Compares the development of two students' understanding of addition and subtraction. One student's understanding is based on memorized rules and the other's on understanding the concept of place value. Discusses the effects of different goals for instruction and the importance of understanding place value. (MDH)

Among 32 ESL students who received training in metacognitive strategies for mathematics problem solving, those students who were the highest achievers in mathematics and whose teachers were involved extensively in project activities were better problem solvers than less able math students or students in low implementation classrooms. Includes…

Presents an alternate form of assignment, called "Special Problems," that incorporates writing in journals into the mathematics classroom. The method requires students to provide process narratives to accompany selected homework exercises. Allows the teacher to monitor the student's thought processes and development. (MDH)

The game "Pythagoras" is an adaptation of the tangram puzzle. Describes the process of finding all the possible convex polygons with seven sides to prove that the solution to a given puzzle shape of seven sides difficult to find was not possible. (MDH)

Relates research findings on the way primary-grade students communicate mathematical ideas through the use of symbols to a framework for students to investigate the part-whole relationship of quantity. Discusses children's problem-solving abilities, linking word problems and symbols, the importance of context for understanding symbols, and the…

Instead of becoming a launching pad for tomorrow, schooling must be worthwhile for today. Learning to learn must overshadow the acquisition of methods, skills, and knowledge. Educators must conscientiously avoid programs that accommodate the masses at the expense of individuals. Principals must exercise influence to replace memorization and rote…

Relationships between brain-lesion location and behavior in 33 males and 31 females with unilateral lesions were studied. Statistical tests suggest that a single model can describe the relationships for females, but in males separate models of the relationships between lesion location, verbal intelligence quotient, and performance intelligence…

This paper discusses a study that explored the mental models of fifth (n=35) and sixth (n=49) graders attending two urban public elementary schools in South Korea in word problem solving. Two levels of mental models (problem model and mathematical model) constructed in the process of word problem solving were investigated. Coding categories for…

Two studies on cognitive performance in mentally retarded children are reported. In the first study, the Bayley Scales of Infant Development were administered to 56 mentally retarded children, aged 2 to 6, to determine the possibility of discerning subsets of items that form a developmental pattern of interrelated subscales, using the SCAMMO scale…

Three learning modules are described and investigated as they reflect different students' conceptions of and approaches to learning. The Schoolwork Module (SWM) focuses on task performance and involves a passive, incremental, piecemeal, and rote memory method of learning, parallel to what might be implied by the Information Processing model of…

This book summarizes and applies the last 2 decades of research on cognitive psychology to the preparation of educational administrators. Following a foreword by Larry Cuban and an introduction by Philip Hallinger, Kenneth Leithwood, and Joseph Murphy, part 1 explores how cognitive perspectives illuminate the conceptualization of problems faced by…

This study examines the construct of problem representation and the processes used by learners to construct or modify problem representations in problem-solving situations. Students (n=14) from freshman calculus courses at the University of California at San Diego participated in videotaped interviews in which they were asked to think aloud as…

A brief discussion of three phases in research on instructional films--whether films can teach (approximately 1910-1950), how films teach (1940 through the late 1950s), and who learns from films (1960-1985)--introduces a review of the research literature on the third phase. The experimental studies reviewed focus on three concerns: (1) use of…

Based on current models of problem solving within cognitive psychology, this study focused on the spontaneous problem solving strategies used by children as they first learned LOGO computer programming, and on strategy transformations that took place during the problem solving process. The research consisted of a six weeks programming training…

The proposed research will thoroughly document the experiences of a small number of fifth grade children in an elementary school computer laboratory using LOGO, an advanced computer language designed for children. This documentation of a LOGO learning experience will offer specific information about the use of current advanced educational…