METHODS OF INSTRUCTION

 

         METHODS OF INSTRUCTION treats of the different branches of knowledge and how to teach them. It embraces three general divisions: 1) The Nature of Knowledge; 2) The Nature of Instruction; 3) The Methods of Teaching Each Branch.

 

                                   The Nature of Knowledge

 

         In order to give instruction skillfully, a teacher should have an idea of the general nature of the different branches of knowledge and their relations to one another. He should see clearly the elements of which the different branches are composed, the relation of these elements to the human mind, and the manner in which the sciences are developed.

         General Division of Knowledge. All knowledge may be embraced under two general divisions: Common Knowledge and Scientific Knowledge. Common Knowledge consists of unsystematized facts, ideas, and truths. It is a knowledge possessed by the common people, and is the basis of Scientific Knowledge. Scientific Knowledge consists of facts, ideas, and truths, systematized and expressed in the form of laws and principles. It enables man to interpret the facts and phenomena of nature, to see the great laws by which the universe is governed, and to previse and predict the events of the future.

         Divisions of Scientific Knowledge. Scientific knowledge has been classified in different methods depending on the purpose of investigation.

         One method divides it into two general branches: the Empirical Sciences and the Rational Sciences. This classification is based upon the relation of their subject matter and methods of development to the human mind.

         The Empirical Sciences are those which are founded on the knowledge derived through the senses: they are developed by Generalization, Classification, and Inductive Reasoning. Geography, Biology, and Physics are examples of the empirical sciences. The facts of these sciences are given by Perception; these facts are classified by Generalization, and their laws and causes are derived by Induction.

         The Rational Sciences are those which are founded on the knowledge given by Intuition. They are developed by Deductive Reasoning. Arithmetic, Geometry, Logic, etc., are examples of the rational sciences. The fundamental ideas and axiomatic truths of these sciences are given by Intuition, and their derived truths are obtained by Deduction. A division of the Rational Sciences is often made, called the Formal Sciences. The Formal Sciences may be defined to be those sciences which treat of the necessary forms in which truth presents itself. They include Mathematics and Logic; Mathematics treating of the form in which quantity is presented, and Logic of the form in which thought presents itself.

         Another method divides scientific knowledge into two branches: the Inductive and the Deductive Sciences. The former include all those branches of knowledge which begin in facts and are developed by generalization and inductive reasoning; as geography, physics, etc. The latter include all those branches of knowledge which begin in ideas, and are developed by the process of deductive reasoning; as arithmetic, geometry, etc. 

         Classification of Knowledge for Purposes of Education. Knowledge may be classified into seven principal divisions, with respect to the matter of which they are composed: 1) Language, 2) Mathematics, 3) Physical Sciences, 4) History, 5) The Arts, 6) Psychology, 7) Philosophy.

         These general branches and their subdivisions are not always entirely distinct from one another. They often overlap one another and intrude upon one another's territory. It is impossible to draw a line, in every case, marking just where one branch ends and another begins. This is true with respect to every classification that has been attempted.

         Language. Language is the instrument of thought and the medium of expression. The term is derived from lingua, the tongue. Primarily, Language is the means of communicating knowledge: it enables one mind to transfer its thought to another mind. It is also found that language is the means by which we think, as well as the medium by which we communicate our thoughts. We cannot think to any great extent, if at all, without language; and the more perfect our language the more powerful our thoughts -as in algebra, arithmetic, etc. We therefore embrace these two uses of language in our definition, and define it to be the instrument of thought and the medium of expression.

         Mathematics. Mathematics is the science of Quantity. The term is derived from mathematike, meaning science. It investigates the relations of quantity, and unfolds the truths and principles belonging to it. It is based on intuitive ideas and truths, and developed by deductive reasoning. The three principal branches are Arithmetic, Geometry, and Algebra. Arithmetic is the science of Number; Geometry is the science of Space; Algebra is a general method of investigating all kinds of quantity by means of symbols.

         Physical Sciences. Physical Sciences are the sciences of the material world. The term is derived from phusis, nature. They consist of facts and phenomena, and the laws and principles which control them. They begin with the observation of facts, compare and classify them, and ascertain the causes which give rise to them and the laws which control them.

         The principal branches of Physical Sciences are  Physics, Chemistry, Biology (including Natural History of two of the three kingdoms of nature, the vegetable and the animal kingdoms), Geography, Geology (including Natural History of the third kingdom of nature, the mineral kingdom), and Astronomy.

         Physics treats of the facts and phenomena of nature. Its object is to ascertain these facts and phenomena, and to discover the causes which produce them and the laws which govern them. Its primary branches are Mechanics, Optics, Acoustics, and Electrics.

         Chemistry treats of the nature and properties of the elements of bodies. It differs from Physics in that the former considers the general laws of matter in the forms in which it presents itself, while Chemistry considers the elements out of which matter is composed, and explains the changes that occur in bodies through the operation of these elements. Its object is to ascertain the composition of material things, and to explain the method of their formation.

         Biology is the science which treats of life, or living matter. It seeks to ascertain the facts and understand the laws of the life principle found in matter, and endeavors to explain the complicated phenomena of living beings. It rises above the other natural sciences in that it treats not only of matter, but of organized matter; it considers not merely force, but that life force which holds matter in its hand, and shapes it into the organic beings of the vegetable and animal world.

         Geography treats of the facts relating to the surface of the earth, classifies them, and investigates their causes and the laws which govern them.

         Astronomy treats of the facts and truths relating to the heavenly bodies. It is closely related to Physics, differing mainly in the subject matter of its investigations. It explains the appearances, changes, motions, etc., of the heavenly bodies, calculates their size and distance, investigates their composition, structure, etc.

         Geology treats of the origin, development, and structure of the earth.

         Elements of Physical Sciences. The several elements of the Physical Sciences are Facts and Phenomena, Systems of Classification, Causes of Facts and Phenomena, Laws governing Facts and Phenomena, and Truths growing out of them. The object of the inquirer in these sciences is to attain these elements.

         Facts and Phenomena. The primary elements of the Physical Sciences are Facts and Phenomena. A Fact is something that is or has been. It is a particular truth in the domain of sense. It is something seen or heard, or that was revealed through one of the senses. It is confined to the present or the past, and does not reach out to the future, as that is the sphere of a truth. Thus it is a fact that "the sun rose this morning," that "there was snow last winter," that water freezes at 32 degree above zero, etc. A Phenomenon is literally an appearance; as the twinkling of a star, the changing of the moon, the rising of the tide, etc. The statement of a phenomenon in a proposition gives us a fact.

         Classifications. Several of the Physical Sciences aim especially at the classification of facts. In Natural History the principal elements are facts and their classification.

         Causes. The grand aim of the Physical Sciences is to ascertain the Causes of things. By a Cause is meant that which produces an event, or but for which some event would not occur. The great question of Physics is why; and the answer to this question gives us a large body of scientific truths. Thus, gravity explains why a stone falls, and also the planetary motions; the earth revolving on its axis explains the phenomena of day and night; elliptical orbits with the sun in a focus explain the changes of the heavenly bodies, etc. These causes are reached through hypothesis and theory.

         Laws. The second great aim of the Physical Sciences is to ascertain the Laws of physical phenomena. By Laws we mean the regular mode or order according to which something operates or events take place. This element is closely related to the inquiry for the Cause, but yet is different from it. Thus, gravity is the cause of a body falling, but it is a law that the force of gravity varies inversely as the square of the distance.

         Truths. A Truth of physical science is a statement of some established principle, or some inference derived from it. Truths embrace both laws and causes, the statement of a law or cause being a truth. The statement of any general proposition which has been verified, or any inference derived from it, is also a truth. Thus, heat expands all metals, or there will be a total eclipse of the sun during such a year, are also truths. The truths of physical science are mainly derived by inductive reasoning, and enable us to predict the future.

         Development of Physical Sciences. The Physical Sciences begin in the common observations of mankind. This common knowledge is, by the power of thought, gradually transformed into scientific knowledge. Through the operation of the natural laws of mental activity, the common knowledge of the race is constantly rising up into the higher and more perfect forms of science. The several elements that enter into their development are Observation and Experiment, Classification, Induction, Deduction, Hypothesis, and Theory.

         Observation. Observation has reference to the perception of nature as she presents herself to our view. By it facts and phenomena are presented to the mind through the senses, and are then retained in the memory for future use. In science, this observation needs to be careful and exact; mere looking or listening is not sufficient, we must look and listen with the eye of reason. Observation must be made with patience, and sources of error must be guarded against. It must also be analytic; facts and phenomena must be analyzed, things must be separated or broken up into fragments in order that the information may be minute and accurate. Man also invents instruments, as the microscope and telescope, to aid the senses in observation, and thus acquire facts which he could not otherwise obtain.

         Experiment. By Experiment, man puts nature into new relations to observe the results. He not only observes, but he prepares his facts for observation. Objects are placed in different relations and conditions, and the changes and results noted and compared. Nature is, as it were, put on the witness stand, and, by a series of cross questions, forced to reveal her secrets. This method of obtaining facts is largely used in Physics and Chemistry.

         Classification. As facts multiply, the mind compares them and perceives points of resemblance between them, and forms them into classes. The perception of the similarities and differences is an act of judgment; the separating of the common qualities to unite them into a general scheme is abstraction, and the forming of the general class idea is generalization. The arrangement of the objects themselves into classes is called classification. This process of classification is necessary in all the sciences; but it is especially prominent in Natural History.

         Induction. Induction lies at the basis of the truths of the Physical Sciences. Observation and Experiment give us the particular facts; Induction takes these facts and finds the laws which contain or control them. Thus from the facts that heat expands iron, zinc, copper, etc., we derive by Induction the general truth that heat expands all metals. It is this process of thought, so generally neglected by the ancients, and made so prominent in the Baconian system, that has given such rapid growth to the physical sciences during the last century.

         Deduction. The method of Deductive reasoning is also used in the Physical Sciences. Having reached a general conclusion by Induction, we apply this truth to new facts by a process of Deduction. Thus, if we discover a new metal, we immediately infer that heat will expand it, from the general principle that heat will expand all metals. The mathematician takes the doctrine of universal gravitation, puts it into an equation, and works out, in the solitude of his study, the position of a new planet; and the telescope, sweeping the field of the heavens, discovers the wanderer, and thus confirms in "the immortal predictions of science." It is thus true that "Induction discovers principles, while Deduction applies them;" or as physicist John Tyndall (1820-1893) observed, "In the study of Physics, induction and deduction are perpetually married to each other."

         Hypothesis. The Physical Sciences are aided in their development by Hypothesis. An Hypothesis is a supposition to account for facts and phenomena. The facts are presented through the senses, and the mind makes some supposition to account for them. Such suppositions, or hypotheses, have given us a large number of the truths of the physical sciences. Nearly all their great truths were once hypotheses. Johannes Kepler's (1571-1630) law of elliptical orbits was once a mere hypothesis; he made and rejected nineteen before he discovered the true one. Newton's theory of gravitation was at first only an hypothesis; and when verified became an accepted truth.

         Verification. Having formed our hypothesis, the next step is to prove it to be true. This is called its verification. To verify an hypothesis, it must be shown that it will account for all the known facts to which it relates. If facts are found that it will not account for, another supposition must be made, and so on until one is obtained that is correct. Great care, however, must be taken, not to accept an hypothesis as true until the facts are so numerous that there can be no doubt of its verification. "To try wrong guesses" said philosopher and science historian William Whewell (1794-1866), "is, with most persons, the only way to hit upon right ones."

         Origin of Hypotheses. The hypotheses of science originate by what is called anticipation. Anticipation is the presaging of a truth before there is evidence to prove it. By the power of anticipation the mind leaps from a few facts to the law which governs them. All hypotheses are the result of what Pierre Simone Laplace (1749-1827) calls "a great guess," or of what Plato so beautifully designates as "a sacred suspicion of truth." The forming of hypotheses requires a suggestive mind, a lively fancy, a philosophic imagination, that catches a glimpse of the idea through the form, or sees the law standing behind the fact.

         Theory. The Physical Sciences are largely made up of Theories. A Theory is an accepted explanation of facts and phenomena. It may also be defined as a verified hypothesis. When an hypothesis is shown to explain all the facts that are known, these facts being varied and extensive, it is said to be verified, and becomes a theory. Thus we have the theory of universal gravitation, the Copernican theory of the solar system, the present theory of atoms, etc., all of which were originally mere hypotheses.

         Value of Physical Sciences.

         1. Study of the physical sciences gives culture to the perceptive powers. The physical sciences begin in the observation of the facts of the external world. The proper study of these sciences requires the pupil to observe these facts closely and accurately. They thus call the perceptive powers into constant and forcible activity; quicken and strengthen the power of the senses, and make the student sharp-eyed and accurate in his observation of things. 

         2. The study of the physical sciences gives culture to the power of classification. The facts of the material world are found in classes, and the natural sciences embrace the classification of the facts, as well as the facts themselves. These classifications, in several of the branches, are the most perfect that can be found in science. The arrangement into species, genera, orders, and kingdoms, as in botany, zoology, etc., has no counterpart in the other sciences. The natural sciences, therefore, transcend all others in affording cultivation to generalization and classification. They, above all other sciences, tend to train the mind to the habit of the systematic and orderly arrangement of knowledge.

         3. The study of the physical sciences cultivates the power of inductive reasoning. All the primary truths of these sciences are derived by induction. In their study we are constantly passing from particular facts to the general laws of which they are examples. In no other sciences is the use of induction anything like so prominent. Though some of these sciences may rise into a deductive stage, yet the entire spirit of these branches is inductive. Induction is the genius which presides over their origin and development. The mind of the student is thus constantly occupied in inferring general laws from particular facts, and acquires the habit of reasoning in this way. The importance of such culture is seen in the fact that this is the kind of reasoning that we use in the questions that meet us in the ordinary duties of life.

         4. The study of the physical sciences tends to modify the dogmatic spirit cultivated by the deductive sciences. The study of the deductive sciences tends to make the mind overbearing and dogmatic. The pure mathematician may be as stubborn as a mule, in his belief. Accustomed to see certain conclusions flow from admitted premises, he may be intolerant of any opposition to his opinions when he deals with social and political questions. Natural science, leading the mind by the path of inductive thought, accustoms it to see how easy it is to be mistaken in an inference, and makes it cautious in its conclusions, and tolerant of doubt. The fact that the pathway of the physical sciences is strewn with the remains of discarded theories, is sufficient to cultivate a spirit of prudence.  5. The physical sciences have contributed to the development of the material interests of mankind. They have done much to lift man up out of a condition of barbarism and ignorance. They have given him machinery by which he can multiply his strength and skill, and do that which his unaided powers could never accomplish.

         History. History is a systematic description of the past acts and conditions of mankind. It embraces the Facts of History and the Philosophy of History. The Facts of History embrace the events that have occurred in the life of individuals and nations. The Philosophy of History endeavors to ascertain the causes which have contributed to produce the different changes in society and nations, and thus to predict the future condition of the human race. In other words, it endeavors "to solve the problem of man's condition and destiny."

         Art. Art is the application of knowledge or power to effect some desired object. It is the outgrowth of practice, and may be defined as practice guided by principle. The arts are divided into two general classes; the Fine Arts and the Useful Arts. The object of the Useful Arts is the attainment of the end of utility; the object of the Fine Arts is the attainment of the end of beauty. These two, though primarily distinguished, are often combined in the same production; as in the manufacture of glass and pottery ware, in architecture, engraving, etc.

         Psychology. Psychology is the science of the human mind. The term is derived from psyche, the soul, and logos, a discourse. According to the methods of attaining to the facts and principles of the science, it is sometimes divided into Empirical Psychology and Rational Psychology. Empirical Psychology treats of the nature of the mind as revealed in the experience of consciousness. Rational Psychology treats of the nature of the mind as determined by the necessary principles given by reasoning.

         Philosophy. Philosophy is the science that studies the fundamental aspects of the nature of existence. Unlike special sciences, which deal only with particular aspects, philosophy deals with those aspects of the universe which pertain to everything that exists. Its purpose is to provide man with a comprehensive view of life.