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Those Juniors, Part 13: Matters of the Mind, #2

by Eric B. Hare

Last week: Concepts, percepts, judgment and reasoning are powers that must be taken into account when teaching. Deduction and induction are the two great principles of teaching, induction being the more beneficial of the two.

Let us take two examples from arithmetic.

An Example of Deduction
TEACHER: This morning, class, I want to show you how we can prove a multiplication problem by the rule of casting out the nines. The rule is: If you add the digits in the number to be multiplied, then subtract all the nines that you can, and write down the remainder, then do the same to the multiplier and also to the product, the product of the remainders opposite the number and the multiplier, after subtracting the nines, will equal the remainder opposite the product. Read the rule again, to make sure it is clear, and now let us demonstrate it on the board. We will multiply 176 by 24: 

Now add the digits in the number 1 plus 7 plus 6, and you get 14. You can subtract one 9, and the remainder is 5. Now add the digits in the multiplier 2 plus 4, and you get 6. You cannot subtract any nines, so the remainder is 6. Do the same to the product 4 plus 2 plus 2 plus 4 and you get 12. Subtract 9 and you have 3. Now multiply the remainders of the number and the multiplier 5 by 6 and the product is 30. You can subtract three 9’s, or 27, and the remainder is 3. Since the remainder from the product of the first multiplication is also 3, our sum is proved correct.

Notice that the teacher did all the talking. He started with a rule and proved the rule with an example. Also, please notice that unless one uses this rule frequently he will very soon forget it.

An Example of Induction
TEACHER: We have another very interesting discovery to make in arithmetic this morning, students. Take your pencils and paper, and write down a number—any number.

Students write.

TEACHER: Reverse the same number and write it underneath the first number.

Students write.

TEACHER: Subtract the smaller from the larger. Add the digits of your answer. If the answer to this addition is a double figure, add again. All right, A, what is your answer?

STUDENT A: The answer is 9. I took 976. After reversing and subtracting (976 minus 679) I had 297; 2 plus 9 plus 7 equals 18; 1 plus 8 equals 9.

TEACHER: All right, B, what is your answer?

STUDENT B: My answer is 9 too. I took 3210. After reversing and subtracting (3210 minus 0123) I got 3087; 3 plus 8 plus 7 equals 18; 1 plus 8 equals 9.

TEACHER: All right, C, what is your answer?

STUDENT C: My answer is 9, too.

TEACHER: How many have 9 for an answer?

Every hand goes up.

TEACHER: All right, class, now let us state this interesting law that we have discovered.

STUDENTS: If we take a number, reverse it, and subtract, then add the digits in the answer, and in turn add the digits in that answer, if there are more than one, the answer will always be 9.

Notice that the students do part of the talking and the demonstrating. They started with examples; then stated what they had discovered. Did you feel the thrill every student would have when he discovered he had the same answer as student A? Had you been one of those students, I think you would always remember this interesting little rule.

Let us take two more examples in doctrine to illustrate these same two principles.

Example of Deduction
“This morning, class, I want to prove to you from the Word of God that the soul cannot exist apart from the body. I turn to Genesis 2:7 and read, ‘And the Lord God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.’ You notice the Creator at the creation of man, used dust and the breath of life to produce a living soul.

“In speaking of death, David tells us in Psalms 146:4, ‘His breath goeth forth, he returneth to his earth; in that very day his thoughts perish.’ Here we find that the things that combined to make a living soul have been separated, and where is the soul? I take some dust, mix a little water with it, and I have mud. I hold the mud over a fire to evaporate away the water, the water disappears, and the dust remains. Where is the mud? The mud cannot exist unless the water and dust are together. Even so the soul cannot exist unless the body and the breath of life remain together.”

Example of Induction
TEACHER: This morning, class, I want you to discover the law which governs the existence of the soul. A, will you please read Genesis 2:7 and tell me the substances God used to make a soul?

A READS AND REPLIES: Dust and the breath of life form the living soul.

TEACHER: B, will you please read Psalms 146:4 and tell me what happens when we die?

B READS AND REPLIES: His breath goes out and his body returns to dust.

TEACHER: Where does the soul go?

B: The text doesn’t mention the soul, sir, but wouldn’t it have to go somewhere?

TEACHER: Well, let us see. What is this I have in my hand, class?

CLASS: An electric light bulb.

TEACHER: I screw the bulb into the socket and turn on the switch. What do I get?

CLASS: A light.

TEACHER: So electricity plus a bulb equals a light. Is that right?

CLASS: Yes, sir.

TEACHER: All right. Now I turn off the electricity and what do I have left?

CLASS: A bulb.

TEACHER: Where is the light?

CLASS: It’s just gone out, sir.

TEACHER: Very well, what have you found out about the relationship of light to this bulb?

CLASS: Light cannot exist without electricity flowing through the bulb.

TEACHER: Now, B, where did the soul go?

B: Yes, sir, I see it now. The soul just cannot exist without the combination of the body and breath.

At once you notice that questions and answers form the foundations of the inductive method, and that the stimulation to think leads to the thrill of discovery.

We need not take time to discuss the advantages and the disadvantages of the research method, the catechism method, the recitation method, the parabolic method. You can see how all may be used, although some are stronger than others, as the tools of the inductive principle.

But even as a gift cannot be said to be given until it has been received, so there can be no teaching until there has been learning. And since the more we think the more we learn, let us diligently study to teach by the principle of induction, the method of discovery.

(Next week: “Tempting to Teach, Part 1.”)

Copyright © 1973 by Eric B. Hare. Used by permission.

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