Many initiatives related to education in the nineteenth century focused on the role of mental development. “Mental arithmetic”--as several of the following resources describe it—was believed to foster the power of imagination in students, which in turn enabled faster and more efficient calculations. Such attributes were vital to a contemporaneous emphasis on “practical mathematics.” Practical math was the idea that arithmetic prepared students for professional life, and while it was directly related to earlier forms of specialized vocational training (see see the "General Books" section of this guide), practical math standardized professionalization by treating all students as potential workers in a number of different careers. As John Penoyer wrote in a textbook called The Rapid Reckoner, students required mental math skills because “Business men demand of their employees speed and accuracy." These ideas became so ingrained that by 1895 Thomas Vickroy defined arithmetic in his Complete Course in Arithmetic as “the solving of problems from its various applications to business life."
For example, one of the oldest numeracy techniques—the word problem—has long been used to apply number skills to real-life contexts, often using illustrations or even stories. But by the end of the nineteenth century, as numerous examples from our collection demonstrate, word problems also came to require students to imagine themselves in different industries, from banking to agriculture. In Orton's Lightning Calculator, for example, there are dozens of illustrations that accompany such problems, each one depicting workers using basic arithmetic as part of their daily work, including the illustration below of a man calculating the amount of lumber in a pile of wood. This connection between arithmetic, imagination, and business preparation extended to many other techniques introduced into nineteenth-century classrooms, including flash cards, manual calculators, and perhaps most surprisingly, even poetry. In each case, the development of mental activity, through the value of imagination, literacy, and other non-mathematical skills, ostensibly aided internal calculation and, by extension, business training.