# Charts and Tables

• Contents

With the advent of relatively large classes of students studying arithmetic in common schools, educators began to prepare special charts to assist in instruction. By 1900, these could be quite extensive. Arithmetic charts, like textbooks and flash cards, reflected contemporary ideas.  Charts made in the 1830s were designed specifically to be used with a numeral frame. Those made in the 1890s showed metric as well as standard weights and measures. A chart from roughly the era of the New Math showed a number line—a mathematical construct not previously taught to young schoolchildren.

### Arithmetic Card for Use with a Numeral Frame

In the nineteenth century, Americans began to teach groups of young children in classrooms. Some institutions were designed especially for these children, and were called infant schools.
Description
In the nineteenth century, Americans began to teach groups of young children in classrooms. Some institutions were designed especially for these children, and were called infant schools. To create a vivid impression on young minds, teachers used a numeral frame or abacus in combination with a chart like this one.
This cardboard chart was part of a larger series. It has printing on both sides. It is labeled on one side: ARITHMETIC CARD II. This side shows a group of common objects on the left, and one of these objects on the right. It was designed to teach adding 1 to 6, 7, 8, and 9. Teachers were told to perform the same operation using balls on an abacus. The other side of this chart is entitled: ARITHMETIC CARD VI. It has groups of vertical lines on the left and two slanting lines on the right, and was meant to teach subtraction of 2. It also was to be used with an abacus.
A mark on the chart reads: INFANT SCHOOL CARDS, PUBLISHED BY MUNROE & FRANCIS, BOSTON. For another chart in the series, see CL.389116.04.
Infant schools were popular in Boston around 1830, and the abacus was introduced into the Boston schools at about that time. Munroe & Francis was in business from the last decades of the 1700s until 1860 or so. In October 1831, The New England Magazine announced that Munroe and Francis had just published “Complete Sets of Lessons on Cards for Infant Schools, consisting of 100 Lessons of every variety, on 50 Boards.” It seems likely that these cards were part of that set.
Reference:
“Works Published,” The New England Magazine, 1 (1831), p. 368.
Location
Currently not on view
ca 1831
maker
Munroe & Francis
ID Number
CL.389116.28
accession number
182022
catalog number
389116.28

### Arithmetic Card for Use with a Numeral Frame

In the nineteenthth century, Americans began to teach young groups of children in classrooms. Some of these institutions were designed especially for these children, and were called infant schools.
Description
In the nineteenthth century, Americans began to teach young groups of children in classrooms. Some of these institutions were designed especially for these children, and were called infant schools. To create a vivid impression on young minds, teachers used a numeral frame or abacus in combination with a chart like this one.
The cardboard chart was part of a larger series. It has printing on both sides. One side is entitled: ARITHMETIC CARD III. It shows groups of like objects on the left, with one slightly different object on the right. Subtracting one fallen tree from two trees leaves one tree standing, Having one of three mounted trumpeters fall off his horse leaves two trumpeters riding. Further illustrations show the loss of one from larger groups. The reverse of this chart is entitled: ARITHMETIC CARD VII. It has groups of vertical lines on the left and three vertical lines on the right, and is designed to teach adding by three.
For another chart in the series, see CL*389116.28.
Infant schools were popular in Boston around 1830, and the abacus was introduced into the Boston schools at about that time. Munroe & Francis was in business from the last decades of the 1700s until 1860 or so. In October 1831, The New England Magazine announced that the firm had just published “Complete Sets of Lessons on Cards for Infant Schools, consisting of 100 Lessons of every variety, on 50 Boards.” It seems likely that these cards were part of that set.
Reference:
“Works Published,” The New England Magazine, 1 (1831), p. 368.
Location
Currently not on view
ca 1831
maker
Munroe & Francis
ID Number
CL.389116.04
accession number
182022
catalog number
389116.04

### Set of Charts, Evans' Arithmetical Study

Around 1900 many American educators advocated the use of objects in teaching mathematics and the sciences. R. O. Evans Company of Chicago published this set of twenty chromolithographed charts.
Description
Around 1900 many American educators advocated the use of objects in teaching mathematics and the sciences. R. O. Evans Company of Chicago published this set of twenty chromolithographed charts. They were designed to apply the object method “to the entire subject of practical arithmetic.” The title chart shows a man in classical garb holding a diagram of the Pythagorean theorem and a pair of dividers, expounding to a child. Other instruments displayed include a pencil, a drawing pen, a magnetic compass, several geometric models, a globe, a telescope, two set squares, an hourglass, and one of Evans’s charts.
Charts include extensive commentary for teachers. There are sheets entitled Counting and Writing Numbers, Reviews and Colors, Addition, Subtraction, Multiplication, and Division,. Other charts discuss Fractions, Weights and Measures, the Metric System, and Mensuration (one chart considers the measurement of flat surfaces, another one 3-dimensional solids). There also are charts on Business Methods (3 charts), Lumber and Timber Measure,Surveying, Percentage, Commercial and Legal Forms, and Book Keeping. A variety of objects are shown.
The paper, cloth-backed charts are held together at the top by a piece of fabric that is tacked to a wooden backing. This backing slides into an oak case decorated with machine-made molding and panels. A mark on the case reads: This is the (/) Property of (/) F. C. Adams (/) Hillsboro N. H. (/) May 28 - 1902 (/) Loaned to (/) Miss L. Hany (?) (/) Teacher School Dist. No. 17. F.C. Adams is probably Freeman C. Adams (1845-1913) of Hillsborough and Manchester, N.H. This suggests that this particular example of Evans’ Arithmetical Study was used by a woman who taught at a school in New Hampshire.
Location
Currently not on view
1897
maker
R. O. Evans Company
ID Number
2009.0086.01
accession number
2009.0086
catalog number
2009.0086.01

### Teacher’s Number Line

From the time of Descartes (1596–1650), mathematicians have described positive and negative integers as evenly spaced points on a line, now called the number line, that extends infinitely in both directions.
Description
From the time of Descartes (1596–1650), mathematicians have described positive and negative integers as evenly spaced points on a line, now called the number line, that extends infinitely in both directions. This usage had made it into some school textbooks by the early 20th century. Particularly at the time of the development of the New Math in the 1950s and 1960s, number lines became part of the school classroom. This example of a number line was developed by Loraine McMillan and sold by Houghton Mifflin Company to accompany the 1972 edition of the textbook Modern School Mathematics. McMillan also prepared the leaflet describing how the number line should be used, as well as a that sold separately.
The teacher's number line consists of eleven cards. Ten of these can be placed end to end to show a number line with the integers from 0 to 100 written in red. The eleventh card is divided into segments but has no numbers marked on it. Each card, unfolded, measures 89 cm. w. x 11 cm. d. The cards were coated with clear plastic so that teachers could mark them with crayons or felt tip markers. The teacher’s guide is printed on blue paper. A mark on it reads: Teacher’s number line; teacher’s guide(/) by (/) Loraine McMillan. Another mark on it reads: houghton (/) mifflin (/) company. A third mark reads: 1972 .
This example appears unused. It was received in 2012, and had been the property of Harvard University mathematician Andrew Gleason.
References:
P. A. Kidwell, A. Ackerberg-Hastings, and D. L. Roberts, Tools of American Mathematics Teaching, Baltimore: Johns Hopkins University Press (2008), pp. 202-203.
Max Beberman and Bruce Meserve, “The Concept of a Literal Number Symbol,” Mathematics Teacher; 48, 1955, pp. 198–202.
Location
Currently not on view