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# Mathematics Departments that Offer a PhD in Mathematics Education

What Courses in Mathematics Education Are Required?

Communicated by *Notices* Associate Editor William McCallum

In the early part of the 20th century the first doctoral programs in mathematics education were initiated in mathematics departments at two institutions: Columbia University (Teachers College) and the University of Chicago

For over 100 years doctoral programs in mathematics education have evolved, both in terms of where they are programmatically housed and in terms of course requirements. Today some doctoral programs in mathematics education are hosted entirely within mathematics departments (e.g., Illinois State University and University of Northern Colorado); others entirely within colleges/schools of education (e.g., Auburn University and University of Missouri); and there are a few institutions where a doctorate in mathematics education can be obtained from either the mathematics department or the college/school of education (e.g., University of Arizona and Oklahoma State University).

Doctorates in mathematics education from mathematics departments include a substantial body of work in mathematics, typically the equivalent of a master’s degree in mathematics or more. In addition, doctoral students take courses in mathematics education designed to increase their expertise in learning and teaching mathematics. This foundational knowledge of mathematics plus their interest in teaching makes graduates with a doctorate in mathematics education from a mathematics department highly desired candidates for teaching collegiate level mathematics in regional institutions

### Survey

A national conference on doctoral programs in mathematics education was held in October 2022 (NSF Grant No. 1932697). About 100 participants from more than 60 institutions with such programs attended the Conference. Thirteen of the institutions at the conference offered their doctorate in the mathematics department. A survey of these participants was done to gather information about the mathematics education courses required to complete a doctorate.

While required courses in a doctoral program are not indicative of the institution’s total course offerings available in mathematics education, they are one indicator of foundational or core knowledge in mathematics education that the department values. This article reports the required courses in mathematics education to complete a doctorate in mathematics education in mathematics departments of the institutions that participated in the conference.

Thirteen institutions participated in the survey. One or more faculty members from each of these 13 institutions provided information about required courses in mathematics education. More specifically they were asked to provide a course title, course description, and semester credit hours for each required course. Due to length considerations, the course descriptions are not included in this article, but could be obtained from the institutional contact.

### Survey results

Here are the titles of the required courses for each of the 13 institutions, along with the faculty contact person(s), and the credit hours in parens:

**Arizona State University** (Naneh Apkarian)

MTE 501: Research in Undergraduate Mathematics Education I (3)

MTE 502: Research in Undergraduate Mathematics Education II (3)

MTE 503: Research in Undergraduate Mathematics Education III (3)

MTE 504: Research in Undergraduate Mathematics Education IV (3)

**Illinois State University** (Craig Cullen and Jennifer Tobias)

MATH 401: Current Research in School Mathematics (3)

MATH 403: Theories of Mathematics Learning (3)

MATH 580: Mathematical Thinking and Learning (3)

MATH 581: Seminar in Research and Development in Mathematics Education (3)

MATH 582: History of Mathematics Education Curriculum (3)

MATH 585: Topics in Mathematics Education Seminar (3)

MATH 586: Mathematics Teaching and Teacher Education (3)*An additional 9 graduate semester hours of electives in mathematics education are required for a total of 30 hours of graduate courses in mathematics education.*

**Middle Tennessee State University** (Sarah Bleiler-Baxter)

MATH 6900: Research in Mathematics Education (3)

MATH 7320: Mathematical Problem Solving (3)

MATH 7330: Ethics in Mathematics Education (3)

MATH 7340: History, Curriculum, and Policy in Mathematics Education (3)

MATH 7900: Teaching and Learning Mathematics (3)

MSE 7310: Theoretical Frameworks in Mathematics and Science Education (3)

MSE 7900: The Nature of Mathematics, Science, and STEM (3)

SPSE 7270: Learning Theories in Mathematics and Science Education (3)

**Montana State University** (Mary Alice Carlson)

M 528: Curriculum Design (3)

M 529: Assessment Models and Issues (3)

M 534: Research in Mathematics Education (3)

**Montclair State University** (Steven Greenstein and Nicole Panorkou)

MATH 745: The Use of Teacher Knowledge in Mathematics Teaching (3)

MATH 811: Mathematics Education Leadership (3)

MATH 813: Geometric and Spatial Thinking and Learning (3)

MATH 814: Algebraic and Analytic Thinking and Learning (3)

MATH 815: Theories of Learning Mathematics (3)

MATH 816: Mathematics Curricula (3)

MATH 821: Mathematics Education in Higher Education (3)

MATH 822: Mathematics Education in Higher Education Practicum (1)

**Portland State University** (Eva Thanheiser)

MTH 692: Research Methodology and Design (3)

MTH 693: Research on the Learning of Mathematics (3)

MTH 694: Research on the Teaching of Mathematics (3)

MTH 695: Topics in Research in Mathematics Education (3)

MTH 696: Mathematical Knowledge for Teaching and Educational Research, Grades K–16 (3)

MTH 697: Advanced Mathematics for Teaching and Educational Research (3)

**San Diego State University/University of California-San Diego** (Susan Nickerson and Jeff Rabin)*SDSU is on the semester system—3 hours. UCSD is on the quarter system—all courses are 4 hours.*

MTHED 603: Seminar on Learning Theories in Mathematics Education (3)

MSED 296 A, B, C: Theories and Applications in Mathematics and Science Education (three courses 4 hours each)

UCSD Cognitive Science (two courses/seminars 4 hours each)

PSYC 201 A and B or EDS 254 and 255 or MATH 282 A and B: Quantitative Research Methods (two 4-hours courses) and MSE 810: Qualitative Research Methods (3)*Two of the courses/seminars MTHED/MSE 600–608:*

MTHED 600: Teaching and Learning Mathematics in the Early Grades (Pre-K to 4) (3)

MTHED 601: Teaching and Learning Mathematics in the Middle Grades (3)

MSE 603: Seminar on Learning Theories in Mathematics Education (3)

MSE 604: Seminar on Teaching Issues in Mathematics (3)

MTHED 605: Algebra in the 7–14 Curriculum (3)

MTHED 606: Seminar on Selected Topics in the 7–14 Curriculum (3)

MTHED 607: Seminar on Research on Undergraduate Mathematics Education (3)

MSE 608: Equity in STEM Education (3)

MSE 820: Research Project (research apprenticeship experiences) (3)

MSE 802: Research apprenticeship experience is 60 hours working on someone else’s project (2). *This represents mentoring in research in mathematics education and research methods in mathematics education.*

MSE 805: Assisting/Teaching Prospective Teachers; MSE 806: Supervised School Practicum; MSE 807: Teaching Assistant for Undergraduate Mathematics (3) or EDS 294 (2) or MATH 500: Teaching Assistant Training (2 or 4) (provides structured support for teaching mathematics) *Two courses from other categories such as Philosophy, Sociology, Equity and Diversity*

MSE 830 and either MSE 899 or MSED 299 (two doctoral research courses)

**Texas State University** (Jennifer Czocher and Sharon Strickland)

MATH 7302: History of Mathematics/Mathematics Education (3)

MATH 7306: Current Research in Mathematics Education (3)

MATH 7324: Curriculum Design and Analysis (3)

MATH 7328: Instructional Techniques and Assessments (3)

MATH 7346: Quantitative Research (3)

**University of Arkansas** (Shannon Dingman)

MATH 610V: Directed Readings—Teaching and Teacher Education (3)

MATH 610V: Directed Readings—Technology and Curriculum (3)

MATH 610V: Directed Readings—Instructional Strategies and Assessments (3)

MATH 610V: Directed Readings—Curriculum Ideologies and Learning Theories (3)

**University of New Hampshire** (Karen Graham)

MATH 958: Foundations in Mathematics Education (1)

MATH 968A: Topics in Mathematics Education I: Teaching and Learning of Mathematics (3)

MATH 968B: Topics in Mathematics Education II: Curriculum and History in Mathematics Education (3)

MATH 959: Introduction to Research Design in STEM Education (3)

MATH 978: Topics in Mathematics Education II (3)

**University of Northern Colorado** (Gulden Karakok)

MED 731: Learning Theories in Mathematics Education (3)

MED 732: Mathematics Curriculum Design (3)

MED 733: Models of Teaching in Mathematics (3)

MED 740: Equity in Mathematics Education (3)

MED 752: Research in Mathematics Education Mentorship (3)

**Virginia Tech** (Estrelia Johnson)

MATH 5624: Research on Mathematical Knowing and Learning (3)

MATH 5634: Research in Undergraduate Mathematics Education (3)

EDCI 5744: Critical Analysis of Mathematics Education Research (3)

EDCI 5714: Topics in Mathematics Education Research (3)

**Western Michigan University** (Laura Van Zoest and Ok-Kyeong Kim)

MATH 6570: Issues and Trends in Mathematics Education (3)

MATH 6580: Psychology of Learning Mathematics (3)

MATH 6590: Research in Mathematics Education (3)*A minimum total of at least 21 hours of mathematics education are required from courses such as:*

MATH 6510: Studies in Teaching Elementary School Mathematics (3)

MATH 6530: Studies in Teaching Secondary School Mathematics (3)

MATH 6540: Secondary School Mathematics Curriculum Studies (3)

MATH 6550: Introduction to Mathematics Education Research (3) *Repeatable*

MATH 6560: Teaching Collegiate Mathematics Education Research (3)

An examination of the course information shows a range of three to over twelve mathematics education courses were required with a mean of about six, and the course titles varied greatly. However, some common themes across programs include research, curriculum, learning theories, teaching, and equity.

One institution provides an in-depth focus on Research in Undergraduate Mathematics Education (RUME), while others include a single course on RUME. Some courses are targeted for doctoral students focusing on teacher preparation at the elementary/middle school or secondary school, with the latter often including a specific focus on mathematical content, such as the learning/teaching of algebra or geometry.

The word “research” appeared in over 25 of the required courses, but reflected many different courses, such as Current Research in School Mathematics, Introduction to Research in Mathematics Education, Research in Mathematics Education, Research on the Learning of Mathematics, Research on the Teaching of Mathematics, Research on Undergraduate Mathematics Education, Critical Analysis of Mathematics Education Research, or Topics in Research in Mathematics Education. An examination of the course descriptions revealed a wide range of topics and issues being addressed as well as the resources used.

Each of these institutions offered additional optional doctoral courses in mathematics education that were not required for completion of the doctorate in mathematics education. A few of these mathematics departments offer both a PhD in mathematics and a PhD in mathematics education. In these institutions, it was reported that some of their PhD students in mathematics can earn a specialization in collegiate teaching by taking some of their required courses in mathematics education thereby enhancing their employment opportunities.

### Using the survey findings

Some institutions have a philosophy that the fewer required courses the better as it provides flexibility and allows a PhD program to be individually tailored to address different career goals. Therefore, the number of required courses in a program are not necessarily representative of the overall learning goals of the program. In fact, some institutions rely heavily on “out of course” experiences such as internships and independent readings. To have a clear understanding of the course offerings and/or learning goals of a doctoral program, it is necessary to carefully examine an institutional website or contact faculty members individually.

When this required course information was shared at the conference it prompted many questions, exchanges, and dialogues among participants. Participants wanted to learn more about the various course offerings at other institutions. Some participants requested syllabi and sought to learn about the textbooks/resources that were used in these courses. This course information also encouraged mathematics faculty members to do some self-examination on their course offerings and think about if and how some of these courses could be included in their own program.

Issues and cultures change, so self-reflection and review of doctoral requirements should be done regularly to strengthen and update programs

## Note

Research for this article was funded by the National Science Foundation No. 1932697. However, the opinions expressed represent this author and do not reflect any endorsement by the National Science Foundation.

## References

- [1]
- E. F. Donogue,
*Mathematics education in the United States: Origins of the field and the development of early graduate programs*, in R. E. Reys and J. Kilpatrick (eds.), One Field, Many Paths: US Doctoral Programs in Mathematics Education, American Mathematical Society/Mathematical Association of America, Washington, DC, 2002, pp. 3–18. - [2]
- R. Reys,
*A report on jobs for doctorates in mathematics education in institutions of higher education*, Journal for Research in Mathematics Education**37**(2006), no. 4, 262–269. - [3]
- B. Reys and R. Reys,
*Strengthening doctoral programs in mathematics education: A continuous process*, Notices Amer. Math. Soc.**64**(2017), no. 4, 386–390.

## Credits

Photo of Robert Reys is courtesy of Robert Reys.