easy task. The exact psychological faculties to be addressed are often difficult to name-the subject-matter must be maintained in its integrity while it is manipulated into a system to suit the capacities of the mind taught. This latter point is all important, as it sometimes happens that the truths of science are sacrificed to error when they appear in Modes of Teaching. It often happens that systems, in their steps or degrees of advancement, do only scant justice to the mind to be taught, because they are too diffuse, too prolix, too narrow in their steps, or too inelastic. These faults of systems are grave ones, and show the teacher uninformed concerning Methods of Teaching. The subject-matter should be properly divided and subdivided, but never below the present attainments of the learner, for mind grows from reaching out after the unknown and the difficult, provided it be not clouded by discouragement in the pursuit. The subject-matter should be carefully freed from all that is not to be learned in that lesson-the steps to be presented should be those which are vital to the system of the subject taught. Too many words and points, and too much related subject-matter, distract the mind of the learner so that the real and vital points are only dimly apprehended. He is most fortunate in the classroom who sets forth, in sharp outline, just the maximum of subject-matter for his class-inspiring a zeal and determination for an increased power on the morrow's lesson.

212. Suppose that a teacher wishes to dis

cover the Method of Teaching children the process of Adding Numbers. How, in practice, shall he proceed?

1. Concerning the nature of the subject-mat

ter:

(a) Addition, being purely mathematical
in its nature, is incapable of being
presented by Object Teaching.
(6) Being capable of a hypothetical ap-
plication to material objects, it can be
taught by Illustrative Teaching.
(c) The numbers to be added together
are but so many forms for the aggre-
gate of many smaller parts, having no
logical connection.

(d) The subject-matter is represented by
certain characters called Figures,

which are arbitrary in their form, and have no logical connection with each other.

2. Concerning the faculties of mind that are primarily active in learning addition :

(a) The Perceptive faculties are required to note, intuitively, the individuals that are presented to them.

(b) Discrimination, or Comparison, distinguishes one individual in Consciousness from another.

(c) Memory in general, or, according to Hamilton, Retentiveness (or Memory), Recollection (or Reproduction), and Representation, preserves for future use the knowledge obtained

through Perception and Discrimina-
tion.

(d) The Power of Detecting Identity, or
the Power of Comparison, or the
Power of Thought, compares or iden-
tifies what may come within Conscious-
ness through Perception, with what
may come there through Memory.
(e) The Power of expressing Thought, or
Language.

3. Having discovered these principles, which are the Method of Teaching addition, he proceeds to invent his Mode of Teaching addition. This Mode may be by illustration, by telling, by questioning, and the like.

213. He regards these particular points: 1. To what degree of power are the faculties of these children grown? 2. Is this System of Addition philosophically constructed? 3. In what quantity of subject-matter shall the points of the system be set to these faculties? He may write out the complete lesson, as he proposes to present it. This is his Mode. He may then appear before the class to teach. His individuality, when presenting the subject-matter, exhibits his Manner.

The only guide possible for procedure in the case is the intelligence of the teacher, who now invents the Mode. If there be deficiency here, it will be no matter for surprise if the children are poorly taught.

When a System of subject-matter is arranged in detail in Modes of Teaching it, the arrange

ment is called Methodical. All methodical discussions for teaching must rest upon Methods of Teaching.

214. In the foregoing procedure, the discovering of the Method of Teaching-the process of discovering the faculties, and the nature of the subject-matter that is to be adjusted to them, comprised under (1) and (2)-is the conception of the Science of Teaching.

215. The Invention of the Mode of Teaching, together with the Manner of exhibiting it in practice, is the conception of the Art of Teaching.

216. The Investigation of the Science and the Art of Teaching constitutes the Conception of the Profession of Teaching.

III.

CONCLUDING REFLECTIONS.

217. Whatever qualifications of mind and person the teacher may have, he is still lacking in a most important element of success if he has not a quick apprehension of adopting means to ends. He must possess versatility of powers to discover Methods of Teaching, in order to invent Modes by which he shall incite to activity the pupil's mind with certainty. To do this, he needs a large stock of "That unacquired, unbought, untaught sagacity, which certain men have by nature," called Common Sense or good sense. (McCosh, Int. of Mind, p. 93, ed. 1870.) "Common Sense is the spontaneous action of right reason. (M. Bautain, Art of Ext. Speaking, ed. 1871.) This ability is needed nowhere more than in the school-room, and he who lacks it should diligently apply himself to cultivating his "good sense, "if he would attain eminence in the Profession of Teaching.

218. "An open-eyed and open-minded physician keeps adding to his knowledge and altering and widening his theories to the day of his death; there is not less to be learned in the world of mind-in the world of the school-room.