The winds of British Columbia rise as they go inland.
Therefore, the winds (atmosphere) in British Columbia become colder as they go inland.
The atmosphere gives out moisture as it becomes colder.
The atmosphere in British Columbia becomes colder as it goes inland.
Therefore, the atmosphere gives out moisture in British Columbia.
=Steps in Process.=--The various elements involved in a deductive process are often a.n.a.lysed into four parts in the following order:
1. _Principles._ The general laws which are to be applied in the solution of the problem. These, in the above deductions, const.i.tute the first sentence in each, as,
The air becomes colder as it rises.
Air gives out its moisture as it becomes colder, etc.
2. _Data._ This includes the particular facts already known relative to the problem. In this lesson, the data are set forth in the second sentences, as follows:
The prevailing winds in British Columbia come from the Pacific; the wind rises as it goes inland, etc.
3. _Inferences._ These are the conclusions arrived at as a result of noting relations between data and principles. In the above lesson, the inferences are:
The atmosphere, or trade-winds, coming from the Pacific rise, become colder, and give out much moisture.
4. _Verification._ In some cases at least the learner may use other means to verify his conclusions. In the above lesson, for example, he may look it up in the geography or ask some one who has had actual experience.
=Deduction Involves a Problem.=--It is to be noted, however, that in a deductive learning process, the young child does not really begin with the general principle. On the contrary, as noted in the study of the learning process, the child always begins with a particular unsolved problem. In the case just cited, for instance, the child starts with the problem, "What is the condition of the rainfall in British Columbia?" It is owing to the presence of this problem, moreover, that the mind calls up the principles and data. These, of course, are already possessed as old knowledge, and are called up because the mind feels a connection between them and the problem with which it is confronted. The principles and data are thus both involved in the selecting process, or step of a.n.a.lysis. What the learner really does, therefore, in a deductive lesson is to interpret a new problem by selecting as interpreting ideas the principles and data. The third division, inference, is in reality the third step of our learning process, since the inference is a new experience organized out of the selected principles and data. Moreover, the verification is often found to take the form of ordinary expression.
As a process of learning, therefore, deduction does not exactly follow the formal outline of the psychologists and logicians of (1) principles, (2) data, (3) inference, and (_4_) verification; but rather that of the learning process, namely, (1) problem, (2) selecting activity, including principles and data, (3) relating activity=inference, (4) expression=verification.
=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.
[Ill.u.s.tration]
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:
[Ill.u.s.tration]
FURTHER EXAMPLES FOR STUDY
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.
I. DIVISION OF DECIMALS
1. _Principles_:
(_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.
2. _Data_:
Present knowledge of facts contained in such an example as .0027 divided by .05.
3. _Inferences_:
(_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.
4. _Verification_:
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.
II. TRADE-WINDS
1. _Principles_:
(_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.
2. _Data_:
(_a_) The most heated portion of the earth is the tropical region.
(_b_) The rapidity of the earth"s motion is greatest at the equator and least at the poles.
(_c_) The earth rotates on its axis from west to east.
3. _Inferences_:
(_a_) The heated air in equatorial regions will be constantly rising.