Jump to:

Admission Info

The Faculty

Recent Grads

Program Details

Admission

Applicants should possess a master's degree in mathematics or mathematics education. Those with a strong bachelor's degree in mathematics apply to the "Master's Degree en route to Ph.D." option. It is expected that students will have had a senior level or beginning graduate level course in each of abstract algebra, linear algebra, point-set topology, and real or complex analysis; applicants not having this background may be required to take additional courses to prepare for the coursework in the program. In addition to the online application -   http://www.unco.edu/grad/admissions/home.htm - applicants must provide an essay of approximately 500 words about personal  educational goals and specific interest in the University of Northern Colorado's Educational Mathematics Ph.D. program. See the Ph.D. program web page or email Dr. Dean Allison, dean.allison@unco.edu, Graduate Coordinator, for more information.

University of Northern Colorado
Department of Mathematical Sciences Faculty

Researchers in mathematics education guiding the program:

• Bill Blubaugh (Ph.D. Mathematics Education, U. of Colorado, Boulder): teacher preparation; technology in K-16 mathematics; mathematical problem solving.
• Michelle Chamberlin (Ph.D. Mathematics Education, Purdue University): collegiate preparation of prospective K-8 teachers; actor-oriented transfer; teacher professional development.
• Shandy Hauk (Ph.D. Mathematics, U. of California, Irvine): culturally responsive research, evaluation, and teaching; self-regulation; K-20 reasoning & proof; web-based homework.
• Robert Powers (Ed.D. Curriculum & Instruction, University of Houston): reform practices of prospective/novice teachers; use of handheld CAS for discrete mathematics teaching & learning.
• Hortensia Soto-Johnson (Ph.D. Educational Mathematics, University of Northern Colorado): practices of prospective/novice teachers; geomtery teaching & learning.

Mathematicians with interest and experience in mathematics education research who teach Ph.D. mathematics courses and participate on Ph.D. dissertation committees (sometimes as co-advisor):

• Dean Allison (Ph.D. Mathematics, U. of Missouri): Differential geometry; undergraduate curriculum reform in discrete mathematics, calculus, and differential equations.
• Ricardo Diaz (Ph.D. Mathematics, Princeton University): Applied partial differential equations.
• Richard Grassl (Ph.D. Mathematics, U. of New Mexico): Discrete mathematics; use of handheld CAS in undergraduate mathematics; reasoning & proof; mathematics competitions; cooperative learning.
• Steve Leth (Ph.D. Mathematics, U. of Colorado, Boulder): Nonstandard analysis; calculus reform; writing and undergraduate mathematics learning; K-8 mathematics enrichment activities.
• Nat Miller (Ph.D. Mathematics, Cornell University): Reasoning with geometric diagrams.
• Jodi Novak (Ph.D. Mathematics, Oklahoma State University): Representation theory and Lie groups; equity in mathematics education; teacher professional development.
• Terry Scott (Ph.D. Physics, U. of Wyoming): Object oriented programming; computer science education teaching, assessment, and curriculum design at the undergraduate level.
• Igor Szczyrba (Ph.D. Mathematics, Warsaw University): C*-algebras, quantum and elementary particle physics, biophysics, numerical analysis, educational mathematics.

Program Details

EDUCATIONAL MATHEMATICS, PH.D.
Degree Requirements - 70 Credits

Admission to the Ph.D. program requires a master's degree in mathematics or mathematics education.
Graduates of the program will be able to teach collegiate mathematics, perform research, and lead the national reform of K-16 mathematics education.

Master's Degree en route to the Ph.D.
Once admitted to the M.A. program, 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 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.

Mathematical Core - 26 semester hours
A. Required Courses - 14 hours

MATH 609 Abstract Algebra I (3)
MATH 623 Abstract Algebra II (3)
MATH 632 Complex Variables (3)
MATH 635 Real Analysis (3)
MATH 700 Advanced Seminar (2)

B. Minimum of 12 hours chosen from the following:

MATH 633 Geometric Analysis (3)
MATH 664 Difference Equations and Chaos (3)
MATH 678 Mathematical Logic (3)
MATH 691 Number Theory (3)
MATH 695 Special Topics (3)
MATH 727 Representation Theory (3)
MATH 728 Topics in Discrete Mathematics (3)
MATH 736 Real Analysis II (3)

At most, one of the following may be included:

MATH 525 Linear Algebra I (3)
MATH 528 Discrete Mathematics (3)
MATH 529 Mathematical Problem Solving (3)
MATH 540 Introduction to Topology (3)

Educational Core - 22 hours (minimum)

A. Required Courses - 16 hours

The content of the four courses MED 610, MED 700, MED 701 and MED 702 forms the main portion of the material for the mathematics education portion of the comprehensive examination.

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)

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

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

B. Elective Courses  - 6 hours

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 Topics in Mathematics Education (1-3)

MED 750 History and Philosophy of Mathematics Education (3)

Dissertation - 16 hours

MATH 797 Doctoral Research Proposal (4)
MATH 799 Doctoral Dissertation (12)

Additional Electives - 6 hours

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

Research Tools

Credits to satisfy the first research tool count as elective hours for the 70 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.

Required

A. Applied Statistics and Research Methods - 10 hours

SRM 502 Applied Statistics (4)

SRM 608 Experimental Design (3) or SRM 610 Statistical Methods III (3)

MED 701 Educational Mathematics Research (3)

Select One Additional Tool

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 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.

Notes:  The department written comprehensive examination, usually taken at the end of the second year in the Ph.D. program, consists of two parts: mathematics and mathematics education. The mathematics portion is 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 consists 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 is given upon successful completion of the written examination and covers 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. Expected completion time for the program: 4 to 5 years