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## Ph.D. in Mathematics Education

**Departmental Requirements for Ph.D. in Mathematics:****Mathematics Education**

The Ph.D. degree with specialization in mathematics education is designed to prepare a student for a career where instruction in mathematics and research in mathematics education are of primary importance. It is especially intended for students with an interest in college teaching of mathematics.

**Credit requirements**: A total of 90 hours above the B.S. degree or 60 hours above the M.S. is required, including 15-24 credit hours for the Ph.D. dissertation.

**Core requirements**: All candidates for the Ph.D. with specialization in mathematics education are required to complete 24 credit hours of core courses. These must include three of the following seven options plus six credit hours from the other courses on this list. A minimum GPA of 3.0 must be maintained in core courses.

- Real Analysis I and II (MATH 5143 and 5153)
- Complex Analysis I and II (MATH 5283 and 5293)
- Algebra I and II (MATH 5613 and 5623)
- Geometric Topology (MATH 5313) and Algebraic Topology I (MATH 6323)
- Numerical Analysis for Differential Equations (MATH 5543) and Finite Element Methods (MATH 5563)
- Partial Differential Equations (MATH 5233) and Ordinary Differential Equations (MATH 5243)
- Probability Theory (STAT 5123) and Statistical Inference (STAT 5223)

**Additional courses**: All candidates are required to complete an additional 12 hours, namely, Introduction to Research in Mathematics Education (MATH 5913), Research in Undergraduate Mathematics Education (MATH 6923), and six hours from the following list: Theoretical Foundations of Inquiry (SCFD 6113), Qualitative Research I (SCFD 6123), Psychology of Learning (EPSY 5463), Statistical Methods in Education (REMS 5953).

Guidance about selecting further courses on research in education is available here.

Comprehensive exams: A Ph.D. student in mathematics education must select three of the areas from the core requirements listed above and for each must pass a comprehensive exam covering material in that area. The mathematics comprehensive exams are administered in January, May/June, and August. See the separate document covering timetables and requirements. A student who elects to take the exam over the statistics sequence must notify the Department of Statistics and take the exam when that department offers exams, which may not coincide with the time when mathematics exams are given. The exam in statistics is governed by that department's rules. Students who have passed two comprehensive exams may, with the approval of the student's advisor, substitute a minor thesis (as described below) for one of the comprehensive exams.

Minor thesis: The minor thesis must be a creative, written work of research or exposition on a topic of mathematical content. Further requirements are given in a separate document.

Language requirement: There is no foreign language requirement; however, it is expected that students in mathematics education exhibit a strong working ability in calculator and computer-assisted instruction, which is then documented in their professional development portfolio (see below).

**Professional development portfolio**: Students in mathematics education must prepare a professional development portfolio documenting professional activities in mathematics and mathematics education undertaken while a graduate student. This portfolio should contain a record of actual activities completed for future inclusion on the student's curriculum vitae. Required components of the professional development plan include active participation in the mathematics education seminar; attending and presenting at other workshops and conferences; attaining broad teaching experience in courses at different levels and with different modes of instruction, including the use of technology; documenting teaching quality with course syllabi and exams given, course evaluations, and letters of recommendation; and participating in a curriculum development project.

**Curriculum development project**: Every mathematics education candidate must participate in a curriculum development project under the supervision of a member of the faculty. A proposal for the curriculum development project should be developed within six months of passing the comprehensive exams and must be approved by the student's advisory committee.

Qualifying exam: The student must pass an oral qualifying exam over the area of specialization for the Ph.D. dissertation. This exam covers material on a reading list presented to the student by the advisory committee. Its purpose is to test the student's readiness to begin dissertation work.

Dissertation proposal: An outline of the proposed dissertation research must be presented to the student's advisory committee for approval.

Dissertation: A dissertation must be written according to Graduate College guidelines. The dissertation consists of an original research contribution in mathematics education. It must be prepared according to the style required of doctoral dissertations and defended.

Graduate College requirements: All requirements listed in the university catalog must be satisfied.