Arithmetic Teaching Apparatus -- Tests
Tests
Throughout most of the nineteenth century, teachers tested the progress of students with oral examinations, often held at the blackboard. By the end of the century, more formal written examinations were used in some states to test graduates of academies in high schools and to accredit teachers. A few universities began to offer advanced degrees in education, and faculty there reflected on the history of mathematics education in this country.
At the same time, as the number of students attending school expanded, as high schools began to offer vocational training, and as manufacturing became more efficient, several authors worried about maximizing the efficiency of schools. A variety of standardized examinations were introduced to predict the performance of students, to point up areas where they needed work, and to evaluate school systems.
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New York State Regents Examinations in Mathematics
- Description
- The Regents of the University of the State of New York began planning examinations to test the accomplishments of students leaving high schools and academies in the 1860s, and continue to give such examinations today. These examples of the Regents Examinations date from between 1907 and 1919. They were collected by Brooklyn high school mathematics teacher L. Leland Locke.
- The tests are:
- 1. Arithmetic, June 18, 1907 (sheet)
- 2. Advanced Arithmetic, June 18, 1907 (sheet)
- 3. Elementary Algebra, June 17, 1907 (sheet)
- 4. Intermediate Algebra, June 17, 1907 (sheet)
- 5. Advanced Algebra, June 17, 1907 (sheet)
- 6. Plane Geometry, June 18, 1907 (sheet)
- 7. Solid Geometry, June 17, 1907 (sheet)
- 8. Trigonometry, June 18, 1907 (sheet)
- 9. Elementary Algebra, January 18, 1915 (sheet)
- 10. Plane Geometry, June 15, 1915 (sheet)
- 11. Elementary Algebra, January 23, 1917 (sheet)
- 12. Plane Geometry, January 24, 1918 (sheet)
- 13. Elementary Algebra, January 22, 1918 (sheet)
- 14. Plane Geometry, January 23, 1919 (sheet)
- Also included under the number (subindex number .15) is a sheet with handwritten equations.
- Reference:
- Nancy Beadie, “From Student Markets to Credential Markets: The Creation of the Regents Examination System in New York State, 1864–1890,” History of Education Quarterly, 39, no. 1 (Spring, 1999), pp. 1–30.
- Location
- Currently not on view
- date made
- 1907-1919
- maker
- University of the State of New York
- ID Number
- 2011.0129.08
- accession number
- 2011.0129
- catalog number
- 2011.0129.08
- Data Source
- National Museum of American History
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New York Training School Certificate Examinations
- Description
- In 1843, the New York State Legislature authorized the state superintendent of schools to set examinations and issue certificates to teachers that were valid statewide. New York was the first state to do this. The law was modified several times over the next few years. By 1909, the Education Department of the State of New York had a complex system of certificates, with separate licenses for college graduates, for graduates of state teacher training schools, and for experienced teachers who did not have these academic qualifications.
- Brooklyn mathematics teacher L. Leland Locke collected Training School Certificate examinations given between 1911 and 1928. Until 1914, these tests were given by the Education Department of the State of New York. From 1914 onward they are listed as given by the State University of New York. Included in this collection are some 32 tests and groups of tests, namely:
- 1. Geography / Physiology and Hygiene, January 19, 1911(sheet)
- 2. Drawing, June 1911 (sheet)
- 3. American History with Civics / Reading, Writing and Spelling, January 15,1912 (sheet)
- 4. Arithmetic, January 16,1912 (sheet)
- 5. Drawing, January 19, 1912 (sheet)
- 6. History of Education, January 19, 1912 (sheet)
- 7. Language, Composition and Grammar, January 16, 1912 (sheet)
- 8. School Management, January 17, 1912 (sheet)
- 9. American History with Civics / Reading, Writing, and Spelling, June 16, 1913 (sheet)
- 10 & 11. Arithmetic, June 17, 1913 (1 white & 1 green sheet)
- 12. Drawing, January 24, 1913 (sheet)
- 14. History of Education, June 20, 1913 (sheet)
- 15. Language, Composition, and Grammar, June 17, 1913 (sheet)
- 16. Language, Composition and Grammar, January 21, 1913 (sheet)
- 17. Psychology, June 18, 1913 (sheet)
- 18 & 19. School Management, January 22, 1913 (1 white & 1 green sheet)
- 20 & 21. School Management, June 18, 1913 (1 white & 1 green sheet)
- 22. American History with Civics / Reading, Writing, and Spelling, January 19, 1914 (sheet)
- 23 & 24. Sheets, Arithmetic, January 20, 1914 (1 white & 1 green sheet)
- 25. Language, Composition and Grammar, January 20, 1914 (sheet) 26. Arithmetic, January 19, 1915 (sheet)
- 27. Drawing, January 22, 1915 (sheet)
- 28. History of Education, January 22, 1915 (sheet)
- 29. Language, Composition and Grammar, January 19, 1915 (sheet)
- 30. School Management, January 20, 1915 (sheet)
- In addition to the subjects listed above, the Training School Certificate examinations ordered in 1909 included tests in teaching English and nature study.
- Reference:
- Charles W. Bardeen, The New York School Officers Handbook: A Manual of Common School Law, Syracuse, NY: C. W. Bardeen, 1910, pp. 287–312.
- Location
- Currently not on view
- date made
- 1911-1915
- ID Number
- 2011.0129.06
- accession number
- 2011.0129
- catalog number
- 2011.0129.06
- Data Source
- National Museum of American History
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Book, Development of Arithmetic as a School Subject
- Description
- This paperbound monograph describes the history of arithmetic teaching in the United States to its time of issue, with particular emphasis on the work and influence of William Colburn. The author, Walter Scott Monroe (1882–1961), was professor of school administration at the Kansas State Normal School. He went on to take an active interest in the development of educational tests (see MA.316371.045) .
- The monograph was issued by the Bureau of Education of the United States Department of the Interior. This copy was the property of L. Leland Locke, a Brooklyn mathematics teacher and an historian of mathematics.
- Location
- Currently not on view
- date made
- 1917
- maker
- Monroe, Walter Scott
- ID Number
- 2011.3051.02
- nonaccession number
- 2011.3051
- catalog number
- 2011.3051.02
- Data Source
- National Museum of American History
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Psychological Test, General Intelligence, Operations of Arithmetic and Silent Reading
- Description
- This collection of tests for students in grades six, seven and eight is an early example of a paper and pencil standardized examination for school children. Included (printed to be read going one direction) are seven tests collectively designed to measure general intelligence. They include multiple choice tests of analogies, arithmetic word problems, vocabulary, matching symbols to numerals (called substitution), verbal ingenuity, arithmetical ingenuity, and synonyms and antonyms. A test of silent reading ability and seven tests of operations of arithmetic are printed to be read going in the other direction.
- These tests were developed at the Bureau of Educational Research at the University of Illinois by Walter S. Monroe and B. R. Buckingham. They were published by The Public School Publishing Company of Bloomington, Illinois, and also are known as the Illinois Examination. This version is copyrighted 1920.
- This example of the test is from the collection of clinical psychologist David Shakow.
- The test is glued to an orange piece of cardboard.
- Reference:
- Edward H. Cameron, Psychology and the School, New York: Century Company, 1921, pp. 317–334.
- Location
- Currently not on view
- date made
- 1920
- maker
- Buckingham, B. R.
- Monroe, Walter Scott
- ID Number
- MA.316371.045
- catalog number
- 316371.045
- accession number
- 316371
- Data Source
- National Museum of American History
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Standardized Test, Stanford Achievement Test, Arithmetic Examination A
- Description
- This paper and pencil arithmetic examination was part of the first (1922) edition of a set of tests developed at Stanford University by professor of psychology Lewis M. Terman, statistician and assistant professor of education Truman L. Kelley, and doctoral student Giles M. Ruch (Stanford PhD., 1922). World Book Company published the tests. Scores on the arithmetic examination are divided into two parts: computation of numerical examples, and word problems. An answer key is included
- The Stanford Achievement Tests were designed to test the accomplishments of school children in grades two through eight. Editions of the examinations are still in print.
- This example of the test is from the collection of clinical psychologist David Shakow.
- Reference:
- Stanford University, Annual Report of the President of Stanford University, Stanford University: By the University, 1922, pp. 186, 281.
- Location
- Currently not on view
- date made
- 1922
- maker
- Kelley, Truman L.
- Ruch, Giles M.
- Terman, Lewis M.
- ID Number
- MA.316371.044.02
- catalog number
- 316371.044.02
- accession number
- 316371
- Data Source
- National Museum of American History
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Teachers Manual for Standard Practice Tests in Arithmetic
- Description
- Just before World War I, Stuart A. Courtis, a teacher at a private school for girls in Detroit, Michigan, developed the first widely available standardized tests of arithmetic. His goal was to measure the efficiency of entire schools, not the intellectual ability of a few students.
- Courtis went on to become supervisor of educational research in the Detroit public schools. There he developed a set of lesson cards in arithmetic for students in the third through eighth grades. The tests were originally published under his name by World Book Company.
- This is a teacher’s manual for a later edition of the drill cards. Courtis’s name does not appear. Courtis withdrew his arithmetic tests from the market in 1938 because he had come to doubt their validity.
- The manual was the property of Brooklyn school teacher L. Leland Locke.
- Reference:
- Kidwell, P.A., A. Ackerberg-Hastings and D. L. Roberts, Tools of American Mathematics Teaching, Baltimore: Johns Hopkins University Press, 2008, pp. 43–46.
- Location
- Currently not on view
- date made
- 1924
- maker
- Detroit Public Schools
- ID Number
- 2011.3051.01
- nonaccession number
- 2011.3051
- catalog number
- 2011.3051.01
- Data Source
- National Museum of American History
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Psychological Test, Diagnostic Chart For Fundamental Processes In Arithmetic
- Description
- Guy T. Buswell and Lenore John published this chart in about 1925 through the Public School Publishing Company of Bloomington, Illinois. The entire package included directions, a pupil's work sheet, a teacher's diagnostic chart, and a pupil's work sheet diagnostic chart. This is the pupil's work sheet. It lists problems in addition, subtraction, multiplication and division.
- For further information about the test and its authors, see 1990.0034.168.
- At the time of the publication, Buswell was in the Department of Education at the University of Chicago and John was at the University of Chicago Laboratory Schools. Buswell and John hoped that their chart would be used to determine the areas of arithmetic in which a student required further work. It served as a “diagnosis” of problems rather than a “prognosis” of future achievement. In later years, Buswell and John collaborated on a series of arithmetic textbooks.
- This example of the test is from the personal collection of U. S. government psychologist and university teacher in education Samuel Kavruck.
- For a related object see 1990.0034.164.
- Location
- Currently not on view
- date made
- ca 1925
- maker
- John, Lenore
- Buswell, G. T.
- ID Number
- 1990.0034.007
- accession number
- 1990.0034
- catalog number
- 1990.0034.007
- Data Source
- National Museum of American History
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Diagnostic Chart for Individual Difficulties. Fundamental Processes in Arithmetic, Teacher's Diagnosis
- Description
- Guy T. Buswell and Lenore John published this chart in about 1925 through the Public School Publishing Company of Bloomington, Illinois. The entire package included directions, a pupil's work sheet, a teacher's diagnostic chart, and a pupil's work sheet diagnostic chart. This is the teacher’s diagnostic chart. It was coauthored by Lenore John (1902-1992) when she was a graduate student in education at the University of Chicago.
- John was the granddaughter, daughter and niece of ministers in the United Brethren Church. Born in Pennsylvania, she moved about with her family as her father, Lewis Franklin John, took various clerical and faculty positions. One of these was at York College in York, Nebraska. Lenore John enrolled in the college and took courses in education, graduating in 1921. She taught high school mathematics in Nebraska and Wisconsin. By about 1927, she was teaching mathematics at the University of Chicago’s Laboratory School and doing graduate work in education. In 1926, she assisted Guy T. Buswell (1891-1994), another York College graduate and child of a United Brethren minister. Buswell was a faculty member in the Education Department at Chicago, They prepared a Diagnostic Chart for Fundamental Processes in Arithmetic, of which this is an example. The Buswell-John chart, as it came to be called by some, remained in use for decades. Buswell and John hoped that their chart would be used to determine the areas of arithmetic in which a student required further work. It was a'diagnosis" of problems rather than a prognosis of future achievement. In later years Buswell and John collaborted on a series of arithmetic textbooks.
- John went on to completer her MA dissertation at Chicago in 1927, and remained on the staff of the Laboratory School, continuing her research in mathematics education. She would serve as vice-president of the National Council of Teachers of Mathematics from 1950-1952. In the 1960s, she played an active role in work of one of the “new math” programs, the School Mathematics Study Group. She received an award from the Illinois branch of the NCTM (the ICTM) as late as 1967, and died in Chicago in 1992.
- This example of the test is from the personal collection of U. S. government psychologist and university teacher in education Samuel Kavruck.
- For a related object, the pupil's worksheet, see 1990.0034.07
- Location
- Currently not on view
- date made
- ca 1925
- maker
- John, Lenore
- Buswell, G. T.
- publisher
- Public School Publishing Company
- maker
- John, Lenore
- ID Number
- 1990.0034.164
- catalog number
- 1990.0034.164
- accession number
- 1990.0034
- Data Source
- National Museum of American History
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Standardized Test, Schorling-Clark-Potter Arithmetic Test
- Description
- By the 1920s, mathematics educators increasingly turned to standardized tests as a way to measure what students knew, to predict what they could learn, and to determine where they had difficulties. This test had sections on addition, subtraction, multiplication, and division. The final two sections were on fractions, decimals, and percentages; and on a combination of problems. The authors were Raleigh Schorling (1887–1950), John R. Clark (1887–1986), and Mary A. Potter (1889–1993?). World Book Company published the four page leaflet in 1928. Versions of the test would be published for decades. The Schorling-Clark-Potter Arithmetic Test (Form A-Revised) was intended for use in grades five through twelve. The test consists of 100 questions.
- By 1926, when the test was first published, Schorling and Clark had obtained their PhDs from Teachers College of Columbia University. After earning his doctorate, Clark headed the mathematics department of the Chicago State Teacher’s College, and then in 1920 returned to teach in the Department of Mathematics Education at Teachers College. He remained there until his retirement in 1952.
- Schorling taught at the Lincoln School of Teachers College. He left in 1923 to become the first principal of the University High School at the University of Michigan, and completed his Teachers College doctorate in 1924. He remained at Ann Arbor for the rest of his career, serving as well as a professor of education at the university. Mary Potter obtained her undergraduate degree from Lawrence College in Appleton, Wisconsin, in 1913. She taught in several Wisconsin school districts, settling in Racine by 1920 and living there the rest of her working life.
- At the Lincoln School, Schorling and Clark worked to reform arithmetic education by emphasizing the affairs of daily life. Their efforts led them to author new textbooks as well as new tests. Schorling, Clark, and Potter were all active in the establishment of the National Council of Teachers of Mathematics in 1920.
- Born in upstate New York, the donor of this example of the test Ruth Estelle Myer (1915-2001) graduated from Hunter College and then moved to Washington, D.C., in 1940. She worked in the War Department, the Department of Commerce, and the Civil Service Commission (now the Office of Personnel Management) for about forty years. Her area of expertise was psychological testing.
- Dt. Myer obtained her M.A. from George Washington University in 1946 and her PhD. in psychology from American University in 1963. This is her personal collection of paper-and-pencil psychological tests. Topics of the tests range from mental ability to scholarly achievement to personality to occupational ratings. Dates range from 1928 to 1952.
- References:
- Michael Ackerman, “Mental Testing and the Expansion of Educational Opportunity,” History of Education Quarterly 35, no. 5 (Fall 1995): 279-300.
- “Ruth E. Myer, Government Worker,” Washington Post, May 8, 2001.
- Accession file.
- Location
- Currently not on view
- date made
- 1928
- maker
- Schorling, Raleigh
- Clark, John R.
- Potter, Mary A.
- ID Number
- 1983.0168.01
- catalog number
- 1983.0168.01
- accession number
- 1983.0168
- Data Source
- National Museum of American History
-
Standardized Test, Arithmetic Reasoning
- Description
- Bruce V. Moore (1891—1977), an industrial psychologist at Pennsylvania State College (later Pennsylvania State University) published this test leaflet in 1941. It consists of twenty word problems involving use of arithmetic, with spaces for writing the answer.
- This is one of a series of psychological tests given to the Smtihsonian by Cincinnati Boss Company.
- Reference:
- For Moore’s autobiography, see the website of the Society for Industrial and Organizational Psychology at: http://www.siop.org/presidents/Moore.aspx.
- Accession file.
- Location
- Currently not on view
- date made
- ca 1941
- maker
- Moore, B. V.
- ID Number
- 2000.3029.06
- nonaccession number
- 2000.3029
- catalog number
- 2000.3029.06
- Data Source
- National Museum of American History
-
Arithmetic Computation Test. Form-AC-1
- Description
- This test consists of four sheets of paper, printed on both sides and stapled together. Included are directions and 50 multiple-choice questions involving numerical calculations. Answers were to be blackened in on answer sheets so that tests could be scored by machine.
- World War I had seen major development of standardized testing in the United States. The new tests developed in World War II did not have as large an impact, although they were widely used. This examination was developed at the War Shipping Administration, a U.S. government agency in business from 1942 until 1946. This example is Form-AC-1.
- Location
- Currently not on view
- date made
- ca 1945
- maker
- War Shipping Administration
- ID Number
- 1989.0710.47
- catalog number
- 1989.0710.47
- accession number
- 1989.0710
- Data Source
- National Museum of American History
-
Standardized Test, SRA Reading and Arithmetic Indices
- Description
- By the 1960s, when this test was published, employers often gave job candidates standardized examinations. This set of one arithmetic and one reading test was designed particularly for adults with limited basic skills in these areas. According to the test booklets, they were developed by Science Research Associates (SRA), a subsidy of IBM.
- This collection contains the Science Research Associates (SRA) Arithmetic Index, the SRA Reading Index, and the Reading and Arithmetic Indexes Preliminary Manual. The SRA Arithmetic Index contains fifty-four questions related to: addition and subtraction of whole numbers, multiplication and division of whole numbers, fractions, and decimals and percentages. The SRA Reading Index contains sixty questions related to: picture-word association, word decoding, phrase comprehension, sentence comprehension, and paragraph comprehension. Both tests contain the original carbon paper. The manual describes the main audience of the tests as being “adults and youths over 14” and “for use with applicants for entry-level jobs and special training programs, where the basic skills of the applicants are often too low to be reliably evaluated by typical selection tests.” The manual is a ten-page long booklet that includes: features of the Reading-Arithmetic Indexes, development and descriptive statistics, administering the tests, score, and interpretation and use.
- Location
- Currently not on view
- date made
- 1968
- publisher
- Science Research Associates, Inc
- ID Number
- 1986.3133.07
- catalog number
- 1986.3133.07
- nonaccession number
- 1986.3133
- Data Source
- National Museum of American History
