusses the role of teacher questioning in the development of a child's concepts of and about mathematics. Proposes the development of mathematical concepts and procedures in problem-solving situations through questioning that engages student thinking and decision making. (MDH)

Discusses the two overgeneralizations "multiplications makes bigger" and "division makes smaller" in the context of solving word problems involving rational numbers less than one. Presents activities to help students make sense of multiplication and division in these situations. (MDH)

The article identifies five incorrect beliefs about mathematics often held by students who have difficulty with mathematics. They include: the relative size of numbers is more important than the relationships between quantities; computation problems must be solved by using a step-by-step algorithm; mathematics problems have only one correct…

This study details the establishment of a teacher/learner laboratory at Monash University in Australia and the information it yielded about the learning and teaching of mathematics. Both instructors and learners understood they were cooperating to help develop an understanding of difficulties in learning and teaching strategies and ways to reduce…

Uses rectangular models for illustrating products of numbers to solve mixture word problems. (MKR)

The purpose of this paper is to demonstrate methods for developing cognitive processes in adult students. It discusses concept formation and concept attainment, problem solving (which involves concept formation and concept attainment), Bruner's three stages of learning (enactive, iconic, and symbolic modes), and visual thinking. A curriculum for…

This manual is part of a series of materials designed to reinforce essential concepts in physical science through interactive, language-sensitive, problem-solving exercises emphasizing cooperative learning. The manual is intended for limited-English-proficient (LEP) students in beginning physical science classes. The materials are for teams of two…

Author presented a selection of examples of the role of connective analogies in invention/discovery. (Author/RK)