Some good advice for teaching beginning arithmetic, from the original Teaching Manual for Ray’s Arithmetic (and other common books at the time).
In the first class, besides those who have never studied Arithmetic, put all who have been poorly trained in the elementary processes. It will be economy of time and labor to do this, even if you have to include the entire school in this division for a time; for, in arithmetic, above all other studies of the common school course, it is of the utmost importance that one step shall be thoroughly understood before the next is attempted. [Good advice even in the home. Lay those foundations solid. -lh] The first two years’ training is of more importance than all the rest the child receives.
Do not attempt to have the children use a book in the primary class. —A book should not be used, because no book contains, and no book can be made to contain, the kind of instruction necessary the first year.
Do not teach the figures in the first lessons, and do not allow the children to do any written work ; but teach orally, illustrating every operation, at first, by means of various objects. —The instruction should be entirely oral, and
should deal altogether at first with concrete numbers. The little child can not grasp abstract ideas. It is true you can teach him to repeat, "2 and 2 are 4;’ "2 from 4 leave 2;" "2 times 2 are 4;’ and "4 divided by 2 equal 2." But, without the proper preliminary work, these words can not possibly convey any clear meaning to his mind. This kind of instruction in a primary class is simply machine drilling on abstract numbers and words which convey no ideas, or at best a mere jumble of ideas to the child’s mind. It is one of the worst, and at the same time one of the most common, faults in the teaching- of arithmetic, and it is one which is very apt to disgust pupils with the subject from the outset.On the other hand, if the proper method of teaching is pursued, which may properly be called the object method, the children are taught to think; they will be interested at the very beginning, and they will be kept interested by this method until they are successfully carried to the point where the object method is no longer necessary, and their minds are ready to grasp the abstract, through careful preliminary drill on the concrete.
Begin the teaching of arithmetic, then, with objects, — blocks, balls, marbles, sticks, books, kernels of corn, apples, shells, pebbles, etc., etc. The more varied your assortment of objects the better. The numeral frame and other mechanical devices are useful, but should not be used exclusively, or the work will become monotonous and tiresome.
Eclectic Manual of Methods – 1885
