Ray's Arithmetic Series



Arithmetic teachers say:

  • "Rediscovering Ray's is the best thing that's happened to arithmetic in a hundred years."
  • "These books produce superior math students."
  • "Their use of story problems develops thinking right from the start."
  • "They are psychologically right in starting with concrete and mental arithmetic before introducing symbols."
  • "Using Ray's this year has definitely improved the achievement test scores in our schools."

Ray's Arithmetics teach arithmetic in an orderly fashion, starting from rules and principles, building knowledge piece by piece, leading pupils from simple to complex. From the very first pages, Ray's Arithmetics incorporate what has become the scourge of today's math students - story problems. Students must READ simple sentences which pose real life problems, decide whether to add, subtract, multiply or divide, and finally arrive at the answer - sometimes mentally - sometimes in writing.

Ray's Arithmetics students learn arithmetic, increase their reading comprehension skills, and learn to think rather than plod through page after page of addition or subtraction problems with a one line direction at the top of each page. A student raised on Ray's will not even know he should be fearful of "story problems" because from day one every problem is posed in a sentence format.

Most early work is to be done with real objects such as fruit, counting blocks, or marbles. Later it is to be done in the head with mental images of the objects. When children are ready to think symbolically, they gradually drop their use of objects and images and learn to compute quickly with digits. Thus the child is carefully led through three growth states in arithmetic: 1) the manipulative stage, 2) the mental image stage, 3) the abstract stage.

Over 120 million copies were sold in American education's golden age. Many millions of children used these Arithmetics in the generations that produced Edison and Bell and Ford. Now it's your turn.

THE CLASSICS ARE BACK AGAIN.


PRIMARY ARITHMETIC. This book introduces the four operations of addition, subtraction, multiplication, and division, along with counting and other basic skills. It can be used to guide your teaching for about two years - through grades 1 and 2. It goes farther than the average second grade course, but with Ray's mental system many second graders are able to do this work.
96 pages, ISBN#0-88062-051-x
Price: . . . . . $8.99

INTELLECTUAL ARITHMETIC. Extends work in the four operations to higher numbers and begins fractions, measurements, ratio and percentage. Can be used with many children through grades 3 and 4.
Available only in softcover
144 pages, ISBN#0-88062-052-8
Price: . . . . . $12.99

PRACTICAL ARITHMETIC. Reviews basic arithmetic skills and carries them to high levels. Also covers topics of measurement, factoring, decimals, percentage, ratio, proportion, powers, roots, and geometry. For grades 5 and 6. good mastery of this book takes a child higher than a usual grade 6 level.
336 pages, ISBN#0-88062-053-6
Order Price: . . . . . $17.00

KEY TO RAY'S ARITHMETICS: PRIMARY, INTELLECTUAL, AND PRACTICAL. Contains answers for problems on topics in Practical Arithmetic. Teachers may draw upon these for preparing tests.
224 pages, ISBN#0-88062-054-4
Price: . . . . . $13.00

TEST EXAMPLES IN ARITHMETIC.
A book of problems on topics in Practical Arithmetic. Teachers may draw upon these for preparing tests.
224 pages, ISBN#0-88062-057-9
Price: . . . . . $13.99

HIGHER ARITHMETIC. Includes philosophical understandings; principles and properties of numbers; and advanced study of common and decimal fractions, measurements, ratio, proportion, percentage, powers and roots, series, business math, geometry. Has challenging work for advanced students and basic work for slower students. Can be used for grades 7 and 8, as well as for high school.
416 pages, ISBN#0-88062-055-2
Price: . . . . . $21.00

KEY TO RAY'S HIGHER ARITHMETIC. Contains answers for problems in Higher Arithmetic.
224 pages, ISBN#0-88062-056-0
Price: . . . . . $13.99

PARENT-TEACHER GUIDE FOR RAY'S ARITHMETICS. by Ruth Beechick. Guides your scheduling and planning through the books above. Shows where you can adapt to the needs of slower or advanced students, making selective use of basic portions that are important for all students and high-level portions that challenge the best students. provides a test for each unit. Describes games and activities which add variety to your teaching.
186 pages, ISBN#0-88062-072-2
Price: . . . . . $12.99

8 VOLUME SET. Includes all eight books,
8 Volume Set, ISBN#0-88062-050-1
Price: . . . . . $100.00


Ray's available only in soft cover


We invite you to look at the sample information that follows.

Or click here to see our new Arithmetic Workbooks.



front cover Ray's New Higher
Arithmetic
front cover
title page
preface
contents
contents 2
introduction
introduction 2
front cover Ray's New Primary Arithmetic
front cover
preface
preface 2
suggestions
lesson 1
lesson 2
lesson 4 & 5
front cover Key to Ray's New Higher Arithmetic
front cover
title page
preface
page 5
page 6
page 7

front cover Key to Ray's New Arithmetic
front cover
title page
preface
answers
page 6
page 7
front cover Ray's New Test Examples
front cover
title page
preface
contents
test examples
page 8
page 9
front cover Ray's New Intellectual Arithmetic
front cover
instruction
page 5
page 6
page 7
Available only in softcover

front cover Parent / Teacher Guide
front cover
title page
copyright page
contents
contents 2
intro
front cover Ray's New Practical Arithmetic
front cover
title page
preface
contents
contents 2
definitions
notations
front cover Ray's Complete Set
front cover




Joseph Ray
1807 - 1855

Joseph Ray, the oldest child of William and Margaret Graham Ray, was born in Ohio County, Virginia (now West Virginia), on November 25, 1807. The Ray farm was located near Battle Run, about two miles north of the old National Road. William Ray remembered his son as a precocious child who learned to read and to "enumerate to hundreds of millions" before entering school at age six, where he quickly reached the head of the class. By the time he was fifteen, Joseph was studying algebra, geometry, and surveying at a school in West Liberty.

At age sixteen Ray began teaching in the rural schools near his home, and in April, 1825, he enrolled in Franklin College at New Athens, Ohio (not to be confused with Ohio University at Athens). He is listed in the graduating class of 1828, although he had already begun the study of medicine with Dr. Joel F. Martin of Warrenton, Ohio. The following year Dr. Martin made arrangements for Ray to attend, free of cost, a course of lectures at the Medical College of Ohio in Cincinnati. By teaching in the summer and studying medicine in the winter, Ray was able to complete his M.D. degree in the spring of 1831. With a promising medical career in view, he married Catherine Gano Burt in August of that year, but the medical practice did not prove successful, and financial needs soon caused him to again seek employment as a teacher.

While Ray was busy completing his own higher education, the foundations of publicly supported education in Cincinnati were being laid. A Cincinnati businessman, William Woodward, had set up a trust in 1826 for the purpose of "better educating of the poor children of Cincinnati." In 1830 he granted a tract of land on Sycamore Street to establish The Woodward High School. A charter was received from the Ohio legislature the following January, and a two-story wooden building was erected. In June 1831, T. B. Wheelock was hired as Professor of Mathematics and Natural Philosophy.

Opening exercises at Woodward High School took place on October 24, 1831, and three weeks later Dr. Ray was appointed as a teacher in the Preparatory Department at an annual salary of $1000. The "preparatory" curriculum included mental and practical arithmetic in the first two years and bookkeeping in the third. There was a more demanding "classical" course of study for "collegiate" pupils that required the study of Latin and Greek, along with algebra, geometry, trigonometry, conic sections, logarithms, surveying and navigation, fluxions (calculus), and astronomy. Nearly 150 pupils attended the school during its first year of operation.

In January, 1836, the Ohio legislature granted a new charter, establishing The Woodward College of Cincinnati. A third story was added to the building in order to accommodate the college classes, and teachers in the high school were immediately appointed as Professors in the College. By this time, Joseph Ray had moved from the preparatory to the collegiate department, so he became Professor of Mathematics. There was little, if any, significant change in the curriculum.

As early as 1830, Cincinnati had become the center of the Western book trade, and it was soon the country's fourth largest publishing center. One of the most successful publishing houses was the firm of Truman & Smith. In 1834 they published An Introduction to Ray's Eclectic Arithmetic, which soon became the cornerstone for a series of arithmetic and algebra textbooks that were among the most popular and widely used American mathematics textbooks of the nineteenth century. More than fifty titles (including revised editions) appeared in Ray's Mathematical Series over the years, but the core of the series consisted of six books: Primary Arithmetic, Intellectual Arithmetic, Practical Arithmetic, Higher Arithmetic, Elementary Algebra, and Higher Algebra.

Even after Ray's death in 1855, new and revised editions were issued under his name. Later titles on geometry, trigonometry, analytic geometry, surveying, astronomy, and calculus were authored by others but listed in Ray's Mathematical Series. As late as 1913, annual sales exceeded a quarter of a million copies, and total sales of the arithmetic books alone are estimated at 120 million copies. A web-based exhibit on Teaching Mathematics in America at the Smithsonian Institution shows the cover of a later edition of Ray's Practical Arithmetic.

The success of Ray's Arithmetic prompted Truman & Smith to seek an author for an "eclectic" set of readers. They eventually contracted with William Holmes McGuffey, who had been teaching at Miami University in Oxford. McGuffey later joined Ray on the faculty of Woodward College, teaching in the department of languages from 1843 to 1845. The McGuffey Readers surpassed even Ray's Arithmetics to become the most popular textbooks ever written.

Thomas J. Matthews, a professor of mathematics at Transylvania College in Kentucky, was elected as Woodward's first President in September, 1832. Ray, Matthews, and McGuffey soon became active in the newly organized Western Literary Institute and College of Professional Teachers, founded in 1832. This was the first professional organization for the advancement of education in Ohio and the West. Most meetings were held in Cincinnati, and Ray served as a Director for the Ohio Section in 1837-38 and as Recording Secretary in 1839-40. He was appointed to various committees charged with preparing reports on the teaching of English composition, the science of arithmetic, the use of blackboards, and the utility of cabinets in natural science education.

In 1851 Woodward College ceased operations as an independent institution, and the building was turned over to the city of Cincinnati for use as a public high school, with Joseph Ray as its principal. That same year he delivered the annual address at the Fourth Annual Meeting of the Ohio State Teachers Association. His message, on "The Qualifications of Teachers," emphasized the importance of what to teach, how to teach it, and ability to teach it.

Ray was President of the Ohio State Teachers Association in 1853. The following year he agreed to be an associate editor of The Ohio Journal of Education, where he initiated a "Mathematical Department," devoted to the solution and discussion of mathematical problems. Over the next six years, more than 100 readers were involved in the posing and solving of nearly 75 problems. Among their names we find Joel Hendricks, W. D. Henkle, Robert W. McFarland, Aaron Schuyler, Eli T. Tappan, and W. H. Young.

Ray served on the board of school examiners and the board of directors of the Cincinnati House of Refuge. He was also a devoted member and an elder in the Disciples' Church. During a cholera epidemic in 1849, he devoted much energy to aiding the sick and needy, thereby impairing his own health and hastening his untimely death, from tuberculosis, on April 11, 1855.

Ray's death was a great loss for the community of Cincinnati. The Joseph Ray Mathematics Prize was established in his memory, to be awarded annually to an outstanding Woodward High School student. A monument to William Woodward stands in front of the present day Woodward High School and, on one side of its pedestal, there is a bronze medallion portrait of Ray. There is also a historical marker along U.S. 40 at Willow Grove, West Virginia, commemorating "Ray's Arithmetic."

Ray sought to carry out the teaching practices of Johann Pestalozzi and Warren Colburn, providing pupils with mental training that would enable them to think clearly. In the Preface to his Algebra of 1848 he wrote, "The object of the study of mathematics is twofold—the acquisition of useful knowledge and the cultivation and discipline of the mental powers. [To] be able to reason correctly, and to exercise, in all relations in life, the energies of a cultivated and disciplined mind … is of more value than the mere attainment of any branch of knowledge."

Ray believed that the ultimate objective in teaching was to develop high moral character. It is said that he would often interrupt a lesson to call attention to some fault of a student and then tell a story about the need for persons with high morals. Story problems in his textbooks portray honest, hard-working men and women on the frontier, plowing fields, planting and harvesting crops, building walls, or buying and selling goods. Problems about boys and girls characterize them as industrious and generous, sharing food and possessions with each other. In one problem a boy receives a reward for returning a purse to its rightful owner.

James Greenwood, Superintendent of Schools in Kansas City gave the following assessment of the popular success of Ray's textbooks. "The reason is, I think, obvious. Dr. Ray was, in a large sense, a self-made mathematician and a self-made teacher. He had learned well the lesson of self-help, and in the preparation of his books he always kept before himself all the difficulties he had experienced in mastering each topic. No one knew better just when and where and how to bear down on certain points. In an eminent degree he possessed that rare combination of assimilation and clear presentation. He knew how to make the subjects stick."

Article by David E. Kullman
Miami University

REFERENCES

  1. Brammer, Mauck (1971). "Winthrop B. Smith: Creator of the Eclectic Educational Series." Ohio History, 80, pp. 45-59.

  2. Dennis, Jerry (1937). "Joseph Ray." Ohio State Archeological & Historical Quarterly. 46 (1), pp. 42-50.

  3. Gano, John A. et al. (1884). Old Woodward: A Memorial. Cincinnati: Old Woodward Club.

  4. Greenwood, James M. and Martin, Artemas (1899). "Notes on the history of American text-books on arithmetic." Washington: Department of the Interior, Annual Report 1897-1898, pp. 789-867.

  5. Kullman, David E. (1998). "Joseph Ray The McGuffey of Mathematics." Ohio Journal of School Mathematics, No. 38, pp. 5-10.

  6. Ray, Joseph (1848). Algebra, Part First. Cincinnati: W.B. Smith & Co.

Order Page Top of Page Home Page