LECTURE VII.

ON

GEOMETRY AND ALGEBRA,

AS

ELEMENTARY BRANCHES OF EDUCATION.

BY F. J. GRUND.

SCIENCE and arts are useful, only in proportion as they contribute to our happiness, either by providing the means of our physical comfort, or by ennobling human nature and increasing the number and intensity of our intellectual enjoyments. Education is the appropriate means of securing these. I shall be justified, therefore, when, in speaking of the two principal branches of mathematical knowledge, algebra and geometry, I first dwell on the general purposes of education, in order to determine the rank which mathematical sciences ought to hold in early instruction, and the bearing which they have on the developement of intellect, and the formation of character.

Education has, at all times, held a distinguished place among the acknowledged interests of civilized nations. It has been successively the subject of thought and research with the most eminent philosophers of antiquity. Statesmen and reformers of empires have bestowed upon it their utmost cares, and

legislators secured and perpetuated its progress by laws. We have seen it keep pace with the political developement of nations; here cramped, chilled, and oppressed, by tyranny and despotism, bearing all the marks and deformities of a gothic age; whilst, on the other hand, we have seen it share and extend the blessings of liberal governments. But education is not only a national cause; it is the cause of humanity, of mankind; the continuance and progress of civilization depend upon it. No one can be indifferent as to its advancement; for there is none, who is not, at least indirectly, interested in its

success.

The truth of these remarks has at no period been felt more strongly than in this; at no time has the call for improvements in education been so general. The increased number of literary institutions in England, France, and Germany, the introduction of Sabbath schools, the number of periodicals, solely devoted to the purposes of education, the efforts of philanthropic societies in almost every part of the civilized world, the patient labors of Badesow, Resewitz, Campe, Salzman, Olivier, Schulz, and Pestalozzi, bear ample testimony to this assertion. Yet there is no country, and perhaps no community, in which this demand for popular education is so loud, so unanimous, as in this; because there is none, whose political welfare, nay, whose very existence, is so intimately connected with its progress. The system of free schools throughout this State, the institution of the Latin and High Schools in this city, the Mechanics' Institute, the Society for the Promotion of Useful Knowledge, finally, the formation of Lyceums in almost every part of the New-England States, are strong proofs of the vigilance of the people, as to moral and intellectual improvement.

Much, however, is yet left to be done, and great caution is to be used, lest the general call for popular and practical instruction, should defeat its very object.

In the minds of perhaps the majority of persons, education still consists in the acquiring of certain facilties for particular

purposes in life. But this does not deserve the name of education. A system of instruction adapted merely to this purpose, enslaves and degrades human nature. It reduces men to machines, by bringing up workmen for a manufactory. Let us, for a moment, consider the errors into which it leads. The mind of the child is considered a mere receptacle, which is to be stored with knowledge. Its pliability is abused into a mechanical and spiritless routine. Neither the individuality nor the peculiar structure of his mind, not even his age, is taken into consideration. His mental faculties are not roused to action; the mind does not operate upon itself; for, in receiving knowledge, the pupil is merely passive. Principles are pronounced dogmatically, and are heaped upon each other without plan or system. Children the most unlike in capacity, are put together in the same class, and have to learn, each day, a fixed portion of one science or another; and the test of their acquirements is a verbal recitation from a book. The memory is charged with the crudest and most heterogeneous conceptions, without allowing the mind the least respite to assort and adjust them, much less the time which it needs to reflect upon them, in order to convert them into part of its own substance. Thus, from the first moment the boy goes to school, until the young man leaves college, he is harassed and haunted with the variety and unreasonable number of studies he is obliged to pursue, without spirit or inclination; and it is indeed a wonder if his mental powers are not in this way prostrated or destroyed.

A bounteous Providence seems to bestow the same parental care upon the preservation of intellect, which it does upon the continuance of certain species in the animal and vegetable kingdoms, where, notwithstanding the ravages of those who feed upon them, and the devastations committed by the fury of the elements, the prodigious number of seeds prevents the race from becoming extinct.

Many men can trace the developement of their minds to the time they left college, or the hot vapor baths of inferior in

stitutions of learning. This is the period of the emancipation of their minds. They are now for the first time, perhaps, permitted to look round, and view calmly the immense territory of science, which lies as yet unexplored before them. They are now allowed to take their own standing, and to strike out a plan for their self-education. Many a happy thought that lay dormant, or was oppressed by the burthen of other studies, for which the student had neither taste nor talent, quickens now into life. One idea gives birth to another. They soon accumulate, and give the mind a tenor which lasts through life; and it is not unfrequent to see men acquire more information from one year's self-discipline, than from all the instruction. they had in schools. Men whose talents, while at school, were considered little above mediocrity, when circumstances call forth their energies, develope, sometimes, powers of mind, which confound those who are acquainted with them, and of which they themselves were unconscious, because they were degraded in their own estimation, and the mechanism of their education, leaving no room for individual efforts, gave them no stimulus to mental action.

Is, then, the object of education to leave to circumstances to raise the edifice of which the corner-stone ought to be laid in early childhood? How many adults can command the leisure which is necessary for a course of thorough self-discipline? Most young men, immediately after leaving school or college, emerge into active life; their minds are engrossed with business; their thoughts become rivetted on interest and gain, as the means of procuring to them physical comfort, the want of which is, in all countries, and at all times, felt more strongly than that of intellectual riches. Physical wants have an immediate bearing upon our own happiness, and impair that of those who depend upon us. They are therefore more pressing, and not so likely to be lost sight of, as the culture of our minds. Are we, then, to leave to men to atone for the faults of their early education? Is it to be left to the man of business to root out the excrescences and to correct the