The Goals of the Mathematics Major/Minor at William and Mary ============================================================ INTRODUCTION ============ As a first step in the decennial re-accreditation process (to occur in 2006), the department must submit to the dean and EPC a statement that describes: A. The goals of the mathematics major in terms of graduating students' knowledge and abilities; B. For each goal in (A), a listing of courses where students would learn whatever is needed to accomplish the goal; C. For each goal in (A), a description of what the department will do (presumably in the next round of assessment) to determine whether our students are achieving the goals that we set for them. That statement is due by June 15. It is clear from conversations in various faculty committees that flippant responses will not be accepted. We have three separate tracks within our major (standard track, applied track, and teaching track) and UCC proposes that we offer a separate response for each track. What appears below are the proposed responses prepared by UCC. Please review and comment on them, sending your ideas to David Lutzer by e-mail or by hard copy by June 1. ========================================================================== THE STANDARD TRACK ================== A. Goals of the standard track 1. Students will learn to read, understand, compose, and write mathematical arguments. 2. Students will have a firm basis in the elementary theory of real analysis and abstract algebra. 3. Students will have a great degree of flexibility in choosing upper division courses based upon their own interests. 4. Students will be prepared for post-bachelors employment and for graduate school in mathematical sciences. 5. Students will show proficiency in computing (at the level of CS 141). B. Where do students learn what they need to meet these goals? ** for goal A1) Math 214, 307, 311, and 490 (or in 495-6). ** for goal A2) Math 214, 307, and 311 ** for goal A3) the department's upper division course offerings ** for goal A4) the entire standard track curriculum ** for goal A5) CS 141. C. How will we show that students have met the goals? ** for goal A1) Collect and evaluate student papers from Math 214, 307, 311 and 490; review honors theses completed for Math 495-6. ** for goal A2) Collect and evaluate students papers from Math 307 and 311. ** for goal A3) Review student transcripts. ** for goal A4) By surveying our alumni to ask them if they were prepared for bachelors-level employment or graduate school. ** for goal A5) Review mathematics concentrators' grades in CS 141. ====================================================================== THE APPLIED TRACK ================= A. Goals for the Applied Track: 1) Students will learn to read, understand, compose, and write mathematical arguments. 2) Students will have exposure to a broad spectrum of mathematical and/or statistical topics that have significant applications in other disciplines. 3) Students will develop significant depth in at least one of Computational Mathematics; Probability & Statistics; Operations Research; or Classical Applied Mathematics. 4) Students will study examples of serious applications of mathematics or statistics to disciplines outside of the mathematical sciences. 5) Students will be prepared for post-baccalaureate employment in the mathematical sciences or for graduate school in the mathematical sciences. 6) Students will demonstrate proficiency in computing (at the level of CS 241). B. Where do students learn what they need to meet these goals? ** for goal A1) Math 214 and (either M307 or M311) ** for goal A2) by taking at least one course in three of the four focus areas Computational Mathematics; Probability and Statistics; Operations Research; or Classical Scientific Applications. ** for goal A3) By taking three courses in one of the four focus areas mentioned in answer (2). ** for goal A4) The precise course content of our courses varies from one semester to another. However, each of the courses listed in the applied focus areas will include examples of serious applications to other disciplines, business, or science. ** for goal A5) Each course in the program prepares students to meet goal A5. ** for goal A6) CS 241. C. How will we show that students have met the goals? ** for goal A1) Collect and evaluate student papers from Math 214, 307, and 311. ** for goal A2) Review student transcripts ** for goal A3) Review student transcripts ** for goal A4) Collect and review course syllabi and student course work. ** for goal A5) Survey alumni from the applied track to ask them if they were prepared for what they encountered in applied employment or graduate school. ** for goal A6) Review mathematics concentrators' grades in CS 141 and 241. ====================================================================== Goals of the Teaching Track ================================ 1. Students will learn to read, understand, construct and write mathematical arguments; 2. Students will fulfill Virginia's certification requirements; 3. Students will take the course needed to study mathematics courses that prepare them for advanced-level teaching in high school mathematics and statistics; 4. Students will study a family of applications of mathematics (including applications in science and business) that can be used to show high school students the real world utility of mathematics; 5. Students will study a general history of mathematics in order to gain some appreciation for the long-term development of the discipline; 6. Students will demonstrate proficiency in computing (at the level of CS141). B. Where do our students learn what they need in order to meet these goals? **for goal A1) Math 214, Math 307, and Math 490. **for goal A2) Math 307, Math 308, Math 412, and Math 416. **for goal A3) Calculus courses, CS 141, Math 211, Math 302, Math 308 **for goal A4) Calculus courses, Math 302, 308, 323, 490. **for goal A5) primarily Math 490 (for teachers) but also other required courses (to a much lesser degree). **for goal A6) CS141. C. How will we know if we have succeeded? ** for goal A1) Collect and evaluate student papers from Math 214, 307 and 490(for teachers), and interview recent instructors in Math 490 (teachers) ** for goal A2) Determine what percentage of students in the pre-college teaching track are approved for Virginia certification; ** for goal A3) Survey teaching-track alumni after they have been teaching ** for goal A4) Survey teaching-track alumni after they have been teaching for several years. ** for goal A5) Collect and review historical reports from Math 490(teachers) ** for goal A6) Review mathematics concentrators' grades in CS141. =================================================================== The Mathematics Minor: ===================== A. Goals A-1) Students will learn the basic 100 and 200 level college mathematics. A-2) Students will sample upper division mathematics B. Where will students learn the material associated with the goals in (A) B-1) Math 111,112,211, 212 and/or 214 B-2) Any mathematics course numbered above 300 C. How will we assess student learning associated with the goals in (A) C-1) Review a sample of final examinations in 100-200 level courses C-2) Review grades achieved by mathematics minors in the 300-level mathematics courses that they choose.