Clifford Stone


Clifford Stone

Cliff W. Stone


The first Laboratory School building, Sabin Hall, was called an “educational palace” when it opened in January 1914.   Designed to be a model school building, the four-story structure was a place where Iowa State Teachers College (ISTC) students could receive instruction on the best teaching methods and then have the chance to practice what they had learned in real classrooms under the observation of experienced teachers.  The new building provided rooms for classes from kindergarten through high school and housed a library of 3,000 volumes as well as motion picture equipment, phonographs, and a player piano.  When it opened, the new “Training School” (as it was called) had 25 teachers, some 350 students, and—over the course of the year—about 500 student teachers.

With the new school came Dr. Cliff W. Stone as Training School Head, a role enlarged in 1916 to include Directorship of the Department of Teaching.  Stone began the long tradition of Lab School leadership in math education and forged the link between ISTC and the Teachers College of Columbia University in New York City, the oldest (1887) and largest graduate school of education in the United States.

Stone was born in Wisconsin in 1874 and was raised on a farm.  He graduated from the State Normal School at Oshkosh, Wisconsin in 1899, and soon after began his long career as a teacher, principal, and director of teaching.

Math Teaching Usefulness

As a principal in Indianapolis, Indiana in 1903, he co-authored an article in The Elementary School Teacher titled “Arithmetic Considered as a Utilitarian Study: What Should Be the Course of Study?”  The three authors conducted interviews of twenty leading Indianapolis business people with the goal of discovering how to square math teaching with real world use. 

The business leaders were given a copy of John W. Cook’s and Nebraska C. Cropsey’s book Arithmetic and left with six questions:

1. Check such divisions of the table of contents as you consider of no use in business.

2. Indicate the most important subjects in order of their value.

3. Add such other subjects as you believe would be of value to a business [person].

4. Tell us wherein you have found your employees strong in arithmetic and wherein weak.

5. In which do you consider pupils should receive more drill—in oral (mental) or written arithmetic?

6. Give us a summary of what you think schools ought to teach below the high school, and how the teaching may best be made real to the pupils.

Among some fifteen subjects named as of no use in business transactions were measurement of cones, pyramids, and the circle; the right triangle; longitude; and the international date line.  The business leaders suggested that valuable additions would be personal accounts and elements of bookkeeping—single and double entry.  Of their employees’ mathematical strengths, the leaders were “uniformly silent,” citing none.  They found their employees especially weak in accuracy of addition and multiplication, and in their ability to handle problems involving decimals and percentage.

Andrew M. Sweeney, the President of the Indiana State Life Insurance Company, offered this rousing summary: “To make the subjects in arithmetic real, each one should be approached from the concrete side, and following upon this should be an immense amount of mental drill by which the pupil is compelled to do much thinking, talking, and explaining.  This process should be faithfully, I might say slavishly, pursued, until speed and accuracy are positively numbered among the pupil’s powers.  Review!  Review!!  Review!!!”

Stone and his colleagues concluded that arithmetic teachers were attempting to teach too many subjects to teach all of them well.   To answer Sweeney’s call to impress students with the use of arithmetic in real world affairs, Stone urged math teachers to adopt several concrete class projects.  (These anticipated the project-based Lab School science curricula that took flight in the 1950s.) 

A project to show the value of measurement involved a 7th-grade class in building a house to scale.  “The utilitarian value of lumber measure was immediately apparent,” Stone explained, “and as the house progressed the need of being able to compute surface measure for lathing, plastering, papering, and carpeting became very real.”

A second 7th-grade math class discovered the various applications of percentage when each member was placed as a new employee in a hypothetical grocery store.  Stone explained that:

Some of the advantages of selecting the grocery business for this particular class are seen in the facts that fully one-third of the pupils had either parents or near relation in the grocery business, fully one-third of the boys had worked in a grocery store, and all the pupils lived in easy reach of the corner grocery [owner], of whom they were required to get their knowledge first hand.  The pupils were encouraged to secure order blanks, actual bills of goods, etc. from their grocery adviser. . . . From bills secured of grocers, children learned usual discounts, and made bills of their own.

Besides bills and their discounts, interest on overdue bills, gain-and-loss computations, taxes, insurance, and even commissions became necessary to compute.  Stone noted that:

At this point the pupils readily realize the utilitarian value of drill in addition.. . . The matter is no longer one between the teacher and pupil, but the situation has become that of a business relation.  So readily is this transition made from the imagined boy to the pupil himself that in the first week’s work pupils had of themselves begun to speak of “Flora’s bill,” “Thomas’s order,” etc. and so real does this become that it is expressed in the titles of some of the notebooks, e.g., “My Experience in the Grocery Business.”  With a class in this condition the teacher may give as long and otherwise tedious columns of numbers for addition drill as desired . . . . The arithmetic is no longer dictation work.  The motive is from within.

The same proved true regarding percentage of gain or loss; many students also found themselves lamentably weak in decimal computations.  Stone wrote that

[i]t required no urging from the teacher to get these pupils to do the most grind kind of  drill work for getting the decimal point in the right place.  They seemed to feel that their employers could not retain them unless they improved.  Boys who seemed on the verge of dropping out of school were caught in this scheme and their whole work improved. . . . A boy who had never done anything for anybody became so enthusiastic with his work that . . . he was allowed to take eighth-grade arithmetic in addition to seventh-grade work.

For the eighth graders, a school bank was created to study interest and its applications.

Arithmetic Testing

Stone built on his real-world focus by becoming an early pioneer in math testing.  He pursued his studies at Columbia University’s Teachers College, where he earned a bachelor of science degree in 1904 and a Ph.D. in 1908.  His doctoral dissertation, published in 1908, was titled Arithmetical Abilities and Some Factors Determining Them.  This work established Stone’s lasting fame as the creator of the Stone Tests of arithmetic operations and reasoning.  Stone involved 26 school systems in his carefully controlled  study: 6 in New England, 11 in New York and New Jersey, and 9 in the Middle West.  Nineteen were public schools, 4 training schools, and 3 private schools.  Superintendents and principals identified 6th grade classrooms in which an approved course of arithmetic study had been carried out in the past 5 l/2 years or more.  These 6th graders would help establish a standard for use in comparing national arithmetic abilities.

Stone personally gave his two tests himself in each classroom to make conditions uniform.  His test for “Fundamental Arithmetic Operations” (addition, subtraction, multiplication, and division) consisted of 14 problems.  The sixth graders were told to do as many of the problems as possible in the 12 minutes allowed for this test.  (Problem 1 was to add 6 (mostly 4-digit) numbers; Problem 2, to multiply 3265 x 20; Problem 3 to divide 3328 by 64, etc.)  Stone’s “Reasoning in Arithmetic” test was comprised of 12 problems to be done in order in 15 minutes.  (Problem 2 was: John sold 4 Saturday Evening Posts at 5 cents each.  He kept l/2 the money and with the other l/2 he bought Sunday papers at 2 cents each.  How many papers did he buy?)  Test trials had shown that all the students could finish the first 6 problems in each test within the time-frames; the remaining problems were for fast workers.

The 6,000 6th grade test papers collected revealed startling facts—even for today.  No correspondence existed between how well a given school system’s students did in arithmetic operations and how its students did in arithmetic reasoning: most differed greatly.   Additionally, of the 4 arithmetic operations, addition was found to be not only just as hard as subtraction, multiplication, and division, but even harder than the others to do correctly.  The difficulty in accuracy decreased from addition to subtraction and multiplication and became least in division.  Both of Stone’s tests also showed a striking difference in accuracy among individual 6th graders, leading him to urge educators to consider whether it was “right from any standpoint to expect to treat children as if they could and ought to do equally well in all subjects, or even in all phases of the same subject?”

Stone’s study also showed no relationship between the time the school systems spent on instruction and the students’ achievement in arithmetic operations and reasoning.  In short, “a large amount of time expenditure [was] no guarantee of a high standard of abilities.”  Stone and his readers then scored the actual 6-year math curricula for each school which led him to the sentences that made his work so persuasive to teachers and administrators in 1908 and after: “That the great variability herein shown would exist if school authorities had adequate means of measuring products is inconceivable; and it is believed that the present study will help standardize the work in arithmetic for the first six grades.  Anyone who wishes can know how his system or school compares with the representative systems of the country.”  Stone concluded this unfolding of what would become known as the Stone Tests with this caution: “Doubtless the most helpful generalization possible from this study is that there is no one factor that produces abilities, that there is no summum bonam [highest good] in teaching arithmetic.” 

Scientific Study of the Teaching of Arithmetic

Following his Columbia Teachers College days, Stone became Head of the Department of Education and Director of the Training School at the State Female Normal School in Farmville, Virginia (today Longwood University).  In 1913, his article “Problems in the Scientific Study of the Teaching of Arithmetic” appeared in the Journal of Educational Psychology.  It reveals why he was an ideal choice for Iowa State Teachers College and its soon-to-be-opened model Training School.

Stone addressed two questions in the article: What arithmetic ought to be taught?  And how can this arithmetic be taught best?  The second question led to his call, not only for testing of current practices, but also encouragement of teachers to attempt methods comparisons—with direct help in how to do so.  Stone laid out important method questions related to the teaching of addition, subtraction, multiplication, division, fractions, denominate numbers, percentage, interest, reasoning, etc.  One general question was “How much of the work should be oral rather than written?”  He then wrote (sounding like the director of a laboratory school): “The question could probably be most readily studied by a single teacher or group of teachers in departmental teaching, though a teacher of one grade can divide her class into two groups, equal as to arithmetical ability, and do much toward answering the question.”  Regarding addition, two questions that could be tested were: “Which is better, to add up or down the columns?  and Does it pay to write down the numbers to carry?” 

In this encouraging article, Stone sought to ease fear of methods study in teachers and administrators.  He noted that:

Teachers often hesitate . . . thinking that anything in the nature of a departure is an experiment, and therefore dangerous.  This hesitation is not usually justified, for even if results show that some groups have been somewhat at a disadvantage, it can be made up to them very readily after the controlled testing is completed.  It will be noted that here, as elsewhere in this discussion, the word experiment is not used. This is done because the word has come to suggest something radical, dangerous, and therefore to be avoided.

Stone urged testing at the beginning of the year, middle, and end—and then at the start of the next year to discover vacation loss.  He suggested similar testing at the beginning and end of separate units.

Stone showed himself even more Socratic in his effort to answer his first vital question: What arithmetic ought be taught?  Here he asked teachers, administrators, and citizens to investigate scientifically the worth of subject matter to be taught both in practical and cultural terms.  As he put it: What Arithmetic is needed in order best to make a living?  and What Arithmetic is needed in order to make the best living?  For the latter, he asked What arithmetic help is needed by the developing child to best further the respective stages of his or her growth?  Furthermore, to what extent is the discipline of the respective parts of arithmetic transferable to other subjects?

Stone focused on these issues while at ISTC, and he also built on his 1908 Arithmetical Abilities and Some Factors Determining Them.  Finding that most work was being done in arithmetic operations, he published in 1916 Standardized Reasoning Tests in Arithmetic and How to Utilize Them, refining his 1908 reasoning test.   This book  was revised and enlarged in 1921 and has been reprinted many times since—the last in 2010.

World War I

Stone’s life and work changed, however, when the United States entered World War I in April 1917. Stone was tapped to serve as a member of the American Expeditionary Force University at Beaune, France.  Following the war, he was hired away from ISTC to be Head of Education at the State College of Washington at Pullman (now Washington State University),where he served until his retirement in 1946.

Though only at Iowa State Teachers College for a few years, Stone ably launched the new model Training School on a rigorous scientific and philosophical path.  He also promoted Eva May Luse to be his Assistant Director of the Training School and then Acting Director during his leave of absence for the war.  She became full Director in 1920 and continued for 21 years the Training School’s leadership in math education and through its ties to Columbia University’s Teachers College, becoming a national and international leader until her retirement in 1941.

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