This dissertation describes a systematic investigation of university student and K-12 teacher reasoning about key ideas relevant to the development of a particulate model for matter. Written assessments and individual demonstration interviews have been used to study the reasoning of introductory and sophomore-level physics students, introductory chemistry students, and pre- and inservice K-12 teachers. In general, the questions sought to probe the extent to which the underlying discreteness of matter is manifest in student and teacher responses as well as the degree to which students and teachers use the particulate nature of matter to explain and predict physical phenomena. A variety of specific incorrect reasoning and response patterns have been identified. The results of our research have been used to guide the development of curriculum for use in special courses for pre- and inservice K-12 teachers. [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://www.proquest.com/en-US/products/dissertations/individuals.shtml.]