Class V. (Two hours weekly.) After the necessary preparation, practice in the three operations with decimal numbers. In connection with the consideration of plane surfaces the children should be given practice in measuring parallelograms, triangles, irregular quadrangles and many-sided surfaces—triangles should predominate.
Mental and tablet exercises parallel each other and are in intimate relation.
Third Division
Class VI. (Three hours weekly.) Preparatory practice in common fractions together with addition and subtraction of fractions having a common denominator and others which can easily be reduced to a common denominator. Multiplication and division using or including fractions. Further development with mental operations growing out of and in connection with tablet work.
Class VII. (Three hours weekly.) Percentage including interest, rebate, and discount. The calculating of cubes, prisms, pyramids, circles, cylinders, cones; also shortened pyramids, cones, and cylinders.
After this a general review so far as time admits.
Simple arithmetical operations occupy the entire field during the earlier years. The elementary algebraic forms and methods of solution are introduced relatively early, and minor geometric relations and operations are presented during the last (seventh) year of the lower schools. These latter features are radically different from our general procedure in the United States. We are in the habit of presenting the various mathematical subjects one at a time, completing one before another is considered to any extent whatever. For example, arithmetic is taken up and gone through, while parts of geometry and algebra which would be great aids in some of the arithmetical solutions are studiously avoided or excluded until the formal study of that particular subject is finally begun. The people of Norway, on the contrary, enter the larger field of mathematics and, in a more rational manner—a more psychological way—utilize available processes and forms at every opportunity. The phases of mathematics are not specialized into isolation but coordinated into a working unity. Instead of studying one subject throughout its intricacies and side issues before admitting consideration of other phases of mathematics, they make it the rule to utilize the elemental factors of the various mathematical subjects in every way possible. They give recognition to the simpler and more fundamental principles and operations regardless of the special phase of the subject to which they belong, and use the entire product as groundwork for succeeding steps in the science. In this way parts of algebra and geometry become valuable contributing preliminaries to higher arithmetical operations.
The texts used by the pupils are little more than a series of exercises. All teaching is done by the teacher and the texts are arranged in such a way that the children may have opportunity to become skilled in the principles evolved in class through application of them in the long lists of problems in their texts. Very little blackboard is provided for the pupils' use, hence but little blackboard work is accomplished. Each room has a small board on which the teacher of a pupil may go through solutions. Never have I seen more than one at a time working at the blackboard. While the limited use of blackboards generally calls for an increased amount of dependence upon intellectual activity and consequent increase in mental alertness, the free use of blackboards relieves the mind of unnecessary burdens which may as well be borne by crayon, and thus provides for the higher centers a freer activity in pushing on the quest for the unknown.
Geography
Aim. To obtain (1) A somewhat complete acquaintance with the fatherland; its conditions, commerce, manner of life. (2) Acquaintance with the geography of Europe, especially the countries to the north and the other longer civilized countries. (3) A view of the different continents and a closer acquaintance with lands and places which are of greatest importance to the fatherland. (4) Knowledge of the most important features of physical and mathematical geography.