This document focuses on a series of studies that viewed aspects of conditional reasoning. The investigations were concerned with the processes children use to acquire patterns of deductive inference and logical relationships pertaining to propositional reasoning. The first experiment, involving 96 children each in grades 2 and 5, investigated the…

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…

Much recent cognitive and artificial intelligence research has focused on the development of "schema theory." This theory supposes the existence of knowledge and memory structures that encode prototypical descriptions of familiar concepts. Schema theory has developed in a scientific environment that stresses interdisciplinary approaches…

Approaches to helping students remember concepts in secondary mathematics are presented. The eleven points listed are: 1) distinguishing between natural and whole numbers; 2) remembering isosceles triangles have two equal sides; 3) finding all possible pairs of integral factors of a given number; 4) recalling the meaning of reflexive, symmetric,…

The purpose of this document is to survey at least some of the important research literature on solving linear equations in order to identify information that might suggest ways to improve teaching effectiveness. The studies that are examined employ a wide range of research techniques, are based often on quite different perspectives, and span over…

The two main objectives of the present study were to get a better understanding of sixth-graders' solution processes with respect to arithmetic word problems and to investigate the possibility of improving children's problem-solving ability through instruction. As background for the study, a hypothetical model of the problem-solving process was…

The componential conception of intelligence is summarized and contrasted with the psychometric conception. A brief history of concepts of intelligence is presented, beginning with Galton's anthropometric approach and Binet's more educationally relevant approach. Spearman's, and later Thurstone's, contributions to factor analysis promoted a…

The purpose of this study was to select a high school using the Individualized Instructional System (ISIS) materials and the Introductory Physical Science (IPS) course and to detect any changes in the students' attitudes toward science and ability to employ specific processes of science at the end of a semester of coursework. Wayne, Nebraska, High…

The booklet focuses on the use of the logical inductive strategy to teach problem solving skills to mildly retarded learners. An introductory section examines three research studies on interventions in the area of problem solving with the retarded learner and concludes, among other things, that mainstreaming has underscored the need for this…

Reported is an attempt to examine the nature of the reasoning used by college students who consistently erred on timer tape problems and a comparison of their performance with that of students who made logical responses. The author suggests that the poor performance of students, classified as intuitive responders, is a result of their use of an…

CHANGES WERE STUDIED IN THE PROBLEM-SOLVING BEHAVIOR OF HIGH SCHOOL STUDENTS AS A FUNCTION OF A CAREFULLY DESIGNED TRAINING PROGRAM. TRAINING WAS DEFINED AS THE DEVELOPMENT OF STUDENT AWARENESS OF PROBLEM-SOLVING STRATEGIES USED. INSTRUMENTS WERE DEVELOPED AND REFINED TO MEASURE PROBLEM-SOLVING BEHAVIOR. SPECIFICALLY TESTED WAS THE FOLLOWING…

A SERIES OF EXPERIMENTS WAS DESIGNED TO STUDY THE VALUE OF TEACHING CHILDREN SUCH A COMPLEX PROBLEM-SOLVING STRATEGY AS TO USE KNOWLEDGE OF RESULTS AFTER A PERFORMANCE TRIAL TO REJECT MORE THAN ONE HYPOTHESIS AT A TIME (MULTIPLE HYPOTHESIS STRATEGY). APPROXIMATELY 150 THIRD-GRADE CHILDREN WERE DIVIDED INTO 3 GROUPS--THOSE TAUGHT THE MULTIPLE…

This study investigated the relationships between Piagetian logical reasoning abilities with an information processing capacity, and first-grade children's performance on verbal addition and subtraction problems. An analysis of simple arithmetic problems indicated that several reasoning abilities identified by Piaget are needed to achieve…

Presented are abstracts of 18 research reports. Topics covered include: (1) The effect of a numeration learning hierarchy on mathematics attitudes in kindergarten children; (2) Children's acquisition and production of mathematical rules; (3) Preschoolers' abilities to recognize counting errors; (4) Young children's solution processes for verbal…

Forty-three first-grade children, who had received no formal instruction in addition and subtraction, were individually administered 20 problems that could be solved using addition or subtraction. The problems were selected to represent the following semantic types: joining, separating, part-part-whole, comparison, and equalizing. Responses were…