# Mathematics Education Ph.D.

The Fariborz Maseeh Department of Mathematics and Statistics offers a Ph.D. in Mathematics Education. The main objective of this program is to develop educators with an understanding of mathematics and its teaching and learning, and with the capabilities for research and professional practice in the field. This program provides a balance between mathematics and mathematics education in order to develop mathematics educators who can become: (i) Faculty members in mathematics departments or schools of education in universities, four year colleges, or community colleges; (ii) Curriculum specialists in mathematics, supervisors of mathematics at the middle school level or secondary school level, or mathematics specialists in state or local departments of education; (iii) Private sector specialists in mathematics education.## Admission:

### Program prerequisites:

Candidates in this program must currently have (or complete during their program) a master's degree in mathematics equivalent to the MA/MS in Mathematics degree or the MS-MTCH degree at Portland State University.In addition to program prerequisites, applicants must meet the university's minimum admission requirements including English language proficiency.

This program admits once per year for fall term only. See instructions on how to apply: https://www.pdx.edu/math/graduate-application-instructions

## Degree requirements

Students are responsible for knowing University-level graduate policies and procedures for obtaining the degree. These policies and procedures are in the Graduate School section of the PSU Bulletin. Several of the most frequently asked questions about University-level graduate policies and procedures can also be found on the Graduate School website.

Candidates must complete an approved program of 84 credit hours consisting of three major components: coursework, a research practicum experience, and dissertation research.

### Coursework must include a minimum of:

- 18 credit hours in Mathematics Education Research Courses (Mth 690-695);
- 18 credit hours of other 500-600 level mathematics courses; and
- 18 hours of graduate coursework in supporting areas outside of mathematics (such as curriculum and instruction, psychology, educational policy, science, computer science, philosophy, sociology, anthropology, etc.)

### Research Practicum Mth 601 (3 credits)

The purpose of the research experience will be to provide candidates with an opportunity to use methodological techniques in mathematics education early on in their course of study. Prior to the dissertation, candidates will be expected to gain experience with the qualitative and quantitative approaches that are now used by many researchers and curriculum developers in mathematics education. Some examples of possible research practicum experiences are: case studies of students' learning documented over time, studies of teachers' practice in the mathematics classroom, documentation of teachers' beliefs about mathematics as they implement new curricula.### Dissertation Research Mth 603 (27 credits)

The Ph.D. dissertation research will ordinarily be conducted under the guidance of a mathematics educator in the Fariborz Maseeh Department of Mathematics and Statistics. The dissertation is the most important part of a candidate's program, and involves identifying and researching a significant problem which builds upon previous research, and which will make an original contribution to an area of research in mathematics education. Dissertation committees consisting of a mix of faculty with expertise in mathematics education, mathematics, curriculum and instruction, and other areas outside of mathematics education will be encouraged. After completing the comprehensive examinations, the chairperson and dissertation committee will be appointed. The student will develop a dissertation proposal which will be defended in an oral presentation to the committee. When the proposal has been approved by the committee, and if necessary by the University Human Subjects Research Review committee, the student will be considered a candidate for the Ph.D. in mathematics education. The dissertation must be completed according to the outlines of the proposal approved by the candidate's committee. Students must register for dissertation credit during each term they are engaged in dissertation research. Upon completion of doctoral thesis work, the candidate will defend the dissertation before the committee in an oral presentation that is open to other interested faculty and students. The student is expected to demonstrate knowledge of the research literature in mathematics education that relates to the particular problem chosen for research, and to show how the dissertation contributes to work in this area.

### Demonstrated competency areas:

Prior to completing their program, candidates in the Mathematics Education Ph.D. program will be expected to demonstrate competency in the following 7 areas:

- mathematics education
- mathematics
- supporting content areas
- teaching
- the use of technology in teaching mathematics
- the application of mathematics education in an urban setting
- research in mathematics education

#### 1. Mathematics Education:

The competency in mathematics education can be met by successfully completing graduate coursework in mathematics education and the psychology of learning and by passing a written, comprehensive exam.*Coursework: *Candidates must successfully complete the 6 graduate seminars in Mathematics Education (Mth 690, Mth 691, Mth 692, Mth 693, Mth 694, and Mth 695) and at least one course in the psychology of learning. Course titles and descriptions are listed below.

*Comprehensive Exam in Mathematics Education: *Prior to being advanced to candidacy, students must pass and orally defend a written, comprehensive exam that covers the key developments and theoretical perspectives on the history of mathematics education, the teaching and learning of mathematics, and the development of curriculum in mathematics. The implications of this information for urban populations and settings will also be included. Students will have two weeks to compose their responses, which they will defend orally before an examination committee.

#### 2. Mathematics:

Applicants to the Ph.D. in Mathematics Education are expected to have at least a master’s degree in mathematics or a degree equivalent to the MS-MTCH degree at Portland State University. The competency in mathematics can be met by successfully completing additional graduate-level coursework in mathematics beyond the masters and by passing a written comprehensive exam.*Coursework*: Candidates must complete an additional 18 graduate-level credits in mathematics beyond the masters (or the equivalent of the MS-MTCH degree at PSU) that together with their master’s program reflects a sufficient breadth and depth of the topics in elementary calculus and analysis, linear and abstract algebra, geometry and topology, probability and statistics, and other applications

*Comprehensive Exams in Mathematics*: Prior to being advanced to candidacy, students must pass and orally defend a written comprehensive exam in mathematics that covers the big ideas of analysis, linear and abstract algebra, plus one of the following areas: probability, statistics, topology, geometry, or applied mathematics. Students will sit for the exam but will have the opportunity to defend their responses orally before an examination committee.

#### 3 Supporting Content Areas:

The competency in supporting content area(s) can be met by successfully completing 18 graduate credit hours in areas outside of mathematics such as, curriculum and instruction, psychology, educational policy, science, computer science, philosophy, sociology, anthropology, etc. Candidates will be expected to plan this portion of their program in consultation with their adviser so that the 18 credits forms a coherent supporting focus and includes at least one course in the psychology of learning.#### 4. Teaching:

It is recommended that candidates in the Ph.D. program acquire mathematics teaching experience at both the K-12 and the college level. At a minimum, candidates must demonstrate competency in teaching mathematics for at least one of these two levels.#### 5. The Use of Technologies in Teaching Mathematics:

Students will be expected to acquire background and experiences in how students best learn mathematics within technologically enhanced learning environments either by working with students in K-12 classrooms or by teaching courses in the department that utilize technology (e.g., pre-calculus, calculus, linear algebra, or differential equations). The role of technology in mathematics education will be addressed throughout the doctoral program. In the seminar courses on teaching and learning (Mth 693 and Mth 694) and in the topics courses (Mth 695) students will become versed in the research literature on technology in mathematics education.The Fariborz Maseeh Department of Mathematics and Statistics also offers

**Mth 588 "Technology for Teachers"**which provides exposure to a variety of technologies including symbolic algebra manipulators (i.e., Maple, Mathematica, and Derive), graphing packages (Derive, various graphing calculators), and geometrical tools (Cabri geometry, Geometer's Sketchpad). In addition students are introduced to the various mathematics resources and information available on the World Wide Web. This course, or its equivalent, will be required of all participants in the program.

#### 6. Applications of Mathematics Education in an Urban Setting:

Portland State University and the Portland Metro area provide a "natural laboratory" for conducting research on the teaching and learning of mathematics within an urban setting. Moreover, integral to the mission of Portland State University is a commitment to work with community partners in the promotion of educational reform K-16. Candidates in the Ph.D. program will be expected to demonstrate competency in working with urban populations and settings either by providing service or conducting research with community partners.#### 7. Research in Mathematics Education:

The competency in research in mathematics education can be met by successfully completing coursework in research in mathematics education, a research practicum project, and the doctoral dissertation.*Coursework: *Students need to demonstrate experience with both quantitative and qualitative research methods which can be done through coursework and within the research practicum. Students must successfully complete Mth 692, Research Methodology and Research Design in Mathematics Education. Some students may also wish to take some additional coursework in research methodologies from outside areas.

### Residency

In a doctoral program, the residency requirement can be satisfied in one of the follow ways:

- Three terms of full-time enrollment (minimum 9 graduate credits applicable to the degree program each term) during the first two years after admission to the program. This may include one or more summer terms.
- Six terms of part-time enrollment (minimum 1 graduate credit applicable to the degree program each term) during the first two years after admission to the program. This may include one or more summer terms.
- A doctoral student who was enrolled in the same major at PSU, and whose matriculation to the doctoral program immediately follows (within one calendar year) the master's degree program, may fulfill the residency requirement during the period in which the student was enrolled in the master's program