Mechanism, understanding and silent practice in the teaching of arithmetic: On the intention, critique and defense of Carl Alfred Nyström’s Digit-Arithmetic 1853-1888

Abstract

This report was written as part of the project "Conceptions of mathematics in the Swedish world of schooling 1880-1980", financed by The Swedish Research Council. It contains a presentation of historical material, pertaining to the teaching of elementary mathematics in Sweden in the last third of the 19th century, and a rather far-reaching and critical analysis of this material. Its length, in combination with its somewhattentative character made it more suitable for publication in a report, rather than in a research article.

My story circles around the civil servant and physicist Carl Alfred Nyström (1831-1891). He worked mainly with telegraphy, a field in which he was a main contributor in Sweden. He was the manager of the educational department of the telegraph office 1873-1879 and then went on to manage the Stockholm telegraphy station a few years in the late 1880’s. In 1881 he represented Sweden at the international committee in Paris for the formulation of proposals for international units in the field of electricity and electro-technics.

I am interested in Nyström because of his Digit-Arithmetic (Sifferräkneläran), which was one of the most popular textbooks for the teaching of arithmetic in Sweden in the second half of the 19th century.As stated in the title of this report, I give an account of the intention, critique and defense (by Nyström himself) of this textbook. My explanation of why the Digit Arithmetic was phased out from use in Swedish public education in the 1880’s involves the topics of the first part of the title: mechanism, understanding, and a particular way of managing pupils, which at the time was called ”silent practice”.

The story about Nyström and thefate of his educational ideas are interesting enough to be made available for a potentially international readership. The numerous quotations, which I would have had to cut out, had I tried to make thetext fit into the article format, will now make it possible for the reader also to interpret the episode in other ways than I have done here.