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A study to determine the impact of adult basic education programs on the upward mobility of disadvantaged workers is presented. The paper industry was chosen for case analysis because of the nature of the upgrading problems, the vast adjustments required by the Civil Rights Act of 1964, and the fact that these ABE programs have been operational for several years. The programs studied were utilized by companies in an attempt to increase the potential for promotion of Negroes who were originally employed for unskilled jobs and consigned to permanent occupation of those jobs. The objective was to improve the educational qualifications of such employees so that they could handle jobs on progression lines or in maintenance. Results were: (1) The ABE programs promised more than they could deliver; and (2) The relation of training to promotion was neither brought out carefully beforehand nor demonstrated after the programs were in effect. The following points were also brought out: (1) Relatively few Negro disadvantaged workers completed the courses; (2) Those who completed the courses showed little improvement in arithmetic and virtually none in reading; (3) There was no relationship between the taking of courses, improvement in test scores, and job advancement; (4) The packaged courses disregarded the cultural characteristics of the trainees; (5) Programmed teaching methods were largely unsuccessful; and (6) The particular conditions and incentives were not such as to produce successful literacy training. (Author/CK)

Eight papers focus upon specific subject programs for educable and trainable mentally retarded (EMR and TMR) students. Three of the papers, concerning driver education and traffic safety education for EMR students, cover driver education guidelines and materials developed in a Michigan state institute involving teachers of EMR and teachers of driver education, Alabama's statewide project for EMR driver and traffic safety education, and a pilot project involving EMR students in a two-part Non-Traditional Driver Education Program emphasizing safety training. Other papers describe in detail the EMR home economics program at Oak Ridge (Tennessee) High School, discuss instructional objectives for work-study programs for EMR elementary through high school students, briefly describe the Northwestern Illinois Athletic Association for Trainable Mentally Handicapped Youth, present a Piagetian approach to arithmetic for the retarded, and examine the team work experience (supervised work in teams in community settings) in work oriented special education programs for retarded persons not able to benefit from the type of vocational training available within the structure of present work study programs on the secondary level. (KW)

The papers contained in this volume are the result of nine seminars conducted during 1972 and the first half of 1973. One concern that dominates many papers is the preparation of individuals for the teaching role. O'Neill reports the evaluation results of a preservice program that maximizes the use of field experiences; Duffey discusses the results of his study designed to evaluate undergraduates in social studies methods courses; Ashlock presents a rationale for the need of certification for elementary school mathematics specialists; after analyzing texts used in reading methods courses, Moretz and Davey assert the need for more consistent use of reading terminology; Amershek urges professional competence as the criterion for the selection of staff members for preschool programs. Another concern reflected in many of the papers is the nature of school programs for learners. Maley describes the impact of a reading emphasis industrial arts program; Gantt advocates a focus on the child's educational environment; Shields discusses reading in the kindergarten; and Hall and Ribovich build a rationale for teaching reading as a form of communication. Following each paper is a brief summary of participant reactions. (WR)

This booklet is a collection of the papers presented at a joint session of the Mathematical Association of America and the National Council of Teachers of Mathematics during the fiftieth annual meeting of the MAA. These papers were presented under the headings of "Geometry and School Mathematics,""High School Geometry," and "School Geometry and the Future." Eight papers are presented in their entirety. An abstract of a ninth paper, "Geometry: The Cambridge Conference View" by Edwin E. Moise is also included. Authors of the individual papers do not act as spokesmen for the MAA or NCTM but express personal viewpoints. (FL)

This publication contains sixteen abstracts of papers presented at the Research Reporting Sessions of the National Council of Teachers of Mathematics (NCTM) Annual Meeting. The investigations reported by Anthony, Creswell, Higgins, and Weise focus on curriculum and classroom innovations in the school mathematics program. Investigations by Gibbons, Pearce, Rector, and Wells relate to instruction and methods for teaching mathematical concepts. Research presented by Carry, Fey, Miller, and Vigilante is concerned with certain logical inference patterns and reasoning abilities in students. Bell and Gorth report the results of a survey of mathematics teachers with respect to current issues and a new design for evaluation in mathematics. Research on behavioral objectives for a seventh grade mathematics and for a freshman calculus course is reported by Bierden and Picard. (RP)

A PAPER PRESENTED TO THE SECTION ON EDUCATION (Q) OF THE 1967 AMERICAN ASSOCIATION OF SCIENCE ANNUAL CONVENTION, THIS DOCUMENT DISCUSSES THE ACTIVITIES OF THE DIVISION OF SCIENCE TEACHING (DST) OF UNESCO. INCLUDED ARE DISCUSSIONS OF (1) THE OVERALL PROGRAM BUDGET, (2) AN HISTORICAL PERSPECTIVE OF THE DEVELOPMENT OF DST AND ITS RELATIONSHIP TO THE EDUCATION SECTOR OF UNESCO, AND (3) A DESCRIPTION OF THE PRESENT OVERALL PROGRAM AND PROJECTIONS FOR THE FUTURE. THE PRESENT PROGRAM IS DESCRIBED UNDER ITS FOUR MAIN PARTS (1) COLLECTION AND EXCHANGE OF INFORMATION, (2) PILOT PROJECTS ON NEW APPROACHES AND MATERIALS FOR THE TEACHING OF BASIC SCIENCES, (3) OTHER ACTIVITIES TO IMPROVE THE TEACHING OF THE BASIC SCIENCES AT UNIVERSITY AND POST-GRADUATE LEVELS, AND (4) STIMULATION OF INTEREST IN SCIENCE. SPECIFIC PROJECTS AND PROGRAMS BEING CARRIED OUT UNDER EACH OF THE FOUR MAIN PARTS ARE DISCUSSED AND THE PRIMARY GEOGRAPHIC AREAS AFFECTED ARE INDICATED. A BIBLIOGRAPHY FOR THE PROVISION OF MORE DETAILED INFORMATION IS INCLUDED. (DS)

The "Television Polytechnic" program of 1966 - 1970 was a joint effort of the Polish Ministry of Higher Education and Polish Television to provide televised education for working students. The subjects taught were those normally included in the first two years of the higher technical schools--math, physics, geometry, chemistry, mechanics of materials, and electrotechnics. Each semester lectures were given by professors from the higher technical schools, and students were provided with texts and access to consultation centers. Assessment indicated that television lectures were helpful to regular students as a complement to their classroom experiences and were a useful means of providing basic instruction to those not enrolled in a higher school. Preparatory and first year television courses will remain as permanent elements in the Polish educational system and the recent implementation of a second channel will lead to an expansion of programs, including many aimed at post-graduate audiences. (PB)

A study of a cemetery can reveal much about the lives of people of the past and can be used as a supplement to classroom experiences. Possible objectives of a field trip to a cemetery might be: (1) to develop an appreciation and awareness of the cemetery as a supplement to the present curricula of art, language arts, history, mathematics, and others; (2) to develop a respect and appreciation for this particular resource that will result in proper care of, and behavior at, the cemetery; (3) to develop an understanding of men of past generations, their relationship to their environment, and their effects upon our present environment; (4) to motivate students to do further study on their own, apart from that done in school; and (5) to have students become aware of their own feelings while in this type of environment. In this study guide, samples of concepts, topics, and questions have been organized into subject matter categories: (JH)

The Money/Counting Kit for Handicapped Children and Youth, frees the teacher from lessons in money and counting concepts and enables a student to learn at his own rate with immediate feedback from activity cards, name cards, thermoformed coin cards (optional), and self-instructional booklets. The activity cards, which may be used individually or in groups, explain games and counting principles. Name cards contain coin names whereas 24 coin cards carry detailed raised impressions of coins. The four self-instructional booklets (each with 24 pages) offer exercises in simple matching, addition and subtraction, matching coin and price, and making change; and may be used in conjunction with real coins, "play" money, or the thermoformed coin cards. (MC)

The objectives of the Los Angeles Model Mathematics Project (LAMMP) are stated by the administration as improvement of mathematical skills and understanding of mathematical concepts; improvement of the pupils' self-image; identification of specific assets and limitations relating to the learning process; development and use of special instructional materials and programs and assessment of their values; selection and use of appropriate commercially developed equipment, instructional materials, and programs and assessment of their values. This report is a preliminary evaluation of the plan and a summary and interpretation of evaluation data. It is hoped that the formative evaluation approach recommended, is adopted. This type of evaluation will be important to provide teachers with enough time to work with the evaluation team and on their own in the preparation of testing materials. This additional demand on time could bring large benefits in the better monitoring of pupil progress and the adequate assessment of newly created instructional materials. (ON)

Attainment tests in English and mathematics were administered to a total sample of 2,011/15-year old students. The English test consisted of a composition and a test battery of objective items. Marking of the composition was made by the test designer on a rapid first-impression reading. The objective test battery consisted of a comprehension test, an interlinear test, a test of critical judgment, a paragraph organization test, and a vocabulary test. The test in mathematics was in general mathematics, with the questions being restricted to traditional mathematics. A try-out of the test was administered to 300 students, and results were subjected to item analysis. The reliability of the test was 0.94. An exploratory comparison of standards grade by grade is presented in the following forms: (1) comparison of mean scores, standard deviations, and test/grade correlations; (2) comparison based on percentile levels of subject test scores grade by grade in both the GCE and CSE samples; and (3) comparison of grades in the form of "ladders" showing both the GCE/CSE overlap and the comparable performance in all the other grades. The essentially tentative results show that English and mathematics tests provide a sharper measure of ability within their respective subjects than do the general ability tests. An appendix provides the method of analysis. (DB)

At this seminar, educational practitioners and researchers affirmed that school curricula must be redesigned to teach the student to reason, explore, and discover for himself. The seminar participants discussed innovations currently available and the steps that should be taken by elementary schools to supplant the teaching of facts with instruction in problem solving skills. Several participants presented position statements on emerging practices in education that bode well for the educational advancement of young learners. These statements and subsequent discussions are summarized under topics having particular implications for student-centered schooling in the coming years. (Author)

Alternate hypotheses are given for Neale's findings that attitudes toward mathematics have little effect on achievement. A schemata of proposed research on affective factors in mathematics learning is presented. (JG)

Described is a physical realization of the Klein four-group which shows the isomorphism of the symmetry group of the rectangle and Piaget's INRC group of logical implications. (MM)

Included are papers presented at the 1969 University of Illinois Colloquium on the Preparation of Teacher Educators in Mathematics. The first paper, "On the Preparation of the Teacher of Teachers" by B. Othanel Smith, examines the prominence of research in the teacher training programs. The second, "Source and Supply of Leadership in Mathematics Education" by Howard F. Fehr, discusses the characteristics of leaders and the tasks of future leaders in mathematics education. The last, "Preparation for Effective Mathematics Teaching in the Inner City" by Irwin K. Feinstein, outlines what should be the mathematical and professional background of those teachers working with inner city children. Following each of these three papers are two response papers written by other mathematics educators. (RS)

Characteristics of the Miami-Dade (Florida) Junior College are presented in this paper to describe the: (1) philosophy of the community college, (2) implications of this philosophy to the mathematics program, and (3) possible solutions to specific problems. Some of the areas needing reform are: (1) the mathematical training of technicians, (2) screening and placement of students, (3) mathematics for the general education student, (4) computer assisted instruction, (5) mathematics for preservice elementary teachers, (6) the remedial student in mathematics. This paper was presented at the 1970 Annula Meeting of the National Council of Teachers of Mathematics. (RS)

The 83 papers presented at the 1972 Conference on Computers in Undergraduate Curricula are reproduced in this volume. With computer science specifically excluded as an area of interest for the conference, papers fall under the following headings: biology, business, chemistry, economics, education, engineering, geography, languages and art, mathematics, physics, social sciences, statistics, and a general section on faculty training, software exchange, and shoestring facilities. (RH)

The primary aim of these five technical papers is to indicate aspects of proof theory which may be of use in the study of non-numerical computing. The three main papers are entitled: "Checking of Computer Programs;""Consistency Proofs and Programs for Translators;" and "Experiments with Computers on the Complexity of Non-numerical computations." The author shows that many theorems on computability in traditional metamathematics are of little use to the computer scientist because they do not lead to feasible algorithms. He also suggests alternative approaches to proof theory which would be of greater applicability. (MM)

Nonadditive analogues of what is considered to be the essential mathematics of additive measurement are presented. The scope of this paper is defined when measurement theories are reformulated in such a way to assign transformations of numbers to transformations of natural objects. This paper is limited to theories of measurement in which empirical transformations are represented by affine measurement. (CK)

A new general approach to the problem of oblique factor transformation is identified and presented as an alternative to the common "blind" transformation techniques currently available. In addition, techniques for implementing such an approach are developed. The first section of the paper contains a brief review of the procrustes problem. The next section contains the rationale for a somewhat related--"quasi-procrustean"--approach to oblique factor transformation. The third section contains the development of new techniques for implementing this approach. Following this derivation, solutions for three well-known sets of data are presented. Finally, some aspects of such an approach in need of further research are discussed. (Author)

Procedures for grouping students into homogeneous subsets have long interested educational researchers. The research reported in this paper is an investigation of a set of objective grouping procedures based on multivariate analysis considerations. Four multivariate functions that might serve as criteria for adequate grouping are given and discussed; a method for optimizing these functions is also described. The set of procedures is illustrated through application to data from two samples of students, each student with scores on either ten or eleven subtests of a criterion referenced mathematics inventory. The results indicate that the procedures discussed provide a promising means for grouping students to minimize classroom heterogeneity. (Author)

This paper presents a method of encoding geometric line-drawings in a way which allows sets of such drawings to be interpreted as formal languages. A characterization of certain geometric predicates in terms of their properties as languages is obtained, and techniques usually associated with generative grammars and formal automata are then applied to the geometric framework. Section 1 of the paper specifies the geometric framework; section 2 develops the background material on formal languages, grammars, and automata; section 3 is concerned with geometric predicates; section 4 covers invariance theorems; and section 5 indicates areas for further investigations. (DT)

Three related documents comprise this final report of a project dealing with the creation, testing and distribution of mathematical software. The first summarizes discussions held by the principal investigators with selected experts on mathematical software, the second consists of a working paper for discussion, and the third is a paper which considers the pros and cons of distributing software via different media. The project's research team conferred with about two dozen leaders in the development of mathematical software, originated the concept of a mathematical software alliance, conducted a Software Certification Workshop, and developed techniques for software distribution. The study recommended that an alliance of institutions should be established to provide a focal point for the creation and dissemination of high quality mathematical software and proposed the formation of a Mathematical Software Advisory Council which would be charged to: 1) initiate a program of research on methods of evaluating mathematical software; 2) assume technical review and policy guidance for selected activities now underway; 3) contract for the development of mathematical software; and 4) provide a plan for the growth of these initial activities. (PB)

The central aim of this paper and its projected successors is to prove in detail that stimulus-response theory, or at least a mathematically precise version, can give an account of the learning of many phrase-structure grammars. Section 2 is concerned with standard notions of finite and probabilistic automata. An automaton is defined as a device with a finite number of internal states. Section 3 presents a treatment of the stimulus-response theory. In Section 4 the most important result of the paper is proved; namely, any finite automaton can be represented at asymtote by an appropriate model of stimulus-response theory. In Section 5 some extensions of these results to probabilistic automata are sketched, and an example from arithmetic is worked out in detail. The central idea is to show that by applying accepted principles of conditioning an organism may theoretically be taught by an appropriate reinforcement schedule to respond as a finite automaton. (RP)

Reports on the AMS Conference on Communication Problems in the Mathematical Sciences which was organized by the Society's Committee to Monitor Problems in Communication is presented. The scientific program of the conference included a number of special addresses and five panel discussions. Among the items discussed were (1) the need for founding a new American survey journal at the research level along the lines of the Russian journal, USPEHI, (2) the Information Exchange Groups established in the field of biochemistry to facilitate preprint exchange, (3) a description of the organization and activities of the American Institute of Physics, (4) the distinction between "important" papers and technical papers, (5) several types of editorial problems, (6) duplication of results, (7) the merits of reviews versus author abstracts, and (8) the history of several reviewing journals from various countries. (RP)

THE FIRST PAPER, "REPORT OF MATHEMATICS CONFERENCE," IS A SUMMARY OF DISCUSSIONS BY 29 PARTICIPANTS IN A CONFERENCE ON CURRENT PROBLEMS IN MATHEMATICS EDUCATION RESEARCH. REPORTED ARE (1) RECENT PROGRESS, PROBLEMS, AND PLANS OF CURRICULUM DEVELOPMENT GROUPS, (2) GENERAL FORMULATION OF CURRICULUM AND METHODS, (3) TEACHER TRAINING, (4) COMMUNICATION, AND (5) RESEARCH MANPOWER. THE SECOND PAPER, "ELEMENTARY MODERN MATHEMATICS FROM THE ADVANCED STANDPOINT," GIVES A RECOMMENDED SYLLABUS FOR THE FIRST FIVE SEMESTERS OF A SIX-SEMESTER COLLEGE MATHEMATICS COURSE TO BE TAKEN BY POTENTIAL HIGH SCHOOL TEACHERS. FINALLY, THE THIRD PAPER, "SCHOOL MATHEMATICS STUDY GROUP (SMSG) AND THE GIFTED CHILD," REPORTS THE REASON FOR INCLUDING EXPLICIT RECOMMENDATIONS FOR EDUCATING THE GIFTED CHILD IN ANY LONG-RANGE CURRICULUM REFORM. (RP)

THIS PAPER PRESENTS A RATIONALE FOR CURRICULUM DEVELOPMENT IN THE PRE-SCHOOL YEARS AND OUTLINES A METHODOLOGY FOR CURRICULUM DESIGN IN GENERAL. AN EXTENSIVE APPLICATION OF THIS METHOD TO THE DESIGN OF AN EARLY LEARNING CURRICULUM WILL BE UNDERTAKEN OVER THE NEXT FIVE YEARS BY THE PRIMARY EDUCATION PROJECT. THE PROJECT AIMS TO DESIGN AND IMPLEMENT AN INDIVIDUALIZED CURRICULUM AND SCHOOL ENVIRONMENT FOR A HETEROGENEOUS URBAN POPULATION. THE PROGRAM WILL BEGIN AT THE PRE-SCHOOL LEVEL, WITH THREE-YEAR-OLD CHILDREN, AND WILL EVENTUALLY BE DEVELOPED THROUGH THE THIRD GRADE. THE EXPERIMENTAL AND DEVELOPMENTAL WORK FOR THIS PROGRAM WILL TAKE PLACE IN A SINGLE PITTSBURGH ELEMENTARY SCHOOL, CHOSEN FOR ITS UNUSUAL DEGREE OF ECONOMIC AND RACIAL HETEROGENEITY. ULTIMATELY, THE PROJECT'S GOAL IS TO DEVELOP A PROGRAM THAT CAN BE IMPLEMENTED ELSEWHERE AT A REASONABLE COST AND WITHOUT THE CONTINUED SUPPORT OF AN OUTSIDE RESEARCH TEAM. DEVELOPED IN THE MAIN BODY OF THIS PAPER ARE (1) NEED FOR AN EARLY LEARNING PROGRAM, (2) CONTENT OF AN EARLY LEARNING PROGRAM, (3) ANALYSIS AND SEQUENCING OF OBJECTIVES, (4) CURRICULUM SEQUENCES AND THEIR USE IN THE CLASSROOM, AND (5) VALIDATION OF CURRICULUM SEQUENCES. THE PAPER CONCLUDES WITH APPENDED REPORTS ON (1) SKILLS FOR INCLUSION IN AN EARLY LEARNING CURRICULUM, (2) CURRICULUM SEQUENCE FOR TEACHING CLASSIFICATION IN A MATRIX FORMAT, AND (3) CURRICULUM SEQUENCE FOR NUMBER CONSERVATION. (RP)

THIS PAPER, CONSISTING OF A COLLECTION OF MATHEMATICS TEACHING IDEAS AND STUDENT ACTIVITIES, IS A COMPILATION OF THOSE FOUND TO BE MOST EFFECTIVE BY THE CONTRIBUTING TEACHERS IN THE 1967-68 CENTRAL IOWA LOW-ACHIEVER MATHEMATICS PROJECT. THE ACTIVITIES DESCRIBED IN THIS PAPER ARE INTENDED FOR JUNIOR HIGH SCHOOL STUDENTS WITH VARYING DEGREES OF COMPETENCE IN MATHEMATICS, INCLUDING THOSE STUDENTS CLASSIFIED AS LOW ACHIEVERS. (RP)

Although recent writings indicate the importance of personal contact structures in diffusing innovations and in determining perceptions, the internal contact structure of the school faculty remains unexamined. This study applies directed graph theory, a new branch of mathematics, to analyzing school contact structure. Sociometric data and perceptions of the school were collected from 48 elementary school faculties containing 1,121 people. Using directed graph theory, 12 indices of the contact structure were derived from the sociometric data and entered into canonical correlations and factor analyses with perceptions of the school, such as faculty innovativeness. Several significant relationships were obtained. (Author)