Grant, Colonel Parker, and others, that a great variety of objects should be used in teaching number; that change from one class of objects to another sustains interest; that seeing and handling many classes of objects train the observing powers to make distinctions and classify things, are sound from the stand-points both of principle and practice. The illustrations used are all good; we only suggest what seems to us an improvement and a great gain.
During the last few years we have been experimenting with classes of children in a variety of ways. One general conclusion from these experiments is that number-lessons can be utilized in teaching children to recognize a large variety of industrial materials, and this too with a positive gain in interest and impressiveness to the work in number itself. Children can be taught in this way to recognize the common and useful trees by their leaves, fruit, wood, etc.; the common rocks, minerals, ores; the more important kinds of goods used in clothing.
The fragments to be had at the shops of the tailor, milliner, dressmaker, upholsterer, of any town, would supply, without cost, all the materials desired in this direction. Samples of these materials could be artistically arranged in numerical designs upon thin board or pasteboard and hung upon the walls for constant reference and review. It is no more difficult to say "two elm-leaves and three elm-leaves are five elm-leaves," "two sandstones and three sandstones are five sandstones," "two broadcloths and three broadcloths are five broadcloths," etc., etc., than to say "two blocks and three blocks are five blocks."
A second conclusion from our experiments is, that measures, weights, and moneys can be taught more efficiently than now, along with the early teaching of the fundamental arithmetical processes.
Number, the idea of the single and plural, enters into all our knowledge both of the external and internal worlds, from the time consciousness begins to act, until death. Our very first act of knowing is the recognition of a difference between two sensations. Distinguishing external objects into the single and plural—the one and the many, the little and the big—is one of the earliest lines of investigation for the infant and child. The work of the first few months of school-life is to bring this unconscious mathematical experience out into consciousness, and to give the child the beginning of the exact and quantitative method of study.
A child can very early learn to count twelve with the objects before him; can then learn to find the number of objects in a given group by counting; then by a single glance, when the groups do not contain a larger number than he has learned to count.
He can just as early and in the same connection learn to recognize an inch, two inches, twelve inches; can draw given numbers of lines of these lengths; can cut them out of paper, pasteboard, and wood. Similar work can be done with the foot and yard. Corresponding