An innovative, conceptually based instructional model for teaching large undergraduate astronomy courses was designed, implemented, and evaluated in the Fall 1995 semester. This model was based on cognitive and educational theories of knowledge and, we believe, is applicable to other large postsecondary science courses. Major components were: (a) identification of the basic important concepts and their interrelationships that are necessary for connected understanding of astronomy in novice students; (b) use of these concepts and their interrelationships throughout the design, implementation, and evaluation stages of the model; (c) identification of students' prior knowledge and misconceptions; and (d) implementation of varied instructional strategies targeted toward encouraging conceptual understanding in students (i.e., instructional concept maps, cooperative small group work, homework assignments stressing concept application, and a conceptually based student assessment system). Evaluation included the development and use of three measures of conceptual understanding and one of attitudes toward studying astronomy. Over the semester, students showed very large increases in their understanding as assessed by a conceptually based multiple-choice measure of misconceptions, a select-and-fill-in concept map measure, and a relatedness-ratings measure. Attitudes, which were slightly positive before the course, changed slightly in a less favorable direction.