doctor of philosophy in mathematics education

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DOCTOR OF PHILOSOPHY IN MATHEMATICS EDUCATION

Mathematics Education (EMAT) is a recently initiated content specialization in the UW College of Education Curriculum and Instruction (EDCI) doctoral program. The purposes for establishing this new program include the creation of innovative emphases and approaches in the preparation of solidly prepared scholar-leaders for the field of Mathematics Education worldwide.

Required Courses

• EMAT 5100: Theory & Research in Learning & Development (3) - Fall of Even Years
• EMAT 5200: Advanced Math Curriculum, Assessment & Evaluation (3) - Spring of Even Years
• EMAT 5300: Theory & Practice in Mathematics Teaching & Teacher Education (3)-Spring of Odd Years
• EMAT 5400: Analysis & Critique of Research in Mathematics Education (3)-Fall of Odd Years
• EMAT 5500: Colloquium in Mathematics Education (1-3)-Every Fall and Spring
• EMAT 5980: Dissertation Research (1-12)-Every semester

Special Joint Electives

•  EMAT 5600 Quantitative Reasoning & Modeling in Mathematics & Science Education
•  EMAT 5700 Principles & Methods for Integrated Teaching & Learning Mathematics & Science

Additional Offerings

• EMAT 5500 Research Seminar in Mathematics Education. 1-3
• EMAT 5490 Individual Problems in Mathematics Education. 1-6
• EMAT 5680 Special Topics in Mathematics for Educators. 1-3
• EMAT 5900 Practicum in Mathematics Education. 1-3
• EMAT 5970 Development of Dissertation Research in Mathematics Education. 1-6
• EMAT 5980 Dissertation Research in Mathematics Education. 1-12
• EMAT 5990 Internship in Mathematics Education. 1-6

Requirements

Overall, the doctoral program will require  at least  81 semester hours completed within a coherent program of study developed and approved by the candidate's Major Professor and Doctoral Committee (which may include transferring up to 30 approved graduate semester hours from work completed toward a master's degree).

The overall structure includes:

To satisfy Mathematics Education hours (18), the following EMAT courses (four required and two joint electives with Science Education) are offered:

• Theory and Research for Mathematical Learning and Development
• Theory and Practice for Mathematics Teaching and Teacher Education
• Advanced Study of Mathematics Curriculum, Assessment and Evaluation
• Analysis and Critique of Research in Mathematics Education
• Quantitative Reasoning and Modeling in Mathematics and Science Education
• Principles and Methods for Integrated Teaching and Learning of Mathematics and Science

These advanced Mathematics Education courses along with graduate study in Mathematics and Statistics, and Quantitative and Qualitative Research Methodologies, collectively build knowledge of theoretical and empirical perspectives to lead to a solid competence for engaging in both scholarly and practical work in the field at all levels. One program goal is to stimulate and guide each student to develop their dissertation research as a first step within a well-defined research program that can encompass the initial years of their post-doctoral scholarship.

Values & Goals

The fundamental programmatic development of each Mathematics Education doctoral student is set against the universal need for reforming to improve the mathematical education of all citizens. Core values promoted within the doctoral program are the premises upon which modern reforms are based and include the following goals:

• Construction of deep conceptual understandings of fundamental ideas
• Development of useful proficiencies for applying powerful technological tools to support new learning and solve significant problems
• Building positive perspectives on the nature and utility of mathematics in human intellective development and in technological societies

Traditional professional domains of advanced theoretical and research knowledge in Mathematics Education are fundamental elements of study and competence for every doctoral student, including the following:

• Student development, learning and thinking, and emotional maturation for building a sound educational experience in mathematics
• Mathematics teacher preparation, practice and enhancement, and professional life
• Mathematics curricular development, implementation and revision
• Student, teacher, and mathematics program assessment, evaluation and accountability

Students may enter the doctoral program with a variety of mathematical backgrounds, but are expected to further their depth and breadth of content knowledge through UW mathematics courses chosen to fit the individual's needs and interests, and to leave the program with substantial knowledge of graduate level mathematics.

Program Identities for Scholarship and Leadership

Beyond the above basic domains of doctoral knowledge, four specific program identities foster specializations for scholarship and leadership in our field:

• Quantitative reasoning --- Based upon a growing societal necessity for all citizens to possess numerical and quantitative literacy, this focus addresses the explicit development of our understandings of the mathematical, psychological, pedagogical, and curricular applications of reasoning with, and about, conceptual quantities experienced and used in the world.
• Mathematical modeling --- Reflective of the power of mathematics to provide frameworks and conceptual tools for building, using, and refining abstracted representations of many real world phenomena and problems, this emphasis provides a context for shifting many important aspects of a sound mathematical education toward constructive, dynamic, relevant problem-solving experiences.
• Technological tools and applications --- Increasingly powerful computing, computational science, and informational technologies have changed how mathematics is developed and used in many domains, and in this emphasis UW faculty and students will explore and investigate the potentials and impacts of new tools upon mathematical learning, teaching, curriculum, and assessment.
• Student and teacher mathematical experiences --- Current mathematics education reforms emphasize fundamental shifts in both content and process, with significant attention to promoting higher quality mathematical experiences that develop student sense making, thinking and reasoning, and motivation and engagement, and UW faculty and students will focus explicit attention to understanding deeply the nature of such experiences.

Each of these focal identities is addressed throughout the courses, seminars, and graduate assistantship duties and experiences as inherent points of emphasis in the overall Mathematics Education culture at UW. Faculty research and development activities will incorporate one or more of these programmatic identities, and doctoral students will be expected to gain further developmental experiences within these opportunities. As appropriate to the interests and directions of the student and the doctoral committee, dissertation research will also mirror the cited core values and embody aspects of one or more of these programmatic identities.

The four program identities also are the focus of work by three Research Teams organized within the Wyoming Institute for the Study and Development of Mathematical Education WISDOM^e [BROKEN LINK] .

Doctor of Philosophy (PhD) in Mathematics Education

Graduate Programs

The Ph.D. program emphasizes research and requires a written dissertation for completion. The program is individualized to meet the needs of graduate students. The student must develop, with the guidance from the major professor and committee, a program that is applicable to their background and interest. The average Ph.D. program requires 4-6 years beyond a master’s degree. The program is comprised of coursework in four major areas.

• Mathematics Education
• Mathematics or a related area
• Cognate Area
• Research Core

This residential program has rolling admission Applications must be fully complete and submitted (including all required materials) and all application fees paid prior to the deadline in order for applications to be considered and reviewed. For a list of all required materials for this program application, please see the “Admissions” section below.

• July 1 is the deadline for Fall applications.
• November 15 is the deadline for Spring applications.
• March 15 is the deadline for Summer applications.

This program does not lead to licensure in the state of Indiana or elsewhere. Contact the College of Education Office of Teacher Education and Licensure (OTEL) at [email protected] before continuing with program application if you have questions regarding licensure or contact your state Department of Education about how this program may translate to licensure in your state of residence.

APPLICATION PROCEDURE

Application Instructions for the Mathematics Education PhD program from the Office of Graduate Studies:

In addition to a submitted application (and any applicable application fees paid), all completed materials must be submitted by the application deadline in order for an application to be considered complete and forwarded on to faculty and the Purdue Graduate School for review.

Here are the materials required for this application:

• Transcripts (from all universities attended, including an earned bachelor’s degree from a college or university of recognized standing)
• Minimum undergraduate GPA of 3.0 on a 4.0 scale
• 3 Recommendations
• Academic Statement of Purpose
• Personal History Statement
• Writing Sample
• International Applicants must meet English Proficiency Requirements set by the Purdue Graduate School

We encourage prospective students to submit an application early, even if not all required materials are uploaded. Applications are not forwarded on for faculty review until all required materials are uploaded.

When submitting your application for this program, please select the following options:

• Select a Campus: Purdue West Lafayette (PWL)
• Select your proposed graduate major: Curriculum and Instruction
• Please select an Area of Interest: Mathematics Education
• Please select a Degree Objective: Doctor of Philosophy (PhD)
• Primary Course Delivery: Residential

Program Requirements

I. mathematics education courses (15 – 18 hours).

In mathematics education, students engage in courses that cover topics in the cognitive and cultural theories of learning and teaching mathematics, and the role of curriculum in mathematics education. A three (3) course sequence is required that consists of:

• EDCI 63500 – Goals and Content in Mathematics Education
• EDCI 63600 – The Learning of Mathematics: Insights and Issues
• EDCI 63700 – The Teaching of Mathematics: Insights and Issues

In addition, students are encouraged to take (6 – 9) hours of EDCI 620: Developing as a Mathematics Education Researcher

II. Related Course Work (minimum 6 hours)

All students should have appropriate course work in mathematics, statistics, educational technology, or a related field. Students without a master’s level background in mathematics may be required to take more courses in mathematics. This will be determined by the student’s major professor and advisory committee.

III. Cognate (9 hours)

Students will take three graduate courses in a self-selected cognate area. Cognate area selection should be discussed with the student’s major professor and advisory committee. Possible cognate areas include: mathematics, psychology, philosophy, sociology, technology.

IV. Research Core Courses (15 hours)

All doctoral students in the Department of Curriculum and Instruction must complete five (5) courses from areas in research methodology and analysis before beginning their dissertation:

• EDPS 53300 – Introduction to Research in Education
• EDCI 61500 – Qualitative Research Methods in Education
• MA 51200 – Introductory Statistics
• Advance electives in either quantitative or qualitative methods
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Amber brown, signe kastberg, rachael kenney, jill newton.

Course Registration, payment, drops/withdraws, and removing holds: [email protected] Career accounts: ITaP (765) 494-4000

Mathematics Education PhD

Doctor of philosophy.

The Doctor of Philosophy (Ph.D.) degree emphasizes research competencies. The degree requires a scholarly dissertation of intellectual merit and sound research methodology. Dissertation research may include analytical studies of the process of teaching or experimental studies of the teaching-learning process, including studies of verbal learning and laboratory practice or historical studies.

Admissions Information

Displaying requirements for the Spring 2024, Summer 2024, and Fall 2024 terms.

• Points/Credits: 75
• Entry Terms: Spring/Summer/Fall

Application Deadlines

• Spring: November 15
• Summer/Fall (Priority): December 1
• Summer/Fall (Final): Rolling

* For details about rolling deadlines , visit our admission deadlines page.

Supplemental Application Requirements/Comments

• Online Degree Application , including Statement of Purpose and Resume
• Transcripts and/or Course-by-Course Evaluations for all Undergraduate/Graduate Coursework Completed
• Results from an accepted English Proficiency Exam (if applicable)
• $75 Application Fee
• Two (2) Letters of Recommendation

Requirements from the TC Catalog (AY 2023-2024)

Displaying catalog information for the Fall 2023, Spring 2024 and Summer 2024 terms.

View Full Catalog Listing

Doctoral Degrees

All candidates for the Ed.D., Ed.D.C.T., or Ph.D. degrees are expected to demonstrate both mathematics and mathematics education competencies through a series of certification examinations taken upon the completion of 60 graduate points. Certification examinations test the student’s knowledge of current research and theory in mathematics education and mathematics content. Examinations are offered once in the fall, spring, and summer terms. Courses recommended as preparation for the examinations in mathematics education include MSTM 6037,  MSTM 4019, and other mathematics education courses; Courses recommended as preparation for the examinations in mathematics are 6000- level mathematics content courses.

Students must demonstrate acceptable proficiency in at least three of the following six mathematics content areas: algebra, analysis, discrete mathematics, foundations of mathematics, geometry and topology, and probability and statistics. Students may sit for the examination in mathematics content during the regular certification examination times. Alternatively, they may register for advanced content courses and, with permission of the program, sit for the content area certification examination upon completion of the course. Incoming doctoral candidates should register for MSTM 6037 Professional Seminar in Mathematics during the first year of doctoral studies.

Doctoral students whose dissertations require statistical analysis should include appropriate statistics courses in their programs. These points can be included either in the mathematics/mathematics education requirement or can be taken as research electives.

Doctor of Philosophy in Mathematics Education

The Doctor of Philosophy (Ph.D.) degree emphasizes research competencies. The degree program requires a scholarly dissertation of intellectual merit and sound research methodology. Dissertation research may include analytical studies of the process of teaching or experimental studies of the teaching-learning process, including studies of verbal learning and laboratory practice or historical studies.

Candidates are encouraged to develop an association with a faculty member early in their studies to identify a problem area of mutual interest to plan a course of studies that leads to the competencies needed to complete dissertation research and prepare for a professional role. Further details are available in the brochures on doctoral studies and in the general descriptions of doctoral programs available from the Office of Doctoral Studies (ODS).

A program of study for the Doctor of Philosophy degree must include at least 45 points taken under Teachers College registration. In order to permit the acquisition of broad and basic scholarship, each program of study should include at least 60 points in mathematics, mathematics education, statistics, and computing. At least 35 points should be in advanced courses – including research courses (MSTM 6500 or 6501 and MSTM 7500). (Any Teachers College course at the 6000 level or above, any Columbia University Graduate School of Arts and Sciences course with a “G” prefix, any “W” course numbered above 4000, or any transferred course with a graduate-level prerequisite will be considered an advanced course.) Further, 15 points in the philosophical, psychological, and curricular foundations of education must be included in every Ph.D. degree program. Students whose dissertations require statistical analysis should include appropriate statistics courses in their programs. These points can be included either in the mathematics/mathematics education requirement or can be taken as research electives.

Candidates for the Ph.D. degree are required to demonstrate competency in two languages chosen from among French, German, and Russian. Students who require other languages for the preparation of their dissertation may petition the program to request one substitution. Students in mathematics may not use computer languages or statistics to satisfy the language requirement.

The Ph.D. dissertation is a scholarly study contributing new theoretical knowledge to the field and should be planned early in the program when sufficient advanced courses have been completed to permit the candidate to enroll in relevant research courses. Ph.D. dissertations in mathematics education should be (1) experimental studies in learning, (2) analytical studies in policy theory in mathematics education, or (3) other scholarly investigations of problems and issues of broad significance in the field.

The website of the Program offers a list of Topic study groups which doctoral students are recommended to join.

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Program Director : Professor Alexander Karp

Teachers College, Columbia University 323 Thompson

Phone: (212) 678-3381 Fax: (212) 678-8319

Email: tcmath@tc.edu

Advisor: See Mathematics Office, Room 3319, Everett Tower

The Doctor of Philosophy in Mathematics Education focuses on K-12 mathematics curricula, teaching and learning mathematics, and research and evaluation in mathematics education. Programs may focus on preparation for mathematics education faculty positions in colleges and universities, supervision and curriculum development positions in school systems, or evaluation positions in education-related institutions.

Admission Requirements

Program requirements, 1. complete the following course work:.

• At least thirty approved graduate credit hours in mathematics and statistics, including general topology (MATH 5220), linear algebra MATH 5300), analysis (MATH 5700 or 6150), abstract algebra (MATH 6300 or 6160), graph theory (MATH 6400), geometry (MATH 6490), and statistics (MATH 6120 or STAT 6620). The remaining courses are to be selected, in consultation with program advisors, from the 5000- and 6000-level offerings in applied mathematics, pure mathematics, and statistics.
• At least six approved graduate credit hours in research methods including a course in quantitative methods (STAT 6620, PSY 6340, or EMR 6450) and a course in qualitative methods (EMR 6480).
• At least 21 approved graduate credit hours in research methods including issues and trends in mathematics education (MATH 6570), psychology of learning mathematics (MATH 6580), research in mathematics education (MATH 6590), and two advanced methods courses (selected from MATH 6510, 6520, and 6530).
• Additional approved graduate credit hours selected from mathematics, statistics, mathematics education, psychology, and professional education sufficient to meet the minimum program requirements.

2. Pass three comprehensive examinations in

• K-12 mathematics curriculum and instruction
• Psychological foundations and mathematical learning
• Research and design in mathematics education

3. Acquire competence in two research tools.

4. complete an internship.

• MATH 7120 - Professional Field Experience Credits: 2-12 hrs.

5. Complete and successfully defend a dissertation in mathematics education

• MATH 7300 - Doctoral Dissertation Credits: 15 hrs.
• Upon admission a student will, within the first year of enrollment, work with a two-member advisory committee to design a program for completing the Ph.D. At this time, any course requirements already satisfied through prior master’s level work will be determined by the advisory committee. After a tentative program has been designed, one of the advisory committee members will be assigned to serve as the student’s advisor for program matters leading up to the formulation of a dissertation proposal. Program may be reviewed for revision and continuation throughout the program.
• A student will schedule comprehensive examinations in consultation with the program advisor. The examinations in curriculum and in psychology will each be three-hour written examinations. The examination in research and design will be a take-home examination written over a period of one week followed within two weeks of submission by a one-hour oral defense conducted with at least two graduate faculty in mathematics education. If a student fails a comprehensive examination, the student must retake the examination within a year of the first attempt. A student who fails a comprehensive examination twice will be dismissed from the program at the end of the semester when the exam was taken.
• By the time a student has passed comprehensive examinations in curriculum and instruction and in psychological foundations, the student will take reading courses from a potential dissertation advisor with the goal of developing a proposal for dissertation research. Depending upon the nature of the proposed research, the student may be required to conduct a pilot study.
• As soon as a student has passed all three comprehensive exams and shown competency in the two research tools, the student will, in consultation with a chosen dissertation advisor, form a dissertation committee. The chosen dissertation advisor will become the student’s program advisor. The dissertation committee shall consist of the dissertation advisor, a second reader, at least one other faculty member, and a member from outside the department. This committee must be approved by the doctoral committee of the Mathematics Education Area Group. At a time mutually convenient to the student and the dissertation committee, the student will give an open public presentation of the proposed dissertation research and answer questions on the proposal. A student will be allowed to take MATH 7300 credits only after a dissertation committee has been formed and the dissertation proposal is accepted by all its members.
• After completing a dissertation and all other requirements for the Ph.D., a student will present an open public defense of the dissertation followed by an open question period. The dissertation committee will then meet in private to decide acceptance or rejection of the dissertation and defense. All committee members must agree on acceptance.

Graduate Degree

Mathematics education - doctor of philosophy, college of natural science, graduate study.

The Doctor of Philosophy degree in Mathematics Education is designed for persons who show promise of becoming leaders in local, state, national, and international mathematics education communities. The program prepares researchers and leaders to address critical issues in mathematics education by developing analytical perspectives for research, engaging in reflective teaching, and deepening mathematical knowledge.

In addition to meeting the requirements of the University and of the College of Natural Science, students must meet the requirements specified below.

The program admits students with a variety of backgrounds.  Some students will have equally strong backgrounds in education and mathematics. Others may have more extensive prior preparation in one of these two disciplines. 

Admissions decisions will be made by an Admissions Committee composed of members of the Mathematics Education Faculty Group.  A student who shows promise for success at doctoral study but who needs additional background to be eligible for admission to the Ph.D. program will be provided with specific conditions to be met before admission.  Upon successful completion of these requirements, the student may reapply.

Requirements for the Doctor of Philosophy Degree in Mathematics Education

The student must complete the requirements listed below. The student’s program of study must be approved by the student’s guidance committee and must include:

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Doctor of Philosophy (Ph.D.) Major in Mathematics Education

Program overview.

Offered through the Department of Mathematics at Texas State, this Mathematics Education Ph.D. program has particular strength in the number of courses it requires in mathematics as a complement to its courses in the teaching and learning of mathematics. Doctoral graduates will have completed a strong mathematics core in addition to the mathematics education core, thus opening a wide variety of employment opportunities.

The program is for people whose career goals will take them into professional leadership roles involving mathematics education within the United States or internationally. This program prepares its graduates for positions as mathematics or mathematics-education faculty in colleges and universities; as decision-makers in state or local education agencies; as researchers in think tanks, corporations, or not-for-profit organizations; as high-ranking staff in foundations or international organizations; or decision-makers within a national ministry of education.

The ideal admittee has an undergraduate degree in mathematics, mathematics education, or a related field. Students, especially those with a degree in a related field other than mathematics or mathematics education, may need to take background leveling courses. This decision will be made on a case by case basis by the appropriate advisor and would be articulated at the time of admission.

Educational Goal

The educational objectives of the program in mathematics education are:

• To develop a well-balanced foundation in mathematics content including in-depth understanding of basic principles.
• To understand the mathematics needed for our rapidly changing technological society.
• To link mathematics content to pedagogy for effective teaching that addresses educational needs through the entire P-20 continuum.
• To understand how to design best and most effective curriculum and ways to deliver this curriculum.
• To contribute to the knowledge in mathematics education by original research.
• To produce Ph.D. graduates who can become the leaders in the state and the nation's educational community concerning the teaching of mathematics appropriate for the demands of the 21 st century.
• To produce high-quality teachers of mathematics at all levels.

Teaching Experience

The Mathematics Education Ph.D. program expects its students to have had two years of teaching experience. A student who has taught full-time in the public school system for two or more years meets this requirement. A student who has not met this requirement upon admission will be required to gain practical teaching experience before graduation. If a student receives a teaching assistantship while in the program, each long term during which the student has a two-course assignment will count as one half of a year of experience. A student who teaches two summer sessions earns one long semester credit toward this requirement. If a student has other forms of practical teaching experience, the mathematics education advisor will determine the amount of credit received on an individual basis.

Financial Assistance

Almost all doctoral students are expected to receive full financial assistance from the department working as instructional assistants or research assistants. You must be accepted as a Ph.D. student in order to apply. In addition, you much submit to the department

a completed employment application form (available from the departmental web site);

at least one letter of recommendation regarding teaching ability (this could be one of the three letters recommending admission to the program); and

a current curriculum vitae.

Please visit the departmental website for more detailed information. The financial aid application deadline is the same as that for graduate admission. Note that the number of positions available for spring semesters is quite limited. Stipends for research assistantships depend on the types of research grants. Additional summer support is available as instructional assistants or research assistants. Contact the department for more information.

In addition to the financial aid from the Department of Mathematics, The Graduate College offers a wide variety of graduate assistantships and scholarships. Visit the Department of Mathematics website http://www.math.txstate.edu/ or The Graduate College website http://www.gradcollege.txstate.edu/ . Please note that the deadlines for these and other scholarships may be different from those for instructional assistantships in mathematics.

Each student is required to pass 36 hours of core courses, a minimum of 24 hours of elective courses, and a minimum of 18 hours of dissertation, yielding a minimum of 78 hours in course work. No grade earned below a “B” on any graduate course may apply toward a Ph.D. at Texas State. However, advisors may modify a student's doctoral program requirements as a result of either the student's performance in the qualifying exams or a change to their research goals.

The Graduate College issues each Ph.D. student a preliminary degree audit used to plan the student's course of study. In the first term of enrollment, students should review the degree audit in consultation with their supervising professor and the program director. Our advisors tailor doctoral degree audits with the individual student in mind. It is, therefore, possible for the individual degree audit to exceed the number of degree hours stated in the catalog.

Application Requirements

The items listed below are required for admission consideration for applicable semesters of entry during the current academic year. Submission instructions, additional details, and changes to admission requirements for semesters other than the current academic year can be found on The Graduate College's website . International students should review the International Admission Documents page for additional requirements.

• completed online application
• $55 nonrefundable application fee

          or

• $90 nonrefundable application fee for applications with international credentials
• baccalaureate degree or higher (or the equivalent thereof) in mathematics, mathematics education, or a related field from a regionally accredited university
• official transcripts from  each institution  where course credit was granted
• minimum 3.0 GPA in the last 60 hours of undergraduate course work (plus any completed graduate courses)
• GRE is not required
• interview with faculty
• statement of purpose (500 words) describing the student's background and professional goals, including the rationale for pursuing a doctoral degree in mathematics education and teaching philosophy
• three letters of recommendation addressing the student's professional and academic background as well as research and teaching potential
• two years of teaching experience 

TOEFL, PTE, or IELTS Scores

Non-native English speakers who do not qualify for an English proficiency waiver:

• official TOEFL iBT scores required with a 78 overall
• official PTE scores required with a 52
• official IELTS (academic) scores required with a 6.5 overall and minimum individual module scores of 6.0

This program does  not  offer admission if the scores above are not met.

Degree Requirements

The Doctor of Philosophy (Ph.D.) degree with a major in Mathematics Education requires 78 semester credit hours for students admitted with a bachelor's degree. Students entering with a master's degree in mathematics can request up to 24 credit hours of transfer course work to be approved by the dean of The Graduate College upon recommendation from the Ph.D. program director.  See the transfer credit section of this catalog for information about requesting transfer work. 

Course Requirements

Students who do not have the appropriate background course work may be required to complete leveling courses.

Qualifying Examination

Typically, after completion of the core courses or by the end of the second year in residence, each student will be required to take written qualifying examinations. To be eligible to take the qualifying examinations, the student normally will have a minimum grade point average of 3.5 on all the core courses including the transferred equivalent courses that the student has completed. A student will choose two of the following topics to be on his or her qualifying examinations: algebra, analysis, topology, statistics, and discrete mathematics. Mathematics education will be the third topic.

Following the successful completion of all qualifying exams, a student may register for a maximum of three of the required eighteen dissertation credits until successful defense of the dissertation proposal.

Comprehensive Examination Requirements

A comprehensive oral examination of the student’s dissertation proposal will take place as part of the proposal defense.

Advancement to Candidacy

Application for advancement to candidacy.

The dean of The Graduate College approves advancement to candidacy once all requirements are met. Doctoral students must be advanced to candidacy within five years of initiating Ph.D. course work applied toward the degree. Students need to indicate their intent to advance to candidacy during the term they complete the 60 hours of required course work and other departmental requirements. The student will need to download the Advancement to Candidacy form from The Graduate College website. The student will need to complete the form and return it to the doctoral program director. The doctoral program director will then submit the completed form to the dean of The Graduate College for review.

The doctoral candidacy requirements include:

• Completion of all required course work with the exception of dissertation credit hours.
• Successful passage of all three qualifying exams.
• Successful passage of the comprehensive exam.
• Approval of the dissertation proposal.
• At least a 3.5 GPA on all doctoral required courses.

Advancement to Candidacy Time Limit

No credit will be applied toward the doctoral degree for course work completed more than five years before the date on which the student is advanced to candidacy. This time limit applies toward credit earned at Texas State as well as credit transferred to Texas State from other accredited institutions.

Requests for a time extension must be submitted to the doctoral program director, who in turn, submits a recommendation to the dean of The Graduate College.

Grade-Point Requirements for Advancement to Candidacy

To be eligible for advancement to candidacy, the student must have a minimum GPA of 3.5. No grade earned below a "B" on any graduate course may apply toward a Ph.D. at Texas State.

Incomplete grades must be cleared through the office of The Graduate College before a student can be approved for advancement to candidacy.

Dissertation Proposal

In order to be advanced to candidacy, a student must select a doctoral dissertation advisor and committee, submit a dissertation proposal, and successfully defend the proposal in an oral examination with the dissertation committee. The examination will address the problem definition and scope, the relevant literature, and the research method of the proposed dissertation topic. Information about the formation of the dissertation committee can be found in the "Dissertation Research and Writing" section of this catalog. 

Recommendation for Advancement to Candidacy

The doctoral program committee recommends the applicant for advancement to candidacy to the doctoral program director, the department chair, and the dean of The Graduate College. The dean of The Graduate College certifies the applicant for advancement to candidacy once all requirements have been met. To be eligible for admission to candidacy, the student must have successfully completed the qualifying and/or comprehensive exam(s), completed all course work, and successfully defended the dissertation proposal.

Dissertation Research and Writing

All doctoral students are required to complete a dissertation. The dissertation must be an original contribution to scholarship and the result of independent investigation in a significant area. Preparation of the dissertation must follow the latest edition of Kate L. Turabian's A Manual for Writers.

Dissertation Enrollment Requirements

After being admitted to candidacy, students must be continuously enrolled each term for at least three dissertation hours. If a student is receiving supervision on the dissertation during the summer or the student is graduating during the summer, the student must be enrolled in dissertation hours for the summer. All candidates for graduation must be enrolled in dissertation hours during the term in which the degree is to be conferred.

Students must complete a minimum of 18 semester hours of dissertation research and writing credit.

Dissertation Time Limit

Students are expected to complete the dissertation within three years of advancement to candidacy. The mathematics education program director will review the students' annual progress to ascertain his or her progress in pursuing the degree. The program director will consult with the student's Ph.D. advisor and dissertation committee on this matter as appropriate.

Dissertation Committee

A dissertation committee must be formed to oversee the research and writing of the dissertation. The dissertation committee will include a dissertation advisor and a minimum of three additional members (one of whom must be an external member).

The members must be chosen from qualified Ph.D. faculty. The dissertation advisor and the committee members must be selected in consultation with the student. The dissertation advisor will chair the dissertation committee and must be from the major department. The dissertation advisor and committee members must be approved by the doctoral program director, the department chair, and the dean of The Graduate College.

The student is responsible for obtaining committee members' signatures on the proper forms and submitting the forms to the department for further routing approval. The forms may be downloaded from The Graduate College website.

Committee Changes

Any changes to the dissertation committee must be submitted for approval to the dissertation committee chair, the doctoral program director, the department chair, and the dean of The Graduate College. Changes must be submitted no less than sixty days before the dissertation defense. The "Ph.D. Research Advisor/Committee Member Change Request form" may be downloaded from The Graduate College website.

Dissertation Defense

The dissertation defense may not be scheduled until all other academic and program requirements have been fulfilled. A complete draft of the dissertation must be given to the members of the dissertation committee at least 65 days before the date of commencement during the term in which the student intends to graduate. After committee members have reviewed the draft with the student and provided comments, the student, in consultation with the research advisor, will incorporate the recommended changes into a second draft of the dissertation. When each committee member is satisfied that the draft dissertation is defendable, dissertation defense will be scheduled.

The dissertation defense will consist of two parts. The first part is an oral presentation of the dissertation research given as a public seminar. The second part of the defense will immediately follow the public presentation, but is restricted to the student's dissertation committee, and will entail an oral examination over the dissertation research. The full committee, including all external members, must be present. Approval of the dissertation requires positive votes from the student's Ph.D. advisor and a majority of the remaining members of the dissertation committee. Specific information on the examination and defense procedure can be obtained from the doctoral program director.

Approval and Submission of the Dissertation

Following approval and signing of the dissertation by the members of the dissertation committee, the student must submit one copy of the dissertation and one signed "Thesis/Dissertation Committee Approval form" to The Graduate College for final approval. Specific guidelines for approval and submission of the dissertation can be obtained from the office of The Graduate College. Dissertations must be submitted in electronic format.

Doctoral level courses in Mathematics Education: ED , MATH

Courses Offered

Education (ed).

ED 7199A. Dissertation.

Original research and writing in Education-Adult, Professional and Community Education, to be accomplished under direct supervision on the dissertation advisor. While conducting dissertation research and writing, students must be continuously enrolled.

ED 7199B. Dissertation.

Original research and writing in Education-School improvement, to be accomplished under direct supervision of the dissertation advisor. While conducting dissertation research and writing, students must be continuously enrolled.

ED 7299A. Dissertation.

ED 7299B. Dissertation.

ED 7310. Instructional Roles in Counseling, Leadership, Adult Education & School Psychology.

This seminar is intended to prepare graduate teaching and instructional assistants in the CLAS Department to function effectively in various instructional and instructional support roles. Required for first-year teaching assistants and GIAs. This course does not earn graduate degree credit. Repeatable with different emphasis.

ED 7311. Educational Philosophy in a Social Context.

This course examines the philosophical foundations of education from the time of Plato through current writings. It frames these foundations through the lens of educational challenges of today. Readings include classical and current writings.

ED 7312. Leadership and Organizational Change.

This course will familiarize students with different perspectives on organizations, different paradigms by which they might be viewed, and a survey of research done on organizations, organizational leadership and change.

ED 7313. Advanced Studies in Adult Learning and Development.

This advanced seminar will examine research and theoretical literature on a variety of topics including: characteristics of adult learners; models of adult cognitive and psychosocial development; adult cognition, memory, and intelligence; and principles for facilitating adult learning. Restricted to Ph.D. in Education degree, Major in School Improvement.

ED 7314. Community Development for Educators.

Examines models and methods of community development as relevant to the practice and scholarship of formal and non-formal education.

ED 7315. Models of Inquiry: Understanding Epistemologies.

This course examines the philosophies informing different research epistemologies, and examples of how these can be actualized methodologically. Philosophies to be analyzed include feminism, and race-based theory. This course will help students see the multiple possibilities for conducting research.

ED 7316. Advanced Studies in Adult Development.

This course examines current theories of adult development, fundamental developmental changes in adulthood, and the implications for practice in adult education. Restricted to students admitted to the Education Ph.D. Program- APCE major or with permission of instructor.

ED 7318. Advanced Studies in Adult Learning.

This advanced seminar will examine research and theoretical literature on a variety of topics related to adult learning such as: characteristics and diversity of adult learners; key theories of adult learning; alternative perspectives on adult learning; intelligence, aging and wisdom; and learning in the digital age. Restricted to students admitted to the Education Ph.D. Program – APCE major or with permission of instructor.

ED 7320. Literature Review for Research Writing.

In this seminar course, students conduct a careful examination of a body of literature related to a research topic in adult/professional/community/lifelong education. The literature review tests research questions in relation to what is published about a topic, discusses various positions, crafts coherent arguments and addresses knowledge gaps. Prerequisites: ED 7352 or ED 7351 , all with a grade of "B" or better. Restriction: Doctoral standing.

ED 7321. Historical and Philosophical Foundations and Contemporary Issues in Adult Education.

Examines historical and philosophical foundations for the study and practice of adult professional, and community education in formal and non-formal settings; and contemporary issues in adult education in a “learning society.” Prerequisites: Core courses or instructor’s permission.

ED 7322. Human Resource and Professional Development.

Examines the methods, practices, and issues of facilitating learning related to occupational, professional, and volunteer roles. Prerequisites: Core courses or instructor’s permission.

ED 7324. Problems and Strategies in Program Planning Seminar.

Addresses principles and procedures, issues and trends, utilization of assessment, goal setting, and other effective strategies for developing learning opportunities and programs responsive to human, professional, and community needs. Prerequisites: Core courses or instructor’s permission.

ED 7326. Theoretical Foundations of Educational Policy, Politics and Practice.

This course examines the historical and theoretical underpinnings informing educational policy, politics and social justice. It addresses both the micro and macro levels of the context, values, and cultural norms guiding policy and practice in a democratic society. Prerequisites: ED 7311 and ED 7312 and ED 7313 , all with a grade of "C" or better.

ED 7327. Education Policy Development.

This course equips students with the skills needed to analyze the origins and consequences of existing policy and to play active roles in policy development for educational equity and social justice. Prerequisite: ED 7326 with a grade of "C" or better.

ED 7328. Research and Analysis in Education Policy.

This course engages students in a field-based educational policy research project using quantitative and qualitative techniques. Students will develop their skills to identify policy issues, gather and analyze data, and draw conclusions, and disseminate findings. Prerequisites: ED 7326 and ED 7327 and ED 7351 and ED 7352 , all with a grade of "C" or better.

ED 7329. Field-Based Experience in Educational Policy.

This course provides fieldbased practice in policy analysis and development from a democratic and social justice perspective. With guidance from a university faculty supervisor and site mentor, the student will develop and implement a policy project related to democracy and social justice. Prerequisite: ED 7328 with a grade of "C" or better.

ED 7331. Foundations of School Improvement.

Examines school improvement efforts from philosophical, political, psychological, cultural, ethical, and technological foundations. Prerequisites: Core courses or instructor’s permission.

ED 7332. Facilitating School Improvement.

Examines school culture, schools as learning communities, the change process, and research-based school improvement models, with experiential applications. Prerequisites: Core courses or instructor’s permission.

ED 7333. Curriculum and Instructional Leadership.

Examines the relationship between curriculum, instructional improvement, and teacher development, with experiential applications. Prerequisites: Core courses or instructor’s permission.

ED 7334. Models of Educational Assessment.

Includes assessment of student learning at the individual, classroom, school, and system level; teacher assessment; and program assessment. Prerequisites: Core courses or instructor’s permission.

ED 7341. Dissertation Proposal Development.

In this course students approaching dissertation stage meet in a seminar designed to help them clarify their research problem and develop a preliminary proposal for the dissertation. Core and concentration courses must be completed with minimum grades of "B" in each course prior to taking ED 7341 . Prerequisites: ED 7351 and ED 7352 , and ED 7353 or ED 7354 , all with a grade of "B" or better. Departmental approval required.

ED 7345. Human Resources and Instructional Management.

This course focuses on the twin areas of human resource administration and instructional improvement. Topics addressed include legal requirements for personnel management, staff supervision, appraisal, and development, curriculum planning and alignment and student assessment. Students taking the course will complete an original research project under the instructor’s direction.

ED 7347. The Superintendency.

This course addressed issues critical to superintendents in Texas. These include leadership, leadership assessment, school board relations, and other governance issues, management strategies, the role of public education in a democratic society, and professional ethics. Students taking the course will complete an original research project under the instructor’s direction.

ED 7349. School Finance and Business Management.

This course focuses on the financing of public schools. Students will examine the school budgeting process, sources of school revenues, principals of taxation, methods of school fund accounting, and techniques of business management. Students taking the course will complete an original research project under the instructor’s direction.

ED 7351. Beginning Quantitative Research Design and Analysis.

Includes descriptive statistics; sampling techniques; statistical inference including the null hypothesis, significance tests, and confidence intervals; and causal-comparative analyses, including t-test and ANOVA. Prerequisites: Core and Concentration courses or instructor’s permission.

ED 7352. Beginning Qualitative Design and Analysis.

Introduces the qualitative paradigm. Includes distinctive features, alternative qualitative traditions, purposeful sampling, common data collection methods, inductive analysis, the role of the researcher, and evaluating qualitative research. Prerequisites: Core and Concentration courses or instructor’s permission.

ED 7353. Intermediate Quantitative Research Design and Analysis.

This course focuses on issues in the design and implementation of quantitative research. Topics include ANOVA, ANCOVA, and MANOVA, correlation analysis, regression analysis, nonparametric tests, and relationships between experimental designs and statistical analysis techniques. Prerequisite: ED 7351 with a grade of "B" or better, or instructor’s permission.

ED 7354. Intermediate Qualitative Design and Analysis.

Focuses on issues in design and implementation of qualitative research. Topics include influence of alternative traditions, literature in qualitative research, access to the field and ethical issues, researcher-participant relationships, purposeful sampling strategies, inductive analysis procedures, developing theory, and reporting research. Prerequisite: ED 7352 with a minimum grade of "B", or instructor’s permission.

ED 7357. Advanced Study in Action Research.

This course examines underlying theory, practice, skills, and issues in action research. Conducting research in the area of action research is also addressed. This course is an appropriate elective for majors in School Improvement or Adult, Professional and Community Education.

ED 7359. Seminar in Quantitative Research.

This course is a small group seminar that focuses on analytic strategies specific to the doctoral student’s dissertation topic. Examples include structural equation modeling, hierarchical linear modeling, log linear modeling, non-parametric analyses, factor analysis, factorial analysis of variance, and other multivariate statistical methods. Prerequisites: ED 7351 and ED 7353 , all with a grade of "B" or better.

ED 7364. Team Development in Education.

This course addresses the development and use of educational teams to improve educational organizations, teaching, and learning. Because of its focus on education, it is recommended only for doctoral students preparing for careers in educational settings.

ED 7371. Anthropology and Education.

This course introduces the student to the basic concepts in anthropology and education and sketches the application of these concepts. It explores the research in anthropology and education with relevance to both K-12 schools and other, more general educational settings. The course is an appropriate elective for Education Ph.D. majors.

ED 7378. Problems in Education.

Individual problems or topics will be designed and completed to emphasize selected areas of study. May be repeated for additional credit at the discretion of the program coordinator.

ED 7379. Independent Study.

Individual problems or topics will be designed and completed to emphasize selected areas of study in the Counseling, Leadership, Adult Education & School Psychology Department. May be repeated for additional credit at the discretion of the program coordinator.

ED 7389B. Seminar in International Educational Research: Chile.

This course develops theoretical knowledge, methodological skills, and scholarly capacity for international educational research. It focuses on research within the complex educational environment of Chile, involving seminar components held at the university and research fieldwork in Chile. International research is framed as a form of service learning. Restricted to students in the PhD in Education program.

ED 7389C. Advanced Theory in Qualitative Research.

This course features advanced study in qualitative research methods. The course studies such methods as ethnography, case study, phenomenology, narrative analysis, post-qualitative research, grounded theory, or more advanced qualitative research in general and their constitutive field techniques. Prerequisites: Introduction to Qualitative Research and Intermediate Qualitative Research.

ED 7389D. Advanced Theory in Qualitative Research: Narrative Research.

The purpose of this course is to explore the possibilities of narrative research. The course will provide an overview of narrative inquiry, look at various theories and corresponding examples of research, and explore, analyze, and interpret data using narrative methods. Prerequisites: Introduction to Qualitative Research and Intermediate Qualitative Research.

ED 7389E. Mexican Perspectives on Mexico - U.S. Immigration.

The course gives U.S. educators an understanding of Mexican to U.S. immigration from Mexican women’s perspectives. Students will read background information and visit Mexico where through lectures, field interviews, and field visits, they will view immigration from the “other side”. They will analyze and write up data when they return. (MULT).

ED 7389H. Oracy and Language Expression for Educators.

This course focuses on the theory and practice of language expression. It emphasizes the relationship between audience analysis, speaker goals, organized outlines, delivery and development of personal style of presentation skills. The course offers direct experience writing, delivering, and constructively evaluating public speeches in a variety of educational contexts.

ED 7389I. Comparative Studies in International Adult Education.

This course compares a model of adult learning, communities of practice (CoP) today with its practice in pre-historical times. It will involve international travel and working with scholars to contrast theory and practice in the United States with the new setting. Students from both contexts will be encouraged to present their work in a conference format.

ED 7389L. Writing for Publication.

Students will hone their writing skills. Students will work individually and in groups, getting feedback from other students and the instructor. Topics include APA style, getting started, first drafts, polishing and tightening, re-writing, submitting a manuscript, responding to feedback/reviews and more. Restricted to masters' and doctoral students.

ED 7389M. Shifting Demographics in Texas: Exploring Education, Democracy and Healthy Communities.

Students will explore the shifting population in Texas through multiple frames including historical, sociological, anthropological and political. Class will canvas the literature and emerging community conditions as a vehicle for imagining possible theoretical, policy and local responses to the conditions we see in schools and local communities.

ED 7389O. Educational Privatization: Policies, Actors, and Effects.

This course interrogates the origins and outcomes of educational privatization. In this course, students will review the foundations of education as a public good, study frameworks and theories of privatization, trace public policies promoting privatization, delineate types of educational privatization over time, and examine the actors involved in educational privatization.

ED 7389P. International Comparative Adult, Community, and Higher Education Research and Study: Italy.

This course develops theoretical knowledge, methodological skills, and scholarly capacity for educational research. It focuses on comparative adult, higher, and socio-cultural education within the complex educational environment of Italy, involving seminar components held at the university and research fieldwork and presentation in Italy. Prerequisite: Should the student not be able to participate in the international component of the course, a domestic alternative can be discussed prior to enrollment.

ED 7389Q. Schools, Communities and Race in a Democratic Society.

The class explores race through a personal lived perspective. This class will view race as a social construct. Students will interrogate the phenomena of race through multiple lens and frames, including but not limited to, an ontological perspective, its use in organizations, and its use in re-segregating society.

ED 7389R. Understanding the Self: Anatomy of Engaged Scholarship.

Successful leadership in school settings requires an understanding of human behavior. This understanding begins with knowledge of self and leads to the understanding of others at the micro and macro levels. The focus of this course is on you, the learner, and your surroundings. The goal is to enhance the student’s self-awareness of values, beliefs, attitudes and the ecological context informing and impacting their school leadership experience. This understanding will inform the past, but also begin to inform your future as you matriculate through your course work. We will employ interdisciplinary literature to inform this work.

ED 7389S. Feminist and Critical Thought in Education.

Feminist and Critical thought provides a means to examine and understand how issues of power shape and impact cultures, societies, and their associated policies and practices. In this seminar, students will engage with varying feminist and critical perspectives, frameworks, theories, epistemologies and methodologies to consider their application in examining their own educational journeys as well as current and systemic issues in education. Course readings and materials will primarily draw from the work of seminal and minoritized feminist and critical scholars, while providing students an opportunity to identify and explore course readings and materials of their choice as well.

ED 7399A. Dissertation.

Original research and writing in Adult, Professional, and Community Education, to be accomplished under direct supervision of the dissertation advisor. While conducting dissertation research and writing, students must be continuously enrolled each semester (including summer) for at least three dissertation hours.

ED 7399B. Dissertation.

Original research and writing in School Improvement, to be accomplished under direct supervision of the dissertation advisor. While conducting dissertation research and writing, students must be continuously enrolled each semester (including summer) for at least three dissertation hours.

ED 7599A. Dissertation.

ED 7599B. Dissertation.

ED 7699A. Dissertation.

The student conducts original research and writing in Adult, Professional, and Community Education, guided by the direct supervision of the dissertation chair. While conducting dissertation research and writing, students must be continuously enrolled.

ED 7699B. Dissertation.

Students produce a dissertation under direct supervision of dissertation advisor. While conducting dissertation research and writing, students must be continuously enrolled. Prerequisites: Core, Concentration, and Methodology courses or instructor’s permission.

ED 7999A. Dissertation.

ED 7999B. Dissertation.

Original research and writing in Education-School Improvement, to be accomplished under direct supervision of the dissertation advisor. While conducting dissertation research and writing, students must be continuously enrolled.

Mathematics (MATH)

MATH 7111. Seminar in Teaching.

Seminar on individual study projects concerned with selected problems in the teaching of mathematics. This course does not earn graduate degree credit.

MATH 7188. Seminar in Mathematics Education.

Students are required to attend weekly research seminars in Mathematics Education and to give at least one research presentation in the seminar during the semester. This course is repeatable for credit.

MATH 7199A. Dissertation.

Original research and writing in Mathematics Education to be accomplished under direct supervision of the dissertation advisor. While conducting dissertation research and writing, students must be continuously enrolled each long semester.

MATH 7299A. Dissertation.

This course represents a Mathematics Education student's dissertation enrollments. The course can be repeated as necessary. The dissertation credit (18 hours) will not be awarded until the dissertation is submitted for binding. Prerequisite: completion of the core and required concentration courses, or approval of student's dissertation advisor.

MATH 7301. Studies in Mathematics.

This course provides basic foundations in Mathematics for students entering the doctoral program in Mathematics Education. This course may be repeated. This course does not earn graduate degree credit.

MATH 7302. History of Mathematics.

A study of the development of mathematics and of the accomplishments of men and women who contributed to its progress.

MATH 7303. Analysis I.

This course covers foundations of modern analysis. Topics include: sequences, LimSup, LimInf, Sigma Algebras of sets that include open and closed sets, sequences of functions, pointwise and uniform convergence, lower and upper semi-continuity, Borel sets, outer measure, and Lebesgue measure. Prerequisite: MATH 4315 .

MATH 7306. Current Research in Math Education.

This course surveys the various current social, political, and economic trends in local, state, national, and international settings that are related to research in Mathematics Education.

MATH 7307. Algebra I.

Applications of Algebra and topics in modern algebra, including permutation groups, symmetry groups, Sylow theorems, and select topics from Ring Theory. Prerequisite: MATH 4307 .

MATH 7309. Topology I.

A course in point-set topology emphasizing topological spaces, continuous functions, connectedness, compactness, countability, separability, metrizability, CWcomplexes, simplicial complexes, nerves, and dimension theory. Prerequisite: MATH 4330 .

MATH 7313. Analysis II.

This course covers the theory of integration with special emphasis on Lebesgue integrals. Topics include: Lebesgue integral, Bounded Convergence theorem, differentiation and integration, absolute continuity, and Lp spaces. Prerequisite: Math 7303.

MATH 7317. Algebra II.

A study of the important algebraic structures of rings and fields. Topics covered include rings, ideals, modules, polynomial rings, Euclidean algorithm, finite fields, and field extensions. Topics also include an introduction to Galois Theory with an emphasis on the geometric applications. Prerequisite: MATH 7307 .

MATH 7319. Topology II: Algebraic Topology.

This course covers the fundamental concepts and tools of algebraic topology. Topics include the fundamental group, covering spaces, homotopy type, the higher homotopy groups, singular homology theory, and the computation of homology groups via exact sequences and applications. Prerequisite: MATH 7307 and MATH 7309 .

MATH 7321. Graph Theory.

Topics in this course include trees, connectivity of graphs, Eulerian graphs, Hamiltonian graphs, planar graphs, graph coloring, matchings, factorizations, digraphs, networks, and network flow problems. Prerequisite: MATH 3398 .

MATH 7323. Theories of Knowing and Learning in Mathematics Education.

This course surveys the major theories of knowing and learning that have influenced mathematics education. These theories include behaviorism, constructivism, sociocultural theories, situated cognition, and others.

MATH 7324. Curriculum Design & Analysis.

This course examines, analyzes, and evaluates the various concepts, topics, methods, and techniques that are related to curriculum design in Mathematics Education for grade levels P-16.

MATH 7325. Statistics 1.

A study of the mathematical and probabilistic underpinnings of the techniques used in statistical inference. Topics covered include sampling, sampling distributions, confidence intervals, and hypothesis testing with an emphasis on both simulations and derivations. Prerequisite: Math 2321 and Math 3305.

MATH 7328. Instructional Techniques & Assessments.

This course examines, analyzes, and evaluates the various concepts, topics, methods, and techniques of instruction in Mathematics Education and the related assessment procedures for each for grade levels P-20.

MATH 7331. Combinatorics.

This course is a study of fundamental principles of combinatorics. Topics include: permutations and combinations, the Pigeonhole principle, the principle of inclusion-exclusion, binomial and multinomial theorems, special counting sequences, partitions, posets, extremal set theory, generating functions, recurrence relations, and the Polya theory of counting. Prerequisite: MATH 3398 .

MATH 7335. Statistics II: Linear Modeling.

A study of the formulation and statistical methodologies for fitting linear models. Topics include the general linear hypothesis, least-squares estimation, Gauss-Markov theorem, assessment of model fit, effects of departures from assumptions, model design, and criteria for selection of optimal regression models. Prerequisite: MATH 3377 and MATH 7325 .

MATH 7346. Quantitative Research Analysis in Mathematics Education.

This course surveys the various research techniques used in quantitative analysis for mathematics education and covers topics such as experimental design, statistical analysis, and use of appropriate design methodologies to achieve the strongest possible evidence to support or refute a knowledge claim. Prerequisite: MATH 7306 and MATH 7325 .

MATH 7354. Advanced Qualitative Research.

This course encompasses the techniques and tools needed for the development, investigation, and demonstration of competence in conducting qualitative research in mathematics education. Principles of qualitative data analysis are a significant focus of the course, with particular attention given to specific methods used to code and analyze data. Prerequisite: ED 7352 with a grade of "B" or better.

MATH 7356B. Advanced Qualitative Research.

This course encompasses investigation, development, and demonstration of competence, design, and execution for mathematics education problems in qualitative research. Prerequisite: ED 7352 or CI 7352 .

MATH 7356C. Action Research in Mathematics Education.

This course examines underlying theory and issues in action research model and the development of action research projects. Prerequisites: MATH 7346 or ED 7352 .

MATH 7358. Advanced Quantitative Research in Mathematics Education.

This course surveys the various research techniques used in quantitative analysis for mathematics education and covers topics such as experimental design, statistical analysis, and the use of appropriate design methodologies to achieve the most substantial evidence to support or refute a knowledge claim. Prerequisite: MATH 7346 with a grade of "B" or better or permission of instructor.

MATH 7361. Seminar in Advanced Mathematics.

Material in course will vary with the interest of students and faculty. A detailed study of subject matter may be chosen from advanced areas of analysis; algebra; topology and geometry; applied mathematics; and probability and statistics. This course is repeatable for credit when subject matter varies.

MATH 7363C. FUNCTNL ANALYSIS.

MATH 7366A. Teaching Post-Secondary Students (Developmental Math, Service Courses, and Majors).

This course examines how to develop and teach post-secondary students. The course references the recommendations of government agencies and professional organizations and allows for the investigation of research-based models. Prerequisites: MATH 7306 .

MATH 7366B. Teaching K-12 Students (Elementary, Middle School, and High School).

This course examines how to develop and teach K-12 students. The course references the recommendations of government agencies and professional organizations and allows for the investigation of research-based models. Prerequisite: MATH 7306 .

MATH 7366C. Teaching Teachers (In-Service; Pre-Service).

This course examines how to prepare teachers of mathematics. The course references the recommendations of government agencies and professional organizations and allows for the investigation of research-based models. Prerequisite: MATH 7306 .

MATH 7366D. Teaching Specialized Content.

This course will be an in-depth study of a specialized content area in mathematics with an emphasis on teaching. The specific content area will vary by instructor. Examples include Euclidean Simplex Geometry and Discrete Probability Spaces with Implications for Public School Curriculum.

MATH 7366E. Developmental Mathematics Curriculum.

This course surveys the research, development, and evaluation of the scope and sequence of developmental mathematics curriculum. The course references the recommendations of government agencies and professional organizations and allows for the investigation of research-based models.

MATH 7366F. Research in Undergraduate Mathematics Education I.

Students will develop the requisite knowledge to become a good consumer of Research in Undergraduate Mathematics Education (RUME) research. The course will cover the theoretical underpinnings of current and historic RUME research. Students will develop the knowledge to understand relevant theoretical stances and the role they play in research. Prerequisite: Math 7306 or permission from the instructor.

MATH 7366G. Research in Undergraduate Mathematics Education II.

In this course, students will develop necessary knowledge to design/conduct RUME research via a topic-driven look at current RUME research. Core topics include proof, analysis/calculus, abstract algebra, linear algebra, and differential equations. Students will develop a depth of knowledge related to these topics and engage in research design and development. Prerequisite: MATH7306 and MATH7366F.

MATH 7371A. Advanced Graph Theory.

Topics in this course include Turan's problems, Ramsey theory, random graph theory, extremal graph theory, algebraic graph theory, domination of graphs, distance problems, and applications. Prerequisite: MATH 7321 .

MATH 7371B. Advanced Combinatorics.

Topics in this course include Block designs, Latin squares, combinatorial optimization problems, coding theory, matroids, difference sets, and finite geometry. Prerequisite: MATH 7331 .

MATH 7371C. Combinatorial Number Theory.

A study of fundamental techniques in combinatorial number theory. Topics will include Waring's problem, additive number theory, and probabilistic methods in number theory. Prerequisite: MATH 7331 .

MATH 7371D. Discrete Optimization.

A study of some fundamental techniques in discrete optimization. Topics include discrete optimization, linear programming, integer programming, integer nonlinear programming, dynamic programming, location problem, scheduling problem, transportation problem, postman problem, traveling salesman problem, matroids, and NP-completeness. Prerequisites: MATH 7321 and 7331 .

MATH 7371E. Algorithms and Complexity.

A study of some fundamental concepts of computability and complexity. Topics include polynomially bounded problems, NP-complete problems, exponentially hard problems, undecidable problems, and reducibility. Prerequisite: MATH 7331 .

MATH 7371F. Probabilistic Methods in Discrete Mathematics.

A study of some fundamental probabilistic techniques used to solve problems in graph theory, combinatorics, combinatorial number theory, combinatorial geometry, and algorithm. Topics include linearity of expectation, alterations, second moment, local lemma, correlation inequalities, martingales, Poisson paradigm, and pseudo-randomness. Prerequisites: MATH 7321 and 7331 .

MATH 7371G. Applied Discrete Mathematics.

This course introduces fundamental concepts in logic, Boolean algebra, and binomial coefficients; and applications in different fields such as complexity of algorithms and network theory. Prerequisites: MATH 2472 and MATH 4307 , all with a grade of “C” or better, or with departmental approval.

MATH 7371H. Combinatorial Networks.

Combinatorial Networks is an area of study of certain types of networks using combinatorial methods extensively. This course introduces fundamental basics as well as the latest development in this area of research. Prerequisite: MATH 5307 /7307 with a grade of "C" or higher.

MATH 7375C. Time Series Analysis.

A study of the theory of time-dependent data. The analysis includes modeling, estimation, and testing; alternating between the time domain; using autoregressive and moving average models and the frequency domain; and using spectral analysis. Prerequisite: MATH 7335 .

MATH 7375D. Advanced linear Modeling.

The course provides an extension of regression methodology to more general settings where standard assumptions for ordinary least squares are violated. Topics include generalized least squares, robust regression, bootstrap, regression in the presence of autocorrelated errors, generalized linear models, and logistic and Poisson regression. Prerequisite: MATH 7335 .

MATH 7378A. Problem Solving, Reasoning, and Proof.

A study of the fundamental concepts of problem solving, logic, set theory, and mathematical proof and applications of these concepts in mathematics curriculum for grades P-20. Prerequisite: MATH 7306 .

MATH 7378B. Connecting and Communicating Math.

This course examines one of the basic principles involved in mathematics education: Connecting and Communicating Mathematics. This fundamental theme will be reviewed, researched, and discussed. Prerequisite: MATH 7306 .

MATH 7378C. Representing Fundamental Math Ideas (Function, Data Analysis, and Enumeration).

This course examines the basic principles involved in mathematics education. The process of representing fundamental mathematical ideas will be reviewed, researched, and discussed. Prerequisite: MATH 7306 .

MATH 7378D. Math Technologies.

This course examines the basic principles involved in mathematics education: Technology. This fundamental theme will be reviewed, researched, and discussed. Prerequisite: MATH 7306 .

MATH 7378E. Developmental Mathematics Perspectives.

This course examines developmental mathematics-specific strands including technological course support and placement tools/decisions. Issues related to the first mathematics core course required of undergraduates will aslo be addressed.

MATH 7378F. Research on Mathematical Problem Solving in Secondary Schools.

In this course a careful study is made of elementary techniques for problem solving in a variety of domains, including algebra, number theory, combinatorics, geometry, and logic puzzles. Students will learn these techniques by actually working on a collection of problems in each of these areas. Students will read and examine research about various aspects of problem solving and research in math education that includes both teacher training and student learning.

MATH 7378G. Discourse Processes, Traditions, and Analysis in Mathematics Education.

Discourse and discourse analysis have been used to answer research questions across disciplines throughout the humanities and social sciences. This course will focus on theory and methods for the analysis of discourse in mathematical settings. We will learn how different approaches to discourse are used to understand mathematics learning. Prerequisite: MATH 7306 .

MATH 7378H. Equity in Mathematics Education.

Equity in Mathematics Education is a course examining research on equity issues in mathematics education. These equity issues will range from race, culture, class, and gender as they relate to the teaching, learning, and schooling of mathematics education. We will look at how equity is framed within the field of mathematics education, what has been addressed, and what has not been conceptualized. The course will help students understand the literature in the field, critique the extant research literature, design research, and consider important facets of teaching for various student groups. Prerequisite: MATH 7306 with a grade of "C" or better.

MATH 7385. Independent Study in Mathematics.

Student will work directly with a faculty member and develop in-depth knowledge in a specific topic area of mathematics. Topics vary according to student’s needs and demands. Repeatable with different emphasis.

MATH 7386. Independent Study in Mathematics Education.

Student will work directly with a faculty member and develop in-depth knowledge in a specific topic area of Mathematics Education. Topics vary according to student's needs and demands. Repeatable with different emphasis.

MATH 7389. Internship.

Students will work under the supervision of a faculty member to gain practical knowledge in Mathematics Education. Student experience can come from industry, government agencies, or other sources but must directly apply to furthering knowledge of mathematics education or its application.

MATH 7396. Mathematics Education Research Seminar.

Collaborative research projects with faculty through identifying an educational issue, reviewing literature, creating a research question, designing a methodology, analyzing data, drawing conclusions, implications, and creating a draft of a publishable paper. Prerequisite: MATH 7356, and ED 7352 or MATH 7346 , all with a grade of "B" or better.

MATH 7399A. Dissertation.

MATH 7599A. Dissertation.

MATH 7699A. Dissertation.

MATH 7999A. Dissertation.

2023-2024 Catalogs

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Doctor of Philosophy in Mathematics

• Fall January 10
• Spring September 10

International students may need to surpass the Graduate School’s minimum English language proficiency exam scores for this program. If the graduate program has unique score requirements, they will be detailed below. Otherwise, please refer to the Graduate School’s minimum score guidelines.

• 540 TOEFL Minimum score for admission
• 75 TOEFLI Minimum score for admission
• 6.5 IELTS Minimum score for admission
• 105 Duolingo Minimum score for admission

Degree Description:

PhD in Mathematics This degree is awarded in recognition of distinctive scholarship and original contributions to knowledge in Mathematics. The PhD program is especially designed to prepare the student for teaching at the graduate level and doing mathematical research in academic, industrial and business settings. Students studying various fields within the realm of pure mathematics would be included in this PhD program.

PhD in Mathematics (Applied Mathematics Option) The specialization of modern academic disciplines provides both a challenge to those who wish to do research at the interface of mathematics and its areas of application and many opportunities to make valuable contributions. The Applied Mathematics Option allows students from a range of backgrounds to pursue a traditional applied mathematics program, while retaining the option to thoroughly learn an area of application. Entering students may not necessarily have a bachelor’s degree in Mathematics. However, they will be required to demonstrate a grasp of the core areas of advanced calculus and linear algebra at the level of a bachelor’s degree in Mathematics. They will then be given great latitude to take specialized courses in Mathematics and their area of application.

PhD in Mathematics with Education Emphasis The degree of PhD in Mathematics with Education Emphasis is awarded in recognition of scholarship and original contributions to the teaching and learning of mathematics. The main difference from the other PhD choices is in the research focus. The requirements for this PhD include competence in core mathematics, as well as study in the research methodologies applicable to research in mathematics education.

Admission Requirements:

Students should have taken upper-level analysis and linear algebra courses before applying, and have the equivalent of an undergraduate degree in mathematics, statistics, or a related field. Additional upper-level courses like abstract algebra, functional or complex analysis, optimization, applied mathematics, topology, etc. will be taken into account.

For international students, either a TOEFL, IETLS or Duolingo score is required. The minimum score for admission is listed above. The minimum score required for assistantship consideration is TOEFL score of 100, IELTS of 7, or Duolingo of 130. Exceptions can be found here:  https://gradschool.wsu.edu/international-requirements/

Students applying to the PhD Mathematics program will be automatically considered for an assistantship position.

The application will require:

• Unofficial transcripts from all previous institutions.
• GPA above a 3.0 on a 4.0 scale.
• Email contact information for 3 references.
• Personal statement. The personal statement is your chance to highlight relevant experiences and discuss your future research interests.
• GRE scores are not required but encouraged.

Career Opportunities:

Academia (tenure-track positions at universities and colleges worldwide), Bio-statistics (health and pharmaceutical companies), Risk analysis (financial and insurance companies, investment management), Research (state or federal government, software development), Mathematics education (publishing, consulting and developing of educational software).

Career Placements:

Graduates from the Mathematics PhD program begin careers in both academia and government or industry. A few examples of career placements in academia from the past few years include:

• Postdoc, USDA Northwest Climate Hub and WSU Center for Sustaining Agriculture
• Assistant Professor, Central Washington University
• Assistant Professor, Marian University (WI)

A few examples of career placements in government and industry from the past few years include:

• Regulatory Data Scientist, Office of Regulatory Innovation and Assistance, Washington State Government
• Quantitative Model Validation Analyst, First Tech Federal Credit Union (OR)
• Data Scientist, Emsi Labor Market Analytics (ID)

Contact Information:

• Graduate Coordinator [email protected]

Natural Sciences and Mathematics

Mathematical sciences.

Doctor of Philosophy in Mathematics

The program offers extensive coursework and intensive research experience in theory, methodology, and applications of mathematics (see  degree requirements ). 

• Faculty members with broad and diverse research interests are available to supervise doctoral dissertations .
• Financial support in the form of assistantships, full tuition support, and scholarships and awards are provided. Additional scholarships are available for US citizens and permanent residents.
• Our students, both domestic and international, have a strong record of starting in full-time jobs right after graduation .
• Students have opportunities to participate in active seminar series in  Algebra and Combinatorics ;   Computational Science ;  Geometry, Topology and Dynamical Systems ; and  Nonlinear Analysis and Dynamical Systems ; and the departmental  Colloquium  series.
• To enhance career prospects, students can pursue  Graduate Certificate in Data Science , and possibly use the certificate courses to fulfill the elective requirements.
• NSM Career Success Center  is available to support professional development and experiential learning of students.  
• GRE test score is not required for admission.

More than 85% of our 45 Mathematics PhD graduates since 2020, both domestic and international, secured full-time employment within a few months of receiving their degrees. 

Placement of 2022 & 2023 Mathematics PhD Graduates

See a more complete list  

Assistantships

Graduate Teaching Assistantships are offered to qualified PhD students on a competitive basis. These assistantships include a monthly stipend (currently set at $2,400) along with a full tuition waiver (covering 9 credit hours per term in the Fall and Spring semesters). The assistantship additionally covers the cost of health insurance purchased through the university and most fees. Graduate Research Assistantships for advanced PhD students are also available on some faculty members’ research grants. Typically, assistantship support is provided for five years and encompasses the Summer semester as well.

All admitted students are considered for assistantships; no separate application is necessary. 

Scholarships, Fellowships & Awards

PhD students are additionally supported through the following awards:

• NSM McDermott PhD Admission Fellowship  (for highly qualified new students, offered at the time of admission)
• Dean’s Fellowship  and  EEF Scholarship  (for highly qualified new students who are U.S. citizens and permanent residents, offered at the time of admission)
• Julia Williams Van Ness Merit Scholarship  and  Mei Lein Fellowship
• Outstanding Teaching Assistant of the Year Award
• Dean of Graduate Education Dissertation Research Award
• Best Dissertation Award ,  David Daniel Thesis Award , and  Outstanding Graduate Student Award

Conference Travel Support

NSM Conference Travel Award  and  Betty and Gifford Johnson Travel Award  are available to provide financial support to PhD students to present their research at professional conferences.

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Doctor of Philosophy in Mathematics

Program description.

The Mathematics PhD degree curriculum at The University of Texas at Dallas offers extensive coursework and intensive research experience in theory, methodology and applications of mathematics. During their study, PhD students acquire the necessary skills to prepare them for high-level careers in fields requiring mathematical sophistication. The PhD program is designed to accommodate the needs and interests of the students. The student must arrange a course program with the guidance and approval of the graduate advisor. Adjustments can be made as the student’s interests develop and a specific dissertation topic is chosen.

Some of the broad research areas represented in mathematics are as follows: algebraic and complex geometry; analysis and its applications; control theory and optimization; dynamical systems and ordinary differential equations; differential geometry; mathematical physics; mathematical methods in medicine, biology, geosciences and mechanics; numerical analysis and scientific computing; partial differential equations; and topology.

Career Opportunities

Graduates of the program seek positions such as: professor in an academic institution, or professional in industry, government or finance and researcher in public or private sector. Available emphases ensure that candidates can tailor their future career by having targeted their educational background to their research interests.

The jobs of a mathematician consistently appears among the top jobs in the rankings of 200 jobs by CareerCast’s Jobs Rated Almanac based upon factors such as work environment, income, hiring outlook and stress. For more information about careers in mathematics, view the career page of American Mathematical Society.

Marketable Skills

Review the marketable skills for this academic program.

Application Deadlines and Requirements

The university  application deadlines apply with the exception that, for the upcoming Fall term, all application materials must be received by December 15 for first-round consideration of scholarships and fellowships. See the  Department of Mathematical Sciences graduate programs website  for additional information. 

Visit the  Apply Now  webpage to begin the application process. 

Contact Information

For more information, contact [email protected]

School of Natural Sciences and Mathematics The University of Texas at Dallas 800 W. Campbell Road Richardson, TX 75080-3021 Phone: 972-883-2416

nsm.utdallas.edu

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• Department of Mathematics

Graduate Studies

• Mathematics, PhD

Doctor of Philosophy in Mathematics (Ph.D.)

Requirements outline.

The Ph.D. degree is a research degree and the principal requirement is that a student writes an original research thesis. The thesis is produced under the supervision of a faculty member and is examined by a committee of three departmental faculty and an outside expert. To qualify to write a thesis, a candidate for a Ph.D. in mathematics first must pass three Preliminary Examinations. It is recommended that Ph.D. candidates discuss possible research opportunities with the Director of Graduate Studies and/or faculty members soon after they enter the Ph.D. Program. Entering students should outline an appropriate sequence of courses to learn the essential material for pursuing their research interests. After a student has passed the Preliminary Examinations they must choose an advisor from the Mathematics Department faculty. A candidate's thesis usually is developed and written with the guidance of this advisor who will later chair the thesis defense committee. The time required to obtain a Ph.D. degree varies a lot. The department does not support graduate students as Teaching Assistants for more than five academic years.

Ph.D. Degree Requirements

The requirements that must be satisfied for a candidate to receive a Ph.D. include:

• The candidate must pass Preliminary Examinations .
• The candidate must obtain a grade of B or better in at least 24 semester credit hours of courses in the Mathematics Ph.D. program. Students should take doctoral research classes MATH 8x98 (where “x” is the number of credit hours) while conducting thesis research. Students must register for. the course MATH 8x99 “Doctoral Dissertation” in the semester when they intend to graduate
• After passing all three Preliminary Examinations the candidate is subject to Annual Performance Review (APR). The APR evaluates research progress of the candidate. The APR is conducted in oral or written form by a committee consisting of at least two faculty members of the Mathematics Department. The APR committee is chaired by the candidate’s advisor. Candidates failing the APR are subject to termination from the Ph.D. program.
• The candidate must be in residence, and take 9 semester credit hours of courses, in two consecutive long semesters, Fall followed by Spring. Alternatively, the candidate must be in residence and take a full load in consecutive Spring, Summer, and Fall terms.
• The candidate must write a Doctoral Dissertation with the guidance of an advisor who is a regular faculty member of the Mathematics Department.
• The candidate must defend their Dissertation in a public examination by a thesis committee consisting of at least 4 members, three of whom are faculty members in the Mathematics Department and at least one member outside UH Mathematics Department.
• NSM Thesis and Dissertation General Guidelines and Instructions
• NSM Thesis and Dissertation Formatting Instructions
• NSM Thesis and Dissertation Submission Instructions
• NSM Checklist for Thesis and Dissertation Review
• NSM Deadlines & Academic Calendar : This link provides deadlines for the submission of Dissertations.
• *The Graduate Record Examination (GRE) is waived for the Ph.D program within the Department of Mathematics.
• International students can not exclusively register for online courses.

Course Selection:

• Information about courses may be found at this link .
• Students can discuss advisor selection process with the Director of Graduate Studies.
• The above is only an outline of the primary requirements for the degree. The Director of Graduate Studies and others can provide more detailed information about conditions. The college and the university may have further requirements as listed at College and websites.
• PhD students can take topics classes at Rice University, UT Health, UTMB, or Baylor College of Medicine. Students must submit the Inter-Institutional Course Registration Form to the Graduate Director for approval. Taking an outside class must be essential for the completion of graduate degree. Thus, students must obtain a prior approval of their PhD avisor (signature on the form).
• Course Selection Requests: Please contact the Director for Instructional Support and Coordination < [email protected] > for more information.

Teaching Opportunities for Ph.D. Students:

As a condition, a student should have experiences of teaching Calculus recitation class with reasonable teaching evaluation. For an international student, by Texas law, the student must pass the English SPEAK test or its equivalence.

All PhD applicants who submit their complete application before the appropriate deadline are automatically considered for Teaching Assistantship.

Please contact the Director for Instructional Support and Coordination for more information about course selection requests .

Preliminary Examinations:

The Preliminary Examination is the final step in assessing the student’s ability and appropriate mathematical background to undertake a program of supervised research and study leading to a Ph.D. in Mathematics. Students who have completed their Master's degree in Mathematics may often be ready to take the Preliminary Examination without further course study.

Preliminary Examinations are three-hour, closed book written examinations that are given in each of the topics listed below. The questions in the examination emphasize problem solving skills and mathematical ability as opposed to rote memorization.

Preliminary Examinations are usually offered twice a year: at the end of the Fall and Spring semesters.

Students who receive support from the Department of Mathematics are expected to pass the Preliminary Examination according to the rules below. For non-supported students, the University rules apply.

All students are supposed to pass three Preliminary Examinations before the beginning of their third year in the Ph.D. program.

The following rules apply:

1. Students must pass three Preliminary Examinations from the different topic groups listed below

2. At least one out of the three Preliminary Examinations must be a core sequence. Core sequences are:

Review information for the preliminary written examinations:

Additional problems from past preliminary exams:

All preliminary exams are based on the content of the corresponding course. Please contact the instructor who taught the corresponding course most recently to obtain the up-to-date information.