SLATES, SLIDE RULES, AND SOFTWARE - TEACHING MATH IN AMERICA
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To teach children basic arithmetic, 19th-century teachers used numeral frames like this one, some purchased and others homemade. The numeral frame was used to teach counting, simple addition, multiplication, and fractions. This frame was used in Mexico.

Textbooks have long been central to teaching mathematics. In early common schools, students brought in whatever texts the family owned, so that there was no uniformity within a class. 

 
Numeral Frame - Click To Enlarge
NUMERAL FRAME
 

By the 1850s, books had become much cheaper and texts more uniform. This cover is from a book in a series of math texts by Joseph Ray (1807-1855), a Cincinnati teacher. Ray’s first arithmetic text appeared in 1834, and his books were widely used as late as 1913.  

 

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Ray's Practical Arithmetic - Click To Enlarge
COVER OF
RAY'S PRACTICAL
ARITHMETIC

 

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The Smithsonian Institution's National Museum of American History, Behring Center