# The Teaching Abacus or Numeral Frame

• Contents

In order to explain basic arithmetic operations, teachers used a form of the Russian abacus known as the numeral frame. The device was first used in classrooms in France and England and then came to the U.S. It was sometimes sold in combination with a slate.

In the 1870s, inventors proposed variations on the numeral frame that made it suited to posing written problems for a class. The numeral frame also sold in the twentieth century as a child’s toy. Forms of the teaching abacus also have been used to teach about place value and to provide instruction for the blind.

### Teaching Abacus, or Numeral Frame

To teach children basic arithmetic, nineteenth century teachers used numeral frames like this one. They resemble a Russian abacus, in that beads move crosswise.
Description
To teach children basic arithmetic, nineteenth century teachers used numeral frames like this one. They resemble a Russian abacus, in that beads move crosswise. However, each bead represents a unit digit (unlike the abacus, where beads in different rows or columns have different place values).
Soldiers returning from Russia after the Napoleonic Wars introduced this kind of abacus into France. In England, teacher and educational reformer Samuel Wilderspin promoted its use. Educators from both France and England brought it to the U. S., where it began to sell commercially in the late 1820s.
Some numeral frames were purchased and others homemade. The device was used to teach counting, simple addition, multiplication, and fractions. Most early numeral frames had 12 or 10 beads in a row. This one has 8 parallel copper wires, each with 18 beads. The instrument was used in Mexico. It came to the Smithsonian in 1979. There are no maker’s marks.
Reference: P. A. Kidwell, Amy Ackerberg-Hastings, and D. L. Roberts, Tools of American Mathematics Teaching, Baltimore: Johns Hopkins University Press, 2008, pp. 87-104.
Location
Currently not on view
ID Number
1979.0693.01
catalog number
1979.0693.01
accession number
1979.0693

### Slate with Numeral Frame

This object combines two common tools of 19th-century American teaching: the slate and the teaching abacus or numeral frame. Both the piece of black slate and the wires of the numeral frame fit in a wooden framework.
Description
This object combines two common tools of 19th-century American teaching: the slate and the teaching abacus or numeral frame. Both the piece of black slate and the wires of the numeral frame fit in a wooden framework. There are two rows of wooden beads, with ten beads in each row. The beads are painted in the colors of the spectrum (red, orange, yellow, green, blue). The unsigned and undated instrument was given to the Museum in 1975.
In the 1870s and 1880s, at least three Americans took out patents for combination slates and abaci. Freeman D’Ossone of Philadelphia proposed a slate with a row of nine numbered beads that moved up and down on a wire in a frame with the slate (US Patent 119,332, dated September 26, 1871). The beads shown in the patent description are spherical.
Henry Stewart of Erie, Pa., proposed an abacus attachment for school slates that fit atop the slate and had two rows of beads with ten beads in each row. The beads are slightly flattened (US Patent 217,749, dated February 6, 1883).
Charlotte Francis Roddey of New York City proposed an “abacus for slates” in which a single row of 25 spherical beads fit into the frame of an abacus (US Patent 339933, dated April 13, 1886). None of these inventions precisely matches this object. It seems likely, however, that this slate with numeral frame dates from about the same period.
ca 1890
ID Number
MA.335281
catalog number
335281
accession number
314637

### Gould's Patent Arithmetical Frame

Many nineteenth-century educators believed that a careful study of arithmetic contributed to general mental discipline among students. To improve such teaching, several inventors proposed special instruments.
Description
Many nineteenth-century educators believed that a careful study of arithmetic contributed to general mental discipline among students. To improve such teaching, several inventors proposed special instruments. This arithmetical frame, patented by John Gould of Chatham, New Jersey, in 1882, was an improved example of an instrument patented by Henry K. Bugbee of Elizabeth, New Jersey, in 1864. Gould soon moved to New York City, where he manufactured not only his arithmetical frame but school furniture.
The tan, brown and black device has a wooden frame that holds 18 rotating wooden slats. Each slat has a round dowel at one end that fits into one side of the frame. The other end of the slat has a knob for rotating the slat, as well as a spring and washer to hold it in place. Eight large numbers are on each side of each slat. At the right side is a smaller number (ranging from 1 to 18) on one side and the same number over a letter on the other side. Each slat has a decimal point between two of the digits on it. The frame could be set in numerous positions, giving different arithmetic problems. Solutions were given in a key (see 1994.0038.02).
The front is marked at one end: PATENTED (/) ARITHMETICAL FRAME (/) JOHN GOULD, 72 MURRAY ST. N.Y. A mark at the other end of the front reads: COMBINATION OF SLATS COPYRIGHTED, 1881.
Gould actively recruited endorsements of his device from both public and private schools (see 1994.0038.03). According to an 1882 advertisement, he sold the instrument in three sizes, for prices ranging from \$2.25 to \$8.00. This object is slightly larger than the smallest size listed in the advertisement.
References:,
H. K. Bugbee, “Arithmetical Frame,” U.S. Patent 43,545, July 12, 1864.
J. Gould, “Arithmetical Frame,” U.S. Patent 262,221, August 8, 1882.
“Gould’s Pat. Improved Arithmetical Frame," The Primary Teacher, vol. 5 #7, March, 1882, p. 270 (advertisement).
Location
Currently not on view
ca 1890
maker
Gould, John
ID Number
1994.0038.01
accession number
1994.0038
catalog number
1994.0038.01

### Pamphlet, A Revised Key to Gould's Patent Artihmetical Frame

This 56-page paper pamphlet, copyrighted in 1881, has the full title A Revised Key to Gould's Patent Arithmetical Frame; Containing Much New and Valuable Matter, Including Common Fractions, Percentage, and the Metric System.
Description
This 56-page paper pamphlet, copyrighted in 1881, has the full title A Revised Key to Gould's Patent Arithmetical Frame; Containing Much New and Valuable Matter, Including Common Fractions, Percentage, and the Metric System. It has a variety of problems in addition, subtraction, multiplication, division and decimal fractions that could be set up on a teaching device called Gould's patent arithmetical frame, along with answers. A section of the pamphlet discusses the metric system, and a variety of other arithmetic problems are included.
On the cover, Gould’s address is given as 72 Murray St., New York. This address is crossed out and Chatham, N.J., is written in in ink.
For a related object, see 1994.0038.01. For related correspondence, see 1994.0038.03.
Location
Currently not on view
1879
maker
Bugbee, H. K.
ID Number
1994.0038.02
accession number
1994.0038
catalog number
1994.0038.02

### Correspondence of John Gould Relating to his Arithmetical Frame

Nineteenth-century inventors of improved school apparatus often collected testimonials from teachers and administrators who would attest to the value of their inventions.
Description
Nineteenth-century inventors of improved school apparatus often collected testimonials from teachers and administrators who would attest to the value of their inventions. This collection of documents includes business documents and correspondence relating to Gould’s Patent Arithmetical Frame, a device patented by Henry K. Bugbee and then improved by John Gould. The lists of potential customers and testimonial letters date from the years 1880 to 1893. At least from 1885, Gould was in Chatham, New Jersey, which is where he was when he received his patent in 1882.
Correspondents include educators in Louisiana, Texas, New Jersey, Ohio, Michigan, Maryland, and New York. The 1881 instructions for the device (1994.0038.02) give an address in New York City. That booklet includes some testimonials, but none of the letters preserved here.
For an example of the arithmetical frame, see 1994.0038.01.
References:
H. K. Bugbee, “Arithmetical Frame,” U.S. Patent 43,545, July 12, 1864.
J. Gould, “Arithmetical Frame,” U.S. Patent 262,221, August 8, 1882.
“Gould’s Pat. Improved Arithmetical Frame, “ The Primary Teacher, vol. 5 #7, March, 1882, p. 270 (advertisement).
Location
Currently not on view
1880-1893
maker
Gould, John
ID Number
1994.0038.03
accession number
1994.0038
catalog number
1994.0038.03

### Toy Abacus

In the 1950s, tools long used to communicate elementary ideas about counting and arithmetic moved from the classroom into the home.
Description
In the 1950s, tools long used to communicate elementary ideas about counting and arithmetic moved from the classroom into the home. The numeral frame, which resembles a Russian abacus, was brought to the United States from Europe in the 1820s, and used in many classrooms to communicate basic arithmetic concepts to groups of students.
By the mid-20th century, numeral frames were sold for use by young children in the home. This brightly painted example has a wooden frame, five metal horizontal cross rods, and a metal support at the back. Each cross rod carries 10 sliding wooden beads. The toy was designed to teach elementary counting, addition, subtraction, and simple fractions. The object is marked: Royal (/) Tot (/) EDUCATIONAL (/) TOY. It also is marked: Box No. 1450. There is a cardboard box. This numeral frame was sold by a pharmacy in Sherman, N.Y., and cost \$1.00.
Location
Currently not on view
1950s
ID Number
2002.3058.01
catalog number
2002.3058.01
nonaccession number
2002.3058

### Place Value Board

This is a device for introducing elementary school students to the concept of place values. Six parallel wires, each in the shape of an inverted U, fit into holes in a wooden block that serves as a base. Each wire carries nine beads.
Description
This is a device for introducing elementary school students to the concept of place values. Six parallel wires, each in the shape of an inverted U, fit into holes in a wooden block that serves as a base. Each wire carries nine beads. The beads on the front of the wire represent digits. A tape that runs across the block contains labels for the wires - from one on the rightmost wire to hundreds of thousands on the leftmost. Robert Naidorf (born 1961), the son of the donors, made the object in about 1968. It was used by Marjorie Naidorf, Robert's mother, as a third grade teacher at Parklawn Elementary School from 1971 until 1991. Place value boards are also sold commercially.
Location
Currently not on view
1968
maker
Naidorf, Robert
ID Number
2005.0055.01
catalog number
2005.0055.01
accession number
2005.0055

### Cranmer Abacus

This modification of the Japanese abacus or sorobon is designed for use by the blind. It sits in a black plastic box, with red felt in the bottom of the box to prevent the beads from sliding inadvertently. A black plastic cross bar is pierced by 13 parallel metal rods.
Description
This modification of the Japanese abacus or sorobon is designed for use by the blind. It sits in a black plastic box, with red felt in the bottom of the box to prevent the beads from sliding inadvertently. A black plastic cross bar is pierced by 13 parallel metal rods. Each rod has one spherical white plastic bead above the crossbar and four below. Raised dots can be felt on the cross bar and the lower rim of the box at each column, and as raised slashes between every 3 dots. At the top of the front are the raised letters: A.P.H.
This type of abacus was designed by Terence V. (Tim) Cranmer (1925-2001) of the Kentucky Division of Rehabilitation Services for the Blind in early 1962, and soon placed on the market by the American Printing House for the Blind. It is still manufactured today. Cranmer was blind from childhood. He made and sold plastic jewelry in his early years, worked briefly at Kentucky Industries for the Blind, and then spent 10 years as a piano technician. In 1952, he began working for the Kentucky Division of Rehabilitation Services for the Blind, rising through the ranks. He was an active member of the National Federation of the Blind, and made several inventions.
The donor, Russell Kletzing of Sacramento, California, was a lawyer blinded as a child. He was active in the National Federation of the Blind, and challenged the view that the U.S. Civil Service register should exclude blind lawyers because they could not read conventionally printed text.
References: Fred L. Gissoni, Using the Cranmer Abacus for the Blind, Louisville, Kentucky: American Printing House for the Blind, 1962.
National Federation of the Blind, "NFB Awards 2000," Braille Monitor, August / September 2000.
Buffe Hanse, "Tim Cranmer Dies," Braille Monitor, January / February 2002.
Deborah Kendrick, “Tim Cranmer: One of Our Great Pioneers,” Access News, vol. 3 #1, January 2002.
Location
Currently not on view