This material is designed to examine the research on how children acquire basic addition and subtraction concepts and skills. Two major lines of theories of the development of basic number concepts, called logical concept and quantification skill approaches, are identified. Major recurring issues in the development of early number concepts are…

A group of 24 14-year-old students were presented with sets of algebra tasks using the Leeds Modelling System (LMS), a computer-based modeling system. Four months later, these same students were given a paper-and-pencil test which covered comparable tasks set by LMS. In addition, certain students were given detailed diagnostic interviews. A…

This paper reports the results obtained with a group of 24 14-year-old students when presented with a set of algebra tasks by the Leeds Modelling System (LMS). These same students were given a comparable paper-and-pencil test and detailed interviews some 4 months later. The latter studies uncovered several kinds of student misunderstanding that…

The difficulty of computer programming and other design tasks is a function of the multiple abstractions that combine to form a program's meaning. Thus, comprehension of the final form of a program design, the program text, involves retrieving multiple sets of relationships between parts. The research presented here addresses which, if any,…

A study was designed to develop an instrument and methodological procedure to assess transitive relations within seriation problems in elementary school children using three criteria: explanations, judgments, and strategies. A secondary analysis to assess transitivity used the three criteria according to whether the children were conservers, in…

This report discusses the cognitive-skills approach to teaching. This approach makes explicit the mental activities engaged in by successful thinkers as they solve problems and master ideas, and it attempts to teach these "high aptitude" thinking activities to "low-aptitude" students. The report begins by illustrating and contrasting high- and…

The reasoning ability of 20 ninth grade, 20 eleventh grade, and 15 college freshman boys was explored. Three tasks in reasoning were given each student. In the "turtles task" the student was asked to test a hypothesis; from his responses the investigator determined whether the student tested the hypothesis by trying to find confirming instance or,…

Perspective transformation is a consciously achieved state in which the individual's perspective on life is transformed. The new perspective serves as a vantage point for life's actions and interactions, affecting the way life is lived. Three conditions are basic to achieving perspective transformation: (1) "feeling" experience, i.e.,…

This document deals with the observation of students in a direct translation scheme in the solution of word problems in a university freshman-level Intermediate Algebra class. It is felt that since successful problem solvers of algebraic equations often have as much difficulty in solving word problems as do other students in the classes, the…

The purpose of this study was to uncover information about and gain a greater insight into the extent to which students who are successful in a basic algebra course: l) demonstrate a reversibility of reasoning processes when solving algebraic problems; 2) demonstrate a flexibility of reasoning processes when solving algebraic problems; 3)…

Thinking-aloud protocols of human problem solvers working on geometry problems are presented and discussed. Protocols were obtained from six individuals working on nine different problems in which constructions were used. Nineteen protocols are presented with annotation and discussion, and other protocols are summarized. The primary purpose of the…

The research described here seeks to characterize the "managerial" aspects of expert and novice problem-solving behavior, and to describe the impact of managerial or "executive" actions on success or failure in problem solving. A framework for analyzing protocols of problem-solving sessions based on "episodes" of…

Teachers in elementary schools, supervisors of instruction, and other educational practitioners are the primary audience for this publication. The paper presents philosophical, psychological, and practical reasons for including a problem-solving approach in elementary school instruction. It draws on the writings of John Dewey, Jean Piaget, James…

The primary objective of this study was to describe those mental processes in which teachers engage while making preactive planning decisions. This objective was approached by means of a detailed descriptive case study of one elementary teacher's planning decisions for a five-month period. The study was designed to address a need for descriptions…

Design and results of an investigation attempting to analyze and improve children's solution processes in elementary addition and subtraction problems are described. As background for the study, a conceptual model was developed based on previous research. One dimension of the model relates to the characteristics of the tasks (numerical versus word…