Before the 1850’s, the United States had a number of small colleges, most of them dating from colonial days. They were small, church connected institutions whose primary concern was to shape the moral character of their students.

Throughout Europe, institutions of higher learning had developed, bearing the ancient name of university. In German university was concerned primarily with creating and spreading knowledge, not morals. Between mid-century and the end of the 1800’s, more than nine thousand young Americans, dissatisfied with their training at home, went to Germany for advanced study. Some of them return to become presidents of venerable colleges-----Harvard, Yale, Columbia ---and transform them into modern universities. The new presidents broke all ties with the churches and brought in a new kind of faculty. Professors were hired for their knowledge of a subject, not because they were of the proper faith and had a strong arm for disciplining students. The new principle was that a university was to create knowledge as well as pass it on, and this called for a faculty composed of teacher-scholars. Drilling and learning by rote were replaced by the German method of lecturing, in which the professor’s own research was presented in class. Graduate training leading to the Ph.D., an ancient German degree signifying the highest level of advanced scholarly attainment, was introduced. With the establishment of the seminar system, graduate student learned to question, analyze, and conduct their own research.

At the same time, the new university greatly expanded in size and course offerings, breaking completely out of the old, constricted curriculum of mathematics, classics, rhetoric, and music. The president of Harvard pioneered the elective system, by which students were able to choose their own course of study. The notion of major fields of study emerged. The new goal was to make the university relevant to the real pursuits of the world. Paying close heed to the practical needs of society, the new universities trained men and women to work at its tasks, with engineering students being the most characteristic of the new regime. Students were also trained as economists, architects, agriculturalists, social welfare workers, and teachers.

children’s numerical skills

people appear to born to compute. The numerical skills of children develop so early and so inexorably that it is easy to imagine an internal clock of mathematical maturity guiding their growth. Not long after learning to walk and talk, they can set the table with impress accuracy---one knife, one spoon, one fork, for each of the five chairs. Soon they are capable of nothing that they have placed five knives, spoons and forks on the table and, a bit later, that this amounts to fifteen pieces of silverware. Having thus mastered addition, they move on to subtraction. It seems almost reasonable to expect that if a child were secluded on a desert island at birth and retrieved seven years later, he or she could enter a second enter a second-grade mathematics class without any serious problems of intellectual adjustment.

Of course, the truth is not so simple. This century, the work of cognitive psychologists has illuminated the subtle forms of daily learning on which intellectual progress depends. Children were observed as they slowly grasped-----or, as the case might be, bumped into-----concepts that adults take for quantity is unchanged as water pours from a short glass into a tall thin one. Psychologists have since demonstrated that young children, asked to count the pencils in a pile, readily report the number of blue or red pencils, but must be coaxed into finding the total. Such studies have suggested that the rudiments of mathematics are mastered gradually, and with effort. They have also suggested that the very concept of abstract numbers------the idea of a oneness,

a twoness , a threeness that applies to any class of objects and is a prerequisite for doing anything more mathematically demanding than setting a table-----is itself far from innate

The Historical Significance of American Revolution

The ways of history are so intricate and the motivations of human actions so complex that it is always hazardous to attempt to represent events covering a number of years, a multiplicity of persons, and distant localities as the expression of one intellectual or social movement; yet the historical process which culminated in the ascent of Thomas Jefferson to the presidency can be regarded as the outstanding example not only of the birth of a new way of life but of nationalism as a new way of life. The American Revolution represents the link between the seventeenth century, in which modern England became conscious of itself, and the awakening of modern Europe at the end of the eighteenth century. It may seem strange that the march of history should have had to cross the Atlantic Ocean, but only in the North American colonies could a struggle for civic liberty lead also to the foundation of a new nation. Here, in the popular rising against a “tyrannical” government, the fruits were more than the securing of a freer constitution. They included the growth of a nation born in liberty by the will of the people, not from the roots of common descent, a geographic entity, or the ambitions of king or dynasty. With the American nation, for the first time, a nation was born, not in the dim past of history but before the eyes of the whole world.