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Mathematical Treasure: Felter’s Arithmetic for Children

Frank J. Swetz (The Pennsylvania State University)

Felter’s First Lessons in Numbers (1865) is an example of an early American arithmetic book written specifically for the instruction of young children. Its organization and form appear to reflect the pedagogical ideas of the Swiss educational reformer, Johann Pestalozzi (1746-1827). Most likely, this book was intended to be a teacher’s reference from which material would be dictated to a class and the students would copy it in their notebooks. The content spans topics including simple number recognition, basic arithmetic operations, fractions, systems of weights and measures, and, finally, time recognition and use of a calendar. The text is wonderfully illustrated with agricultural and bucolic scenes, reflecting 19th century American life. The author, Stoddard A. Felter, lived his early life in Cullman, Alabama, graduated from a normal school, and was a mathematics professor at the Brooklyn Polytechnic Institute. He went on to compose a series of mathematics texts for young children.

The title page for the text alludes to the author’s accomplishments.

The teaching of addition begins with dictation of oral problems concerning simple situations and advances to written symbolic form.


The introduction of the operation of subtraction follows a similar format.

Multiplication instruction follows, introduced as the operation and later explained as “repeated addition”.

Division is also introduced directly as an operation. Felter often supplied pedagogical advice in footnotes.

The operation of division is also demonstrated as the inverse operation of multiplication.

The discussion and teaching of division is followed by the topic and concept of fractions.

Several systems of weights and measures are introduced for the young learners. These measures reflect on household life in middle nineteenth century America, at the time of the Civil War.


The text’s instruction ends with a consideration of the calendar and the seasons. Once again, the illustrations on the calendar reflect an agricultural existence.

The images above were obtained through the courtesy of the Dibner Library of Science and Technology, Smithsonian Libraries.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Felter’s Arithmetic for Children," Convergence (May 2017)