This paper, presented at the 1979 meeting of the American Educational Research Association (AERA), investigates student errors in high school mathematics. A conceptual framework of hypothetical information-handling processes such as procedures, frames, retrieval from memory, visually-moderated sequences (VMS sequences), the integrated sequence,…

Instructors in 14 Navy electronics "A" schools (12 basic core and 2 advanced) were presented with a list of 70 mathematical skills and asked to indicate: (1) how important they were to successful school performance, and (2) whether they were prerequisite, reviewed, or taught in the "A" schools. They were also asked to state the number and type of…

This paper reviews literature related to two questions: (1) How do preschoolers acquire numerical concepts? (2) What range of basic numerical knowledge do beginning kindergarteners possess? The first section briefly highlights main ideas of learning theories. The second section discusses Piaget's concept of conservation of number and how young…

The Materials in this bulletin indicate suggested teaching procedures needed to implement the teaching of "mathematics, 9th Year" as outlined in Curriculum Bulletin No. 3, 1958-59 series, Course of Study Mathematics 7-8-9. Whereas the course of study suggests the application of mathematical principles such as commutativity,…

Information is provided on the methods, rationale, and tests used by PMDC investigators to obtain data on the status of first and second graders during the first five weeks of the school year. Instruments to assess general intelligence, cognitive mathematical concepts and skills, socioeconomic status, and school environment of students from seven…

In Fall 1975, PMDC investigators administered a battery of tests to 185 first graders and 152 second graders to assess children's progress in acquiring mathematical concepts and skills during the beginning school years. Two tests were constructed by PMDC and this document reports item statistics and results from these tests; copies of the tests…

This document contains 15 case studies developed by the group teachers during a teaching experiment. Background information on each second grader, behavior and achievement characteristics, and analyses of the evaluation interviews are presented. (MS)

The author investigates elementary school students' performance when solving selected open distributive sentences in relation to three factors (Open Sentence Type, Context, Number Size) and identifies and classifies solution methods attempted by students and students' errors in performance. Eighty fifth-grade students participated in the…

The paper presented relates to a study done examining the ability of children from grades one through six to locate a point in one, two, and three dimensions and to order a temporal series of events in one, two, and three dimensions. The performance of the subjects was also used to examine a small part of Piaget's theory of cognitive development.…

The sixteen chapters of this book provide the core material for the Elements of Mathematics Program, a secondary sequence developed for highly motivated students with strong verbal abilities. The sequence is based on a functional-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is…

The sixteen chapters of this book provide the core materials for the Elements of Mathematics Program, a secondary sequence developed for highly motivated students with strong verbal abilities. The sequence is based on a functional-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is…

The sixteen chapters of this book provide the core material for the Elements of Mathematics Program, a secondary sequence developed for highly motivated students with strong verbal abilities. The sequence is based on a functional-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is…

In this report, the theoretical background and procedures for a study of concept learning are discussed. Several definitions of the term "concept" are analyzed, and the relations among concepts, chains of concepts, and hierarchies of concepts are explored. Conceptual learning is discussed from several points of view, and axiom systems for the…

In this volume, the results of a study of concept learning are presented. (The background for the study, and descriptions of the treatments--rote reception, rote discovery, conceptual reception, and conceptual discovery--are provided in Part 1.) Several hypotheses concerning the effectiveness of these treatments in learning concepts and on the…

Using this guide and the four popular books noted in it, a student, working independently, will learn about some of the classical ideas and problems of topology: the Meobius strip and Klein bottle, the four color problem, genus of a surface, networks, Euler's formula, and the Jordan Curve Theorem. The unit culminates in a project of the students'…