10. DISCOVERER’S METHOD OR THE REAL INDUCTIVE METHOD ADAPTED TO CLASS ROOM WORK.
A revolt has already set in against this insatiate desire to teach knowledge, rather than to teach the child. Many schools are permitting a study of those topics which vitally concern every day life. Less attention is being given to formal discipline, and more attention to self activity. Gradually will the scheme of education be directed toward fitting the school work to the child, rather than fitting the child to the school work. When this new thought in education is fully upon us, then will every device and method be directed toward giving full scope to the spirit of inquiry, which so completely possesses every normal child.
It now remains for us to indicate ways in which the spirit of inquiry, or the “discoverer’s method,” may be adapted to school room work. In the first illustration, we shall outline the topic as it is generally given in the average school where attention is paid to development work. This will then be followed by a second outline which may be suggestive of the discoverer’s mode of procedure.
First illustration. School Room Method.
I. Aim: To teach addition of business fractions.
II. Preparation: (Only type examples given).
| (1) | (2) | (3) | |
| 3 bushels | 3 parts | Rule: | Only like numbers |
| + 5 bushels | + 5 parts | can be added. | |
| 8 bushels | 8 parts | ||
III. Presentation:
| (1) | (2) |
| 3 ninths | 3/9 |
| + 5 ninths | + 5/9 |
| 8 ninths | 8/9 |
| (3) | (4) |
| 2/3 = 4/6 | 2/3 = 8/12 |
| 1/6 = + 1/6 | 3/4 = + 9/12 |
| 5/6 | 17/12 |
IV. Summary:
(1) Only like fractions can be added.
(2) Change unlike fractions to like fractions.
(3) Add the numerators, placing the sum over the common denominator.
V. Application:
Examples and problems involving similar and dissimilar fractions.
Before undertaking to illustrate the discoverer’s method, it may be well to designate in order the evident steps as they would appear to the pedagogue:
(1) Motivate the topic to be presented.
(2) Bring to mind appropriate “foundation facts.”
(3) Make evident the “crucial fact.”
(4) Lead to the forming of an hypothesis through analogy.
(5) Afford ample opportunity to prove the hypothesis.
Discoverer’s Method Adapted.
Lesson Plan.
I. Aim: (1) By playing upon the curiosity or by exposing a vital need, create a strong desire to know how to add business fractions. (Motivate the topic.)
Curiosity: “We all know what a fraction is and we know, too, how to change fractions to higher or lowerterms.” “Now I wonder how many know how to add fractions, such as 2/5 and 1/5?” “Don’t you tell any one, Mary, but just write your answer on a piece of paper and show it to me.” (Mary’s answer shows that she has thought correctly, but figured incorrectly. John, after having raised his hand, shows his answer to the teacher.) “John has the right answer.” “That’s fine, but let us keep the secret, John.” “I wonder how many others there are in this class who will find the right way?” etc., or
Vital need: Discuss with the class the various occupations of life and secure expressions of preference. Some may plan to be real estate agents, others contractors or book keepers, etc. “George, you plan to be a book keeper.” “Let us suppose that I have given you the job of book keeper in my factory.” “Show that you are worth your wages by adding these numbers: 1243⁄4, 6472⁄3.” “What! can’t do it?” “Then I don’t want you!” etc.
II. Preparation:
(2) Bring to the foreground the necessary foundational knowledge. Suggestions:
| 4 bushels | 8 parts |
| + 3 bushels | + 2 parts |
| 7 bushels | 10 parts |
III. Presentation:
(3) Make evident the crucial fact. Suggestions:
| Add | 2 fifths | 3 eighths | 3/8 |
| + 1 fifth | + 1 eighth | + 1/8 | |
| 3 fifths | 4 eighths |
(4) Without further suggestion, give the young discoverer suitable opportunity for finding the sum of 3/8 and 1/8. In the act of discovering, an implicit hypothesis takes form in the mind through analogous reasoning. This point marks the climax of the lesson—the supreme moment, when the skill and tact of the teacher is assessed to the limit. Just here the child must have a comfortable environment where perfect concentration is possible. Nothing must be forced; and there should be nothing suggestive of disgrace or shame, if the youthful Columbus is unsuccessful. The first attempt should be without books. If more help is needed, access to books may be given. If the investigation is still without definite result, then as a last resort the teacher may, in the presence of the child, add fractions, solving with deliberation example after example, until the child believes he has discovered the process.
(5) Stimulate a desire to verify the facts discovered.
Suggestions leading to verification: Afford opportunity for mathematical demonstration. Illustrations: The fractions 1/4 and 3/8 have been added in this way—
1/4 = 2/8
3/8 = + 3/8
5/8
Use is now made of the crucial fact, when the example assumes this form—
2 eighths
+ 3 eighths
5 eighths
Or if the class has been trained in the use of the diagram the following may be the form of proof:
1⁄4
━━━━━━━━━━
──────────
━━━━━━━━━━
──────────
━━━━━━━━━━
3⁄8
──────────
━━━━━━━━━━
──────────
━━━━━━━━━━
Explanation from diagram. I see that 1⁄4 equals 2 parts and 3⁄8 equals 3 parts; the sum of 3 parts and 2 parts are 5 parts. But the name of the part is eighths; hence the answer 5 parts may be written 5 eighths, or 5⁄8. Thus the final form is
2 parts
+ 3 parts
5 parts = 5⁄8
Give opportunity to consult answers in text books as further verification.
The summary and application of adding fractions according to the “discoverer’s method,” are virtually the same as the corresponding steps in the “school room method.”
Second Illustration of Discoverer’s Method.
David P. Page in his Theory and Practice of Teaching well illustrates the discoverer’s method in conducting a general exercise in nature study. We cannot do better than to quote from him:
“It is the purpose of the following remarks to give a specimen of the manner of conducting exercises with reference to waking up the mind in the school and also in the district. Let us suppose that the teacher has promised that on the next day, at tenminutes past ten o’clock, he shall request the whole school to give their attention five minutes to something that he may have to show them. This very announcement will excite an interest both in school and at home (playing upon the curiosity); and when the children come in the morning they will be more wakeful than usual till the fixed time arrives. At the precise time, the teacher gives the signal agreed upon, and all the pupils drop their studies and sit erect. When there is perfect silence and strict attention by all, he takes from his pocket an ear of corn and in silence holds it up before the school. The children smile, for it is a familiar object (foundational knowledge already in hand); and they probably did not suspect they were to be fed with corn.”
Teacher. “Now, children,” addressing himself to the youngest, “I am going to ask you only one question about this ear of corn. If you can answer it, I shall be very glad. As soon as I ask the question, those who are under seven years old, and think they can give an answer, may raise their hand. What is this ear of corn for?”
Several of the children raise their hands, and the teacher points to one after another in order, and they rise and give their answers.
Mary. It is to feed the geese with.
John. Yes, and the hens, too, and the pigs.
Sarah. My father gives corn to the cows.
Laura. It is good to eat. They shell it from the cobs and send it to the mill, and it is ground into meal. They make bread of the meal and we eat it.
“I am sorry to tell you that none of you have mentioned the use I was thinking of, though, I confess, I expected it every minute. I shall now put the ear of corn in my desk, and no one of you must speak to me about it till to-morrow. You may now take your studies.”
The consequence of this would be that various families, father, mother and older brothers and sisters, would resolve themselves into a committee of the whole on the ear of corn: and by the next morning several children would have something further to communicate on the subject. The hour would this day be awaited with great interest and the first signal would produce perfect silence.
The teacher now takes the ear of corn from the desk and displays it before the school; and quite a number of hands are instantly raised as if eager to be the first to tell what other use they have discovered for it.
The teacher now says pleasantly, “The use I am thinking of you have all observed, I have no doubt; it is a very important use, indeed; but as it is a little out of the common course (crucial facts) I shall not be surprised if you cannot give it. However, you may try.”
“It is good to boil,” says little Susan, almost springing from the floor as she speaks. “And it is for squirrels to eat,” says little Samuel. “I saw one carry away a whole mouthful yesterday from the cornfield.”
Others still mention other uses. Perhaps, however, none will name the one the teacher has in his own mind; he should cordially welcome the answer if perchance it is given. (Supposing that it has not been given.) “I have told you that the answer I was thinking of was a very simple one; it is something you have all observed and you may be a little disappointed when I tell you. The use I have been thinking of for the ear of corn is this: It is to plant. It is for seed, to propagate that species of plant called corn.” (Verification.) Here the children may look disappointed as much as to say, We knew that before. The teacher continues: “And this is a very important use for the corn; for if for one year none should be planted, and all the ears that grew the year before should be consumed, we should have no more corn. The other uses you have named were merely secondary. But I mean to make something more of my ear of corn. My next question is: Do other plants have seed?” Here is a new field of inquiry, etc., etc.
From the standpoint of “the greatest amount of knowledge in the shortest possible time,” this mode of presentation consumes an inexcusable amount of time and is, therefore, “impracticable.” But when viewed from the ground of interest, originality, initiative, and conquest—the watchwords of the “new thought in education”; there is no real waste in either time or energy. The spirit andmethod of the discoverer will no doubt be the educational slogan of the future age.
Epitome of Discoverer’s Method, adapted to the class room:
(1) Motivate the topic to be presented.
(2) Bring to mind, if necessary, the “foundational facts.”
(3) Make evident the “crucial fact.”
(4) Furnish every opportunity for a first-hand discovery of the “lesson-point” (establishing hypothesis through analogy).
(5) Let the hypothesis be verified.
The entire situation must be one of freedom, zeal, originality, and initiative.