Programs and Courses

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Graduate Programs in Mathematics Education

Ph.D. Program


The goal of the Ph.D. degree program in Mathematics Education is to build on the educational, professional, and life experiences of each of its students so as to meet their needs, take into account their career goals, and graduate mathematics educators who are well versed and capable in the areas of scholarship, research, teaching, and professional service. Our graduates have accepted positions at major research universities across the country.

While students who apply for admission to the doctoral program typically have three years of full-time teaching experience at the elementary, middle, or high school levels. We welcome students who have not had these experiences, or who have non-traditional teaching experiences.


Past the master's degree, the student should expect typically to spend at least three years completing this program. The doctoral program for each student is jointly developed by the student and his or her major professor. Upon acceptance, students are assigned a faculty advisor.

The Ph.D. degree includes major and minor coursework, a Second-year Research Project, a preliminary exam addressing students' depth of knowledge, a dissertation proposal, a dissertation, and an oral defense. Each is described on this page.


During the first four semesters of doctoral study, most mathematics education graduate students take many of the same courses, which include:

      • C&I 810 (Goals, Content and Programs in Mathematics Education)
      • C&I 712 (Introduction to Curriculum & Instruction: Research and Resources)
      • C&I 675 (Research Methods in Mathematics and Science Education)
      • C&I 811 (The Instruction of Mathematics)
      • C&I 812 (Curricular Issues in Mathematics Education)
      • C&I 715 (Design of Research in Curriculum and Instruction)
      • Electives (including required courses in the doctoral minor or methods of research)​

Ph.D. Minor

Each doctoral student in Curriculum and Instruction is required to complete a minor. The minor may be in a single area outside of Curriculum and Instruction (Option A), or it may be a combined areas minor (Option B). The Option A minor consists of at least 10 graduate credits in a single department/major field of study. Among the Option A minors that have been chosen by doctoral students in mathematics education are: (a) mathematics, (b) educational policy, and (c) educational psychology. The Option B minor consists of at least 12 graduate credits in two or more departments not including. (See the Graduate Catalog for more details about the Option A and Option B minors.)

During the first year of doctoral study, most students take one course each semester in their minor as one of their elective courses. Doctoral students usually complete their minors during their second or third years of residence. Other elective courses outside of the minor frequently include:

    • Curriculum and Instruction courses in curriculum theory, instructional theory, qualitative research methods, educational technology, and teacher education/professional development.
    • Educational Psychology courses in child development and quantitative research methods. Two highly recommended electives are (1) Ed Psych 760 (Statistical Methods Applied to Education I, 3 credits) and (2) Ed Psych 761 (Statistical Methods Applied to Education II, 3 credits).
    • Mathematics courses
    • Statistics courses

For a listing of all courses offered by Curriculum and Instruction, go to listing of courses. Click the following links for listings of courses available from the departments of Educational PsychologyEducational Leadership and Policy AnalysisEducational Policy Studies, and Mathematics.

Second-year Project

The second-year project is an empirical study in which the student plans a small-scale study, collects and analyzes the data, and reports the results. The project consists of two components:

    1. 25-35 page paper about the study (including its significance, a review of relevant literature, description of methods, discussion of results, and conclusions)
    2. 20-30 minute presentation about the project to UW-Madison math-ed community

The primary purpose of the second-year project is to give students experience with planning and conducting a study before they reach the dissertation stage. In some cases, the project may serve as a pilot study for a student’s dissertation, but it doesn’t have to fulfill that purpose. It will, however, give students experience with designing a study, collecting data, analyzing data, developing research questions, and so forth before they embark upon the higher-stakes dissertation study.

Preliminary Examination

Later in their doctoral study (usually within a year of completing the Second-year Project) students take a Preliminary Examination. To be eligible for the Preliminary Examination, the student must have successfully completed the Second-year Project.

The Preliminary Examination for the Ph.D. degree provides evidence that the student is able to address a problem or question in curriculum and instruction by drawing on relevant literatures, theories, and methodologies. The examination is tailored to the individual preparation and experience of the student. ​It provides the student a vehicle for synthesizing and interpreting what has been learned and for preparing for the research work to come.

Dissertator Status

Upon successful completion of the Preliminary Examination, a student achieves dissertator status. In addition to passing the preliminary exam, a student seeking dissertator status also must have completed the minor, have no outstanding incomplete course work, and fulfill other requirements of the Graduate School and Department. Dissertators generally take a reduced course load and begin work on their dissertations.

Dissertation Proposal

In order for a student to complete the Ph.D. degree, a faculty committee is appointed who read and approve a Dissertation Proposal. The student will typically defend the proposal to the committee, and once the proposal has been approved, the student conducts the study outlined in that document--the Dissertation.

Final Oral Examination

Once a student has completed her or his dissertation, the Final Oral Examination is taken. This is an oral examination and is one in which the student "defends" her or his dissertation to a faculty committee consisting of five persons. Three of the faculty members on this committee also serve a members of the student's Reading Committee. One member of the final examination committee must be a member of the faculty of the department in which the student completes her/his minor for the Ph.D. degree. When the student successfully completes the dissertation, he or she is awarded a Ph.D. degree by the University. The diploma indicates that the student has a Ph. D. degree in Curriculum and Instruction; the student's records also indicate that her/his specialty for the degree was Mathematics Education.

M.S. Program


The M.S. in Curriculum and Instruction prepares students for advanced work in education. The goals of the master's degree program are to 1) continue the professional development of practicing, licensed school mathematics teachers, and 2) enrich and to develop the scholarly and research knowledge of graduate students whose interests are or are allied with mathematics education. Students attain a master's degree for the purposes of updating their professional qualifications, developing specialized knowledge that will prepare them for leadership roles, or as preparation for further graduate work in mathematics education.


The master's degree includes 24 credits of graduate-level courses, a master's thesis or professional paper, and a comprehensive master's examination. Twelve of the 24 credits must be from courses taken in the Department of Curriculum and Instruction. Each student's program is planned by the student, in collaboration with his or her advisor, to take into account his or her professional and educational experiences, interests, and career goals.

Students must complete either a master's degree thesis or a professional paper. The thesis is composed of a research project conducted and analyzed by the student, while the paper can consist of a literature review of existing research on a particular topic, a theoretical piece, or an expanded version of a final project. Students who choose the thesis option undergo an oral examination on their topic, while students who choose the paper option take a written examination addressing issues and problems in curriculum, instruction, learning, and assessment in mathematics education.

Those interested in a master's degree in Curriculum & Instruction should visit the graduate school website for general information about the UW-Madison graduate programs. Visit the description of Curriculum & Instruction graduate programs for more information about financial aid, admission, courses, and criteria for satisfactory progress.


While no specific courses are required for the master's degree, most students in mathematics education take at least two of these three courses:

  • C&I 810 (Goals, Content and Programs in Mathematics Education)
  • C&I 811 (The Instruction of Mathematics)
  • C&I 812 (Curricular Issues in Mathematics Education)

12 of the 24 credits must be taken from within the Department of Curriculum and Instruction. For a listing of courses offered by the department, go to its listing of courses. Students frequently choose to take additional courses from the departments of Educational PsychologyEducational Leadership and Policy AnalysisEducational Policy Studies, orMathematics.

Representative Courses

C&I 708/EdPsych 708 The Study of Teaching
This course explores several research paradigms and programs in the study of teaching (e.g., process-product, expert-novice, teacher cognition) as well as examines the influence of new views of learning (e.g., situated cognition, social cognition) on the process of learning to teach. Through course readings, discussions, presentations, and projects students examine: theoretical issues related to research on teaching and the process of learning to teach, including the assumptions underlying major research programs; various research designs and methods that have been used in the study of teaching; and major findings in research on teaching and learning to teach and the impact of these findings on educational practice, theory, research, and policy.

C&I 710 An Introduction to the Literature of Mathematics Education
This course serves as an introduction to current mathematics education thinking and practice in grades K-14. In particular, the course includes a focus on the development of mathematics education programs in the United States; current mathematics programs and recommendations for improvement and change; investigation of instructional strategies; and recent trends in student performance on national and international mathematics assessments.

C&I 810 Goals, Content, and Programs in Mathematics Education
This course focuses on scholarly research and thinking underlying the goals, content, and programs of school mathematics. The course examines the forces that have shaped recent reform efforts in mathematics education, from the perspective of history, of student performance on national and international studies, and of changes in the discipline of mathematics, in the concept of mathematical literacy, in the workplace, and in national demographics. The course considers questions such as the following: What is mathematics? What does it mean to know or to do mathematics? How have views of mathematics influenced school mathematics? What are the currrent issues related to the goals, content, and programs in mathematics education? What are the recommendations and underlying rationale for reforming school mathematics?

C&I 811 The Instruction of Mathematics
This course focuses on research on the learning of mathematics and is designed to provide students with an understanding of how people learn mathematics. The course serves to introduce students to the major learning theories that have guided mathematics education over the past fifty years (e.g., behaviorism, constructivism, sociocultural/sociohistorical perspectives). Pragmatic implications of these different theoretical perspectives will also be examined. For example, questions such as the following are considered: What are the implications for organizing instruction if one takes a particular theoretical perspective? What are the implications for assessment? What is the nature of the mathematical goals that one holds for students if one takes a particular theoretical perspective?

C&I 812 Curricular Issues in Mathematics Education
This course considers the learning and development of both novice and experienced teachers with an emphasis on learning to teach in ways that are consistent with reform-based ideals. The course explores theory, research, and practice related to topics such as methods of mathematics teacher education, the process of learning to teach mathematics, mathematics teachers' acquisition of professional knowledge, and preparing mathematics teachers for a diverse student population. In addition, several major programs of professional development in mathematics are examined. A primary goal of the course is to help students begin to understand the complexity of the field of research on mathematics teaching and mathematics teacher education.

C&I 842 Seminar on Special Topics in Mathematics Education
This seminar focuses on a variety of topics related to the teaching and learning of mathematics with the target audience being practicing mathematics teachers. Topics examined might include teaching and learning in various content domains (e.g., algebra, geometry, statistics and probability), the nature and design of assessment used in mathematics education, and the design of action research related to teaching mathematics.

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