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Reports a survey concerned with the future of mathematics in Australia which identified the number of "experts" in particular areas of mathematics who are working in Australia. Findings show increased research work in the past five years but conclusions indicate that many mathematical areas continue to be neglected. (JT)

This history of binary arithmetic begins with details of Thomas Hariot's contribution and includes specific references to Hariot's manuscripts kept at the British Museum. A binary code developed by Sir Francis Bacon is discussed. Briefly mentioned are contributions to binary arithmetic made by Leibniz, Fontenelle, Gauss, Euler, Benzout, Barlow, DeMorgan, Cantor, Muller, Peano, and Bouton. (DT)

The United States Training and Employment Service General Aptitude Test Battery (GATB), first published in 1947, has been included in a continuing program of research to validate the tests against success in many different occupations. The GATB consists of 12 tests which measure nine aptitudes: General Learning Ability; Verbal Aptitude; Numerical Aptitude; Spatial Aptitude; Form Perception; Clerical Perception; Motor Coordination; Finger Dexterity; and Manual Dexterity. The aptitude scores are standard scores with 100 as the average for the general working population, and a standard deviation of 20. Occupational norms are established in terms of minimum qualifying scores for each of the significant aptitude measures which, when combined, predict job performance. Cutting scores are set only for those aptitudes which aid in predicting the performance of the job duties of the experimental sample. The GATB norms described are appropriate only for jobs with content similar to that shown in the job description presented in this report. A description of the validation sample is also included. (AG)

Children will become more proficient in mathematics if they do mathematics rather than merely learn about mathematics. Once educators overcome the misconception that the average student can't do math, they can develop new mathematical activities for children, such as those invented by the staff of the Artificial Intelligence Laboratory at Massachusetts Institute of Technology. These use computational mathematics projects (in which, for example, a computer regulates the movement of a toy) as vehicles for teaching transferable concepts. They force teachers and students to identify concepts which enable the math beginners to discuss clearly their thinking, they foster personal involvement in mathematics and they encourage children to make creative discoveries. These processes also lead to an understanding of the concepts of debugging, formalization, side-effects and simplification. In short, computational math is superior to the traditional method of teaching math because it teaches children to mathematize, because it develops heuristic concepts, and because it attends to the mathematical primitives. (PB)

Based on information furnished by 227 doctorate-granting institutions in their applications for NSF traineeships, graduate enrollment in the sciences and engineering declined slightly between 1969 and 1970. The 1969-70 decrease and the declining trend in the rate of growth during 1967-69 contrast markedly with the nine percent annual rate of increase in enrollment for advanced degrees in the sciences and engineering that characterized the seven year period: 1960 to 1967. In contrast to the decline in graduate enrollment, the number of faculty and post doctorals increased during 1969-70, but at annual rates that were far below the comparable figures for 1967-69. The science doctorate departments covered in the present study accounted for more than 75 percent of the graduate enrollment and more than 90 percent of the doctorates granted in the sciences and engineering by U. S. universities and colleges. (Author/CP)

This book is a reissue of the second edition which appeared in 1940. It has the distinction of being the first vintage mathematical work published in the NCTM series "Classics in Mathematics Education." The text includes a biography of Pythagoras and an account of historical data pertaining to his proposition. The remainder of the book shows 370 different proofs, whose origins range from 900 B.C. to 1940 A.D. They are grouped into the four categories of possible proofs: Algebraic (109 proofs); Geometric (255); Quaternionic (4); and those based on mass and velocity, Dynamic (2). Also included are five Pythagorean magic squares; the formulas of Pythagoras, Plato, Euclid, Maseres, Dickson, and Martin for producing Pythagorean triples; and a bibliography with 123 entries. (RS)

The need for adequate knowledge of the personality patterns associated with professional competence, especially that of women professionals, spurred the authors to study this relationship, using 221 professional woman as subjects. The subjects, professionals from nine different occupations, were administered the Wechsler Adult Intelligence Scale (WAIS) from which the patterning of subtest scores provides the basis for the Gittinger Personality Assessment System (PAS). Primary emphasis was placed on the development of stable reference groups based on the complex interaction of PAS variables. A "good" reference group is defined as a set of individuals subject to similar psychodynamic mechanisms which encompasses a large number of persons within its defined limits. But it must be narrow enough to allow prediction of behavior on a within-group basis. Of the sampled professions, only realtors and social workers failed to contribute any members to the three established reference groups. Meaningful reference groups within these two professions were found, however. It is suggested that the pattern derived from the largest reference group, the Professional Generalists, could prove advantageous in university career counseling for women. (TL)

A brief biography of Pythagoras, including discussions of his contributions to philosophy and mathematics, is presented. (CR)

The history of mathematics is briefly reviewed and illustrated with postage stamps from several countries. (SD)

The life of Fibonacci is summarized, and his importance in the development of mathematics is assessed. Several problems first solved by Fibonacci are posed. (SD)

In his presidential address to the Australian Association of Mathematics Teachers, the writer, who is a research mathematician, discusses relationships between research mathematics and mathematics education. (SD)

The published views of French mathematicians Thom and Dieudonne regarding modern mathematics programs are discussed. (SD)

Discusses early Euclidean cosmologies, inadequacies in classical Euclidean cosmology, and the development of non-Euclidean cosmologies. Explains the present state of the theory of cosmology including the work of Dirac, Sandage, and Gott. (CP)

This study traces the development of nondecimal numeration from the 16th century to the present. The first six chapters detail the contributions of mathematicians as well as people from other fields. Applications to computers are covered in one chapter, while another chapter discusses the coverage of numeration systems in college textbooks for future elementary school teachers, in School Mathematics Study Group (SMSG) seventh grade materials, and in references for secondary school teachers. The final chapter consists of a chronology of important events in the development of numeration systems since 1500 A.D. There is a bibliography at the end of each chapter. (DT)

This volume reports on a survey of undergraduate training in the mathematical sciences, the data for which were collected during the academic year 1970-71 by means of questionnaires sent to chairmen of mathematical science departments in both 2- and 4-year colleges and universities. The data obtained through the survey include information on enrollments in undergraduate mathematical science courses; mathematical science faculty; and other aspects of undergraduate programs such as computer access and utilization, mathematical science courses as graduation requirements, entrance and placement examinations, and curricular innovations in undergraduate mathematics programs. (HS)

Opportunities for university graduates with mathematics and science backgrounds are discussed. Statistics concerning the occupational disposition of graduates as of the date of their graduation are presented. (JP)

Proliferation of mathematical knowledge prohibits individual reduplication of all results and causes mathematicians to accept much on faith. To convey the spirit of the mathematical community, and provide maximum content coverage, instruction should allow students to accept some theorems without proof. Students would then find mathematics less remote to society. (SD)

Brief biographies of Hypatia, Maria Agnesi, and Emmy Noether are presented. (SD)

A discussion of career opportunities in mathematics and the qualifications required of persons who pursue certain mathematics-related careers are presented. (FL)

Describes the development of one of Euler's infinite series for pi. Includes a computer program for computational verification output of two series which converge to pi. (RS)

Biography of Arab scholar and mathematician, Thabit ibn Qurra. Presents some original proofs of the Pythagorean theorem and his extension to a general triangle. (RS)

Creative Ss had a stronger cathexis of research activity and were highly flexible, original, and rejecting of outside influence. They had identified primarily with their fathers, and that their interest in mathematics had arisen from sublimation or search for autonomy in fantasy rather than from reaction formation or withdrawal. (Author)

Examined are important factors that have produced the present mathematics curriculum. The impacts of society, the psychology of learning, and groups of mathematicians are examined. (CT)

Reprinted are articles related to the early years of The Mathematical Association of Great Britain. Some of the topics include reports from curriculum committees, tributes to persons associated with The Mathematical Association, and the teaching of mathematics. (CT)

This brief history of a living worker in the vineyards of documentation is acknowledge to be only a description of relevant aspects of a very active life and in no sense an assessment of his work. (Author)

Presents a biography of the theologian and philosopher, Francis William Newman (1805-1897), the brother of John Henry Newman. His mathematical contributions were primarily in the area of analysis. (RS)

Author introduces distinctions that occur between the inductive and deductive approaches to mathematical analysis thereby helping teachers, interested in innovative teaching methods, to understand more clearly the problems they are up against. (Author/RK)

Author suggests that new'' or modern'' mathematics never had a valid reason for existing and recommends reform of traditional mathematics curriculum. (RK)

Author looks at how technology has affected mathematics instruction and argues that fundamental concepts should be emphasized over arithmetical skills because of computers. (HB)