This is a project-oriented course offering the opportunity to discover how a variety of real-world problems can be described and analyzed with the aid of simple mathematical models and computer simulations. Possible project topics include: operation of a fuse, spread of pollutants in a river, propagation of an infectious disease, traffic flow on a highway, oscillating chemical reactions, etc. Specific selection of problems will depend on the background and interests of students enrolled in the course. Students seeking elementary teacher certification or secondary certification in science or math are particularly welcome. The course incorporates constructivist principles and has been designated as an MCTP course for students in the Maryland Collaborative for Teacher Preparation program. Prerequisite: MATH 225.
Students who enroll in this course will generally be juniors who are declared majors in an undergraduate math or science program. (The teacher education programs at UMBC provide State-approved certification programs at all levels, but students must complete an academic major to be recommended by the Education Department for certification. Over 40 students in UMBC teacher education programs are currently math or science majors. The majority are seeking secondary certification.) If students have not yet had a course in differential equations (MATH 225 or equivalent), they may seek the permission of the instructor to enroll in the course. Such students will be interviewed at length to determine if they are qualified. Those with little or no math background are unlikely to receive permission. Not all students who enroll will be seeking teacher certification. However, this will not affect the manner in which the course is taught.
Suggestions of real-world modelling problems will be generated by the faculty course development team. However, students will not be limited to these problems and will be actively encouraged to seek alternatives though discussion among themselves, with the primary instructor and with members of the faculty team. The class will be asked to form into groups of two or more students to work on a problem. Students will be expected to work on at least two problems during the semester (i.e., each student will be a member of at least two modelling groups--individual person projects will be discouraged).
Each modelling project group will be asked to provide by the end of the semester a co-authored written project report describing the model, and each student will also write an individual account of his/her own experience with the two (or in rare cases, three?) projects on which he/she worked. An oral presentation from each group may also be included (perhaps in the context of progress reports) in order to stimulate general class discussion and to promote wider sharing of experience.
The primary instructor, Professor Seidman, has had prior experience in teaching an advanced course in modelling (organized similar to the one being proposed, but targeted primarily for math majors) and is thus a good choice to lead the proposed course. Major challenges for the course development team will be (in addition to providing suggestions of appropriate modelling problems) how to "guarantee" the application of contructivist principles in course delivery and how to assess student performance. We also anticipate a more heterogeneous mix of students than had been previously encountered, since in addition to math majors we will actively seek to enroll students from the basic science disciplines (e.g., chemistry, biology and physics) and perhaps also from computer science and engineering.