Arithmetic textbooks of two centuries: Goals, target groups and traditional values

Abstract

This article recounts a survey of six arithmetic textbooks, written in Icelandic and published in the eighteenth, nineteenth and early twentieth century, their goals, target groups, relations to each other and to European cultural currents, and the values they represent. All of them adhere to the European arithmetic tradition of the Late Middle Ages in their introduction of Indo-Arabic numerals and arithmetic methods. The two eighteenth century textbooks were the first substantial arithmetic textbooks printed in Icelandic. They were offshoots of the Enlightenment movement, deliberately published in order to raise the educational standards of Icelanders in the field of arithmetic. Their authors, Ólafur Olavius (1780) and Ólafur Stephensen and Magnús Stephensen (Ólafur Stefánsson, 1785), were educated in Copenhagen, in direct contact with the cultural currents of Northern Europe of their time; the German- Danish Enlightenment movement, based on Evangelic-Lutheran protestant heritage. While Olavius is concerned with presenting a variety of methods to solve arithmetic problems under indirect influence from Comenius, the Stephensens present strictly academic content, drawn directly from an introductory course at the University of Copenhagen. The two nineteenth century authors, Jón Guðmundsson (1841) and Eiríkur Briem (1869; 1880), were educated in Iceland only, under the influence of the champions of the Icelandic Enlightenment movement. Both of them introduced to their fellow countrymen the art of arithmetic in a rule-based way, but in the spirit of self-instruction. They made deliberate efforts to teach young people economical allocation of their resources and avoidance of squandering their income on imported luxuries. The twentieth century authors, Sigurbjörn Á. Gíslason (1911a; 1911b; 1912) and Elías Bjarnason (1927; 1929; 1939; 1940; 1941a; 1941b; 1963; 1964; 1965), lived in a society of increasing urbanism. However, they also had firm roots in the vanishing rural society, reflected in their examples and problems. Their employment in schools is also reflected in their books, but in a different way. While Sigurbjörn Á. Gíslason in the 1910s may have been influenced by Pestalozzi’s educational ideas of releasing children from the tyranny of methods, Elías Bjarnason in the 1920s is more concerned with teaching particular methods to ensure necessary skills. This agrees with concurrent trends detected in Denmark by Hansen (2009). Elías Bjarnason’s textbook was chosen for free national distribution in 1939, republished in a revised edition in the 1960s and was to have a dominating influence for the age group 10–13 through the 1970s. The authors shared some characteristics. Firstly, they were filled with a youthful enthusiasm. Ólafur Olavius was only in his early thirties when he imported the country’s first print shop to print secular literature, and Magnús Stephensen was merely 23 years old when he rewrote his father’s manuscript of a textbook, according to his professor’s lecture notes, thereby importing the novelties of decimal fractions and algebra to Iceland. Jón Guðmundsson and Eiríkur Briem, who wrote his book at the age of 23, later became, as well as the Stephensens, outstanding personalities in the advancement of Iceland to modern society. Secondly, the target groups of all the authors except Sigurbjörn Á. Gíslason were self-educating youngsters in the absence of schools. Even if schools were an emerging phenomenon in the 20th century, the majority of children through the 1920s attended itinerant schools which required children to stay at home, studying on their own for long periods, and lower secondary schools only became commonly accessible in the 1930s. While all the authors’ interests in the progress of Icelandic society are beyond doubt, their visions were to maintain the values of the old self-sufficient rural society, and to teach the public to make the most of its current resources. Only Olavius in the eighteenth-century and Sigurbjörn Á. Gíslason in the early twentieth-century were concerned with giving their readers versatile learning experiences in accordance with recent educational theories. Reflecting upon their educational vision one may wonder if attitudes and opinions of the general public on the nature of mathematics would have developed differently if their textbooks had achieved more far-reaching effects.