our thanks?" "Who will love our Fatherland must know how to learn." "So wrote Goethe, when he was a student, to his sister Cornelia, and that is the motto which I wish you all to remember to-day.” Then the year's prizes were distributed, and each prize-winner shook hands with the rector, an honour which, I am told, is much prized, but it tended to become mechanical. Finally the proceedings finished with the song of Deutschland über alles. Girls and boys, piano, teachers, and many of the parents, all took part lustily. In one hour twenty minutes from the commencement the celebration was over. The impression made upon me was profound; a grave, pious, solid assembly, met in no Mafeking spirit of riotous jubilation, but in a sober, grateful, Godfearing way to celebrate their great triumph. With such a people it would be much to be friends; it would be disquieting to have them for enemies. CHAPTER X ARITHMETIC Frankfort. Primary School.1 Class VII. First School Year. A large class of girls of six and seven years of age, under a woman teacher. Questions in arithmetic were asked by the head master. Question. How many fingers do I hold up? Question. Take away two. How many now? Answer. Three. Question. Now take away one, how many are left? Five is two and how many more? Answer. One. Question. And three is five less? This seems trivial to us, but we must remember the absence of the infant school training, and also the limitation of the Lehrplan. In the first school year children are not expected to deal with numbers higher 1 In Frankfort and Hamburg the complete primary school course is divided into seven standards or classes, in Berlin and Leipsic into eight. than 20, in the second year 100, in the third year 1000, and in the fourth year 1,000,000. Leipsic.-Primary School. Class VII. Second School Year. Forty-six children present, seven to eight years of age. In this class the numbers dealt with do not exceed 100 as a total. The lesson opened, as is almost invariably the case in German schools, with mental exercises, given out orally, not written on the blackboard. These children added the tens first and then the units; but I do not know if this method obtains generally. At my request the teacher was kind enough to give the following problem : Fred has 36 apples, Charles has 12 more than Fred has. How many have they together? This was too much for the class, and the teacher substituted : How many has Charles? My next problem was : In one field there are 37 trees, in another 12, in another 7, and in another 9. How many altogether? This was too difficult; but, when, at my suggestion, |