## Educational Mathematics Ph.D.

## Degree Requirements - 71 Credits

See:"Educational Mathematics Ph.D."

## Master's Degree en route to the Ph.D.

Students may apply for admission to the Ph.D. in Educational Mathematics and complete their M.A. in Mathematics with either a Liberal Arts Emphasis or Teaching Emphasis on the way to completion of the doctoral program. Once admitted, the student will work closely with their academic advisor to develop a Plan of Study that meets both M.A. and Ph.D. program requirements. Students must complete all program requirements for the M.A. in addition to the hours required for the Ph.D. Students must be conferred with the M.A. degree prior to admission to doctoral candidacy.

## Ph.D. Requirements

## Content Core - 27 semester hours

A. Required Courses - 12 hours

MATH 609 Abstract Algebra I (3)

MATH 623 Abstract Algebra II (3)

MATH 632 Complex Variables (3)

B. Minimum of 15 hours chosen from the following courses:

MATH 622 Directed Studies (1-4)

MATH 633 Geometric Analysis (3)

MATH 644 Differential Geometry (3)

MATH 664 Difference Equations and Chaos (3)

MATH 678 Mathematical Logic (3)

MATH 727 Representation Theory (3)

MATH 728 Topics in Discrete Mathematics (3)

At most, two courses may be included from the following: (The two courses may both come from Category I but at most one course can be from Category II.)

Category I

MATH 532 Basic Analysis II (4)

MATH 540 Introduction to Topology (3)

Category II

MATH 528 Discrete Mathematics (3)

MATH 529 Mathematical Problem Solving (3)

MATH 560 Introductory Complex Variables (3)

## Educational Core - 10 hours (minimum)

A. Required Courses (4 hours)

MED 703 Teaching and Learning K-12 Mathematics (3)

MED 710 Seminar in Post-Secondary Mathematics Teaching (1)

B. Elective Courses (6 hours) (Advisor must approve courses)

MED 622 Directed Studies (1-3)

MED 630 Technology in Mathematics Education (2)

MED 673 Teaching and Learning Mathematics on the Elementary Level (3)

MED 674 Teaching and Learning Mathematics on the Secondary Level (3)

MED 675 Teaching and Learning Mathematics on the Post-Secondary Level (3)

MED 678 Special Topics in Mathematics Education (1-3)

MED 750 History and Philosophy of Mathematics Education (3)

## Additional Electives - 6 hours

Electives in this category can include any approved 600 or 700 level courses or any two approved additional 500 level courses. Courses taken for one of the two research tools may be counted for these electives.

Credits to satisfy the first research tool count as elective hours for the 71 hour total; credits for the second research tool do not count in that total. A student must complete research tool "option A" and may select any one of the remaining three options.

## Research Core - 12 hours

MED 610 Survey of Research in Mathematics Education (3)

MED 700 Cognitive Processes in Mathematics (3)

MED 701 Educational Mathematics Research (3)

MED 702 Qualitative Research in Mathematics Education (3)

## Research Proposal/Dissertation - 16 hours

MATH 797 Doctoral Proposal Research (1-4) (Take 4 hours)

MATH 799 Doctoral Dissertation (1-12) (Take 12 hours)

## Research Tools

A. Applied Statistics and Research Methods

SRM 502 Applied Statistics (4) (or approved equivalent)

MED 701 Educational Mathematics Research (3)

SRM 608 Experimental Design (3) (or approved equivalent)

orSRM 610 Statistical Methods III (3)

Select One Additional Tool (0-3hours)

B. Qualitative Research Methods.Student's doctoral committee will approve a combination of coursework (including at least SRM 680 and MED 702) and experience (evaluated by the committee) to appropriately support the student's proposed dissertation research.

C. Collateral Field. Contact the departmental graduate coordinator for a detailed list of approved courses in cognition, instruction, measurement and evaluation, psychology and human development and curricula.

D.Computer Science. Student's doctoral committee will approve and evaluate a combination of advanced computer experience, proficiency and/or coursework only if relevant to the proposed dissertation research.

E. Foreign Language. Student's doctoral committee will approve and evaluate a combination of foreign language experience, proficiency and/or coursework only if relevant to the proposed dissertation research.Note(s): Electives must have the approval of the student's advisor and doctoral committee.

MED 701 may be used as a substitute for the Graduate School's SRM 700 requirement. MED 710 is normally taken the first semester of your program.

The department written comprehensive examination consists of two parts: mathematics and mathematics education. The mathematics portion of the comprehensive examination will consist of a four-hour examination over either: a) the Math 635, Math 632 sequence or b) the MATH 609, MATH 623 sequence. The mathematics education portion will consist of a four-hour examination over the material in the research core (MED 610, MED 700, MED 701 and MED 702) and a list of required readings. The oral examination will be given upon successful completion of the written examination and will cover the entire program of the candidate.

Students must receive a grade of "B" or better in both courses of the required mathematics sequence over which they do NOT take the comprehensive examination. A student who does not receive at least a "B" may, in lieu of repeating the course, elect to take an examination over that sequence.

A student in this program is required to write a scholarly dissertation. Dissertation topics may range from mathematics with pedagogical applications to topics in educational mathematics such as cognitive processes, educational reform and instructional issues.

joyce.hays@unco.edu |