is suggested on the supposition that the answers are not contained in the book; as, in ordinary cases, they should not be.

6. A review may be made very interesting and profitable by changing one of the numbers in each question, increasing or diminishing it by one or some other number. If the answer is given in the book, let the teacher change one of the conditions of the question, and then require the class to say what change will consequently be found in the answer. Let these estimates be written down, and then let them be tasked when the class comes up for recitation.

These are some of the ways in which, without the aid of a text book in higher Intellectual Arithmetic, much may be done to relieve pupils from their bondage to written figures, and place them on independent ground, which shall make their calculations resemble more the transactions of business in real life.

In proportion as the system shall prevail, which shall give its due prominence to the purely intellectual processes in arithmetic, will the studies of childhood and youth in this branch become the true foundation for the practice of mature years. The schoolroom will be linked more closely to the labors and studies of the stirring world around it; and its lessons and recitations will become, in a higher degree than they now are, the initiatory to the countingroom, the higher mathematics, to every occasion, in short, which shall call for the exhibition of knowledge, or the exercise of power in numbers.

LECTURE VI.

ON

COUNTY

TEACHERS' INSTITUTES,

BY SALEM TOWN,

THE subject assigned me for discussion, deserves an able investigation. The interests involved, and the benefits contemplated in carrying forward Teachers' Institutes to a successful issue, comprise the elements of an education more comprehensive and thorough, a wider and more general diffusion of knowledge. The means employed, are not confined to a stereotype routine of antiquated modes, nor the professed attainment of just such an amount of learning, by having committed to memory certain prescribed rules, but look forward to regular, annual advancements, and higher perfection in all those branches that characterize a well educated people.

Such are the prominent objects contemplated by Teachers' Institutes: and if those agencies now employed are judiciously directed, ultimate success is believed to be attainable.

With such improvements as experience shall from time to time suggest, I entertain no doubt these Institutes, so far at least as Common Schools are concerned, are destined to form a new era in educational matters. What has already been accomplished in the past is reliable evidence of what may be expected in the future.

Perhaps a brief statement of the origin of these voluntary associations would not be altogether out of place, prefatory to a more detailed account of their subsequent progress.

The suggestion was first made at a convention of Teachers in Tompkins County, in New York, and the question was, on the practicability of getting out any considerable number of them, to spend a few days together, in reviewing their studies, and devising ways and means by which the several schools in their own county could be improved. After much deliberation, some few individuals pledged their attendance at such a meeting, in case the call should be made. In April following, 1843, a circular was issued, and although the county is small, when the day arrived, just one hundred Teachers of Common Schools presented themselves prepared to engage in such exercises, and submit to such discipline, as should be required by a Board of Instruction provided for the occasion.

This, in all probability was the first self-created Teachers' Institute ever organized in this country, or elsewhere, for the specific exercises in which the members were to be engaged. Here, probably for the first time, was seen, what no man had before witnessed, one hundred practical Teachers, voluntarily convened from one county, in one place, not only for mutual improvement in the art of teaching, but with special reference to combined effort in behalf of all their schools, collectively and individually.

The sight was animating, and the occasion full of interest. It was an experiment. High expectations were entertained on the part of the members, and the most intense solicitude by the Board of Instruction. The results, if successful, were prospectively to reach, and improve the qualifications of something like seventeen thousand Teachers of our own State, and through them, impart higher degrees of moral and intellectual culture to the seven hundred thousand pupils, annually under their training.

These were considerations sufficient to awaken the deepest interest in all, and direct every mind in search of such expedients, and the adoption of such measures, as seemed best calculated to have the most direct bearing on all practical matters, involving the proper development of the intellectual powers and rightly forming the moral character. After mature deliberation, the same general course of exercises was then introduced which subsequent experience now sanctions and sustains. Such, in brief, was the origin of those voluntary associations in the State of New York, called Teachers' Institutes.