=Example of Deduction as Learning Process.=--A simple and interesting lesson, showing how the pupil actually goes through the deductive process, is found in paper cutting of forms balanced about a centre, say the letter X.
1. _Problem._ The pupil starts with the problem of discovering a way of cutting this letter by balancing about a centre.
2. _Selection._ Principles and Data. The pupil calls up as data what he knows of this letter, and as principles, the laws of balance he has learned from such letters as, A, B, etc.
3. _Organization or Inference._ The pupil infers from the principle involved in cutting the letter A, that the letter X (Fig. A) may be balanced about a vertical diameter, as in Fig. B.
Repeating the process, he infers further from the principle involved in cutting the letter B, that this result may again be balanced about a horizontal diameter, as in Fig. C.
4. _Expression or Verification._ By cutting Figure D and unfolding Figures E and F, he is able to verify his conclusion by noting the shape of the form as it unfolds, thus:
The following are given as further examples of deductive processes.
The materials are here arranged in the formal or logical way. The student-teacher should rearrange them as they would occur in the child's learning process.
(_a_) Multiplying the dividend and divisor by the same number does not alter the quotient.
(_b_) To multiply a decimal by 10, 100, 1000, etc., move the decimal point 1, 2, 3, etc., places respectively to the right.
Present knowledge of facts contained in such an example as .0027 divided by .05.
(_a_) The divisor (.05) may be converted into a whole number by multiplying it by 100.
(_b_) If the divisor is multiplied by 100, the dividend must also be multiplied by 100 if the quotient is to be unchanged.
(_c_) The problem thus becomes .27 divided by 5, for which the answer is .054.
Check the work to see that no mistakes have been made in the calculation. Multiply the quotient by the divisor to see if the result is equal to the dividend.
(_a_) Heated air expands, becomes lighter, and is pushed upward by cooler and heavier currents of air.
(_b_) Air currents travelling towards a region of more rapid motion have a tendency to "lag behind," and so appear to travel in a direction opposite to that of the earth's rotation.