This dissertation describes the teaching methods and educational philosophies of natural philosophy instructors at several of the colleges in colonial and early national North America. It finds two distinct approaches: the demonstrative, in which the instructor centers the course on visually engaging lecture-demonstrations, and the catechetical, in which the course objective is to master a set of facts and definitions through memorization and repetition. The roots of the demonstrative approach lay in the culture of public lecture-demonstrations that emerged in western Europe during the Scientific Revolution and Enlightenment. The catechism, while having a much longer history as a religious teaching tool, gained new currency in the period through the concern for moral education. Ultimately, both approaches were intimately tied to European Enlightenment ideas about the place of science in the public sphere and the means by which the human mind learns new information. Individual schools, and even individual instructors, had great discretion in choosing which approach, or combination of approaches, to use. Instructors could present lecture-demonstrations as part of the social training of students, who as citizens would be expected to attend lectures and participate in scientifically-informed discussion. Catechetical lessons, however, would be more useful to instructors who favored keeping natural philosophy similar in appearance to other subjects. The catechism, with its systematic presentation and familiar format, was more readily adapted to examinations. Two instructors in particular--William Smith and John Ewing, both at the University of Pennsylvania--serve as exemplars of the demonstrative and catechetical methods, respectively. The recognition of these two approaches, and the larger recognition of the prominence of natural philosophy in the North American curriculum, has implications for the received narratives of both early American science and early American education. For the former, this work promotes the interconnectedness of American scientific approaches and methods with the corresponding institutions in Europe. For the latter, it emphasizes the extent to which American colleges were not merely imitations of their European counterparts, but rather sought to meet the local needs that the instructors perceived. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]