The recreational mathematics activities of ordinary nineteenth century Americans: A case study of two mathematics puzzle columns and their contributors

Abstract

This study analyses two American recreational mathematics columns from the end of the nineteenth century—one from Atlanta, Georgia’s Sunny South and one from Wilmington, Delaware’s Delaware Gazette and State Journal. Each was an active forum, used by ordinary, educated laypeople to participate in a culture of mathematics by contributing problems and solutions, and in some cases entering into heated discussions. This period was one of dramatic change in American mathematics, in which researchers, educators and textbook authors ended their isolation from developments in Europe and shifted emphasis from rote procedures and practical calculations toward reasoning about abstract mathematics. The mathematics columns in Sunny South and the Delaware Gazette reflect these two different views of mathematics that were percolating in American culture at the time and offer a window into the mathematical beliefs and understanding of the ordinary Americans who contributed to them.

Acknowledgments

Sian Zelbo is a mathematics teacher at the Brearley School in New York and a PhD candidate at Columbia University, Teachers College. She would like to thank Alexander Karp of Teachers College for his guidance and support. She is grateful also to the journal’s anonymous readers for their helpful feedback on the article.

Disclosure statement

No potential conflict of interest was reported by the author.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Notes

1 The population grew from approximately 5.3 million in 1800 to approximately 62.6 million in 1890, with increases between 22 and 36 percent every decade in between (Dept. of the Interior 1895, xi).

2 The geographic center of population moved from a location near Baltimore, Maryland (near the Atlantic Coast) in 1800 to a location near Columbus, Indiana in 1890, more than 900 kilometers west (Dept. of the Interior 1895, xxxvii).

3 Even the systems of public education that existed for white children in the South before the war were poorly developed, and most people ‘fended for themselves wholly on a fee basis’ (Kaestle 1983, 182), a situation that left many children without a formal education (Hyde 2016, ch. 3).

4 For example, Massachusetts, the state that pioneered public education in America, spent $18.47 per student annually in 1880 while North Carolina, in the South, spent only $ 0.87 (White 2017, 586).

5 Ozanam's ‘cell’ puzzle starts with a square abbey divided into a three-by-three array of cells, with the abbess in the center cell and three nuns in each of the other eight cells. The abbess, who is blind, checks to see that the nuns are there at night by counting the number of people along each edge of the abbey and finds that there are always nine. Four men enter the abbey, and yet the sum along each edge remains the same. The four men then abduct four nuns, and with twenty people in the abbey, still the sum along the edges remains the same. The puzzle asks how this can be true.

6 The ‘fifteen’ puzzle starts with fifteen tiles, numbered one through fifteen, placed randomly on a four-by-four grid. The goal is to slide the tiles, one by one, into the empty spaces and thereby ultimately rearrange them into numerical order. With some starting arrangements the puzzle has no solution.

7 In the account given by the US census report from 1880, when General Sherman captured Atlanta in 1864, he issued an order evacuating the city and then ‘nearly annihilated’ it, leaving behind a ‘mass of ruins’ with only a single structure left in the downtown area (Dept. of the Interior 1887, 158).

8 Atlanta grew from 21,789 residents in 1870 to 37,409 residents in 1880 (Dept. of the Interior 1882, 123).

9 One record shows that on 31 July 1863 Seals was drafted as a private in the Confederate Army and was supposed to report for duty to the Third Battalion of Georgia’s State Guards, but for at least part of the time Seals was marked ‘absent without leave’ (Civil War Service Records 1863).

10 The city’s population had grown almost forty-five percent over the previous decade to 61,431 in 1890 (Dept. of the Interior 1895, cxxvi).