Teachers College, Columbia University
Department of Mathematics, Science and Technology
Program Study Guide for:
Mathematics Education
Degree: Ph.D.
Major Code: MATH
This academic Program Study Guide has been developed to assist you in planning your
course of study at Teachers College. Below you will find the Study Guide for the program
to which you have been admitted.
We hope this Study Guide provides a helpful introduction and orientation to your
program. Given the richness and complexity of graduate and professional programs at
Teachers College, these Study Guides are intended to be illustrative, rather than definitive.
The TC Catalog, for the year in which you were admitted, is available online
(http://catalog.tc.columbia.edu/tc/) and remains the official reference document for College
policies and program requirements and, if applicable, the appropriate doctoral
requirements bulletin.
Congratulations, again, on your admission to graduate study at Teachers College,
Columbia University!
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2
TEACHERS COLLEGE COLUMBIA UNIVERSITY
Department of Mathematics, Science and Technology
MATHEMATICS EDUCATION PROGRAM
Doctor of Philosophy in Mathematics Education
Doctor of Philosophy Degree (Ph.D.)
Major Code: MATH
Brief Program Description
The Doctor of Philosophy in Mathematics Education degree program emphasizes research and
intensive specialization in some area of mathematics education. The degree requirements allow
students significant flexibility in choosing a particular field of interest. This description is
devoted primarily to particular requirements for the Ph.D. degree in mathematics education. For
further details concerning the general degree requirements, students should consult the bulletin,
Requirements for the Degree of Doctor of Philosophy, available in the Office of Doctoral
Studies. URL:
http://devweb.tc.columbia.edu/manager/form/files/719_Ph.D.%20Requirements%20Bulletin_Se
p_2014.pdf
Prerequisite Requirements
Admission to a Doctor of Philosophy program requires a Master’s degree in mathematics or
mathematics education that includes a combined undergraduate/graduate total of at least 45
semester hour credits in mathematics. Exemplary prior academic achievement at both the
undergraduate and graduate levels is expected of Ph.D. applicants.
The admission of a Ph.D. student to candidacy involves two stages. The first stage results in
“admission to a program of studies leading toward certification for the Ph.D. degree.” The
second “fully certified” stage represents full candidacy for the degree.
Minimum Point Requirement
The student, in consultation with an advisor, plans a program of study consistent with the
student’s prior education and oriented toward professional goals. This program plan is approved
by the advisor and then submitted to the Office of Doctoral Studies.
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Required Courses / Program Plan
The program plan for the Ph.D. must indicate completion of all requirements
for the degree within a prescribed period following the candidate’s first
graduate registration at Columbia University.
A program of study for the Ph.D. degree must include at least 45 points (or at
least 30 points if transfer credits come from Columbia University) taken under
Teachers College registration. In order to permit the achievement of broad and
basic scholarship, each program of study should include at least:
A. 60 points in mathematics, mathematics education, statistics, and computing.
At least 35 points should be in advanced courses – including MSTM 6037
Professional Seminar. Within these 35 points, 12 points should be in
research courses (MSTM 6500, MSTM 7500). (Any Teachers College
course at the 6000 level or above, any Columbia University Graduate
School of Arts and Sciences courses with a “G” prefix, and any “W”
courses above 4000, or any transferred course(s) with a graduate-level
prerequisite will be considered an advanced course).
Breadth Requirement
B. 15 points in the philosophical and psychological foundations of education.
Preparation in computing and statistics also is recommended. Programming
competencies in at least one computer language and further computer
science training equivalent to at least 6 points of graduate study are
desirable. Students whose theses involve statistical analysis are required to
include appropriate statistics courses in their program. These points can be
included either in the mathematics/mathematics education requirement or
can be taken as electives.
Other Program Requirements Such as Grade Requirements and Other Special Degree
Requirements
Language Requirement: Candidates for the Ph.D. 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 thesis may petition the Department to request substitution.
Students in mathematics may not use computer languages or statistics to satisfy our language
requirement.
Program Plan: All doctoral candidates must have a program plan approved by their advisor. The
approved plan should then be forwarded to the Office of Doctoral Studies. Refer to the PhD
Requirements Bulletin, obtainable from the Office of Doctoral Studies, for a fuller description.
Dissertation Guidelines: The Ph.D. dissertation is a scholar study contributing new knowledge
to the field and should be planned early in the doctoral program when sufficient advanced
courses have been completed to permit the candidate to enroll in relevant research-techniques
courses and pertinent advanced study to enable efficient preparation for the thesis. Ph.D.
dissertations in mathematics education should be (1) experimental studies in learning, (2)
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analytical studies in policy theory in mathematics education, or (3) other scholarly investigation
of problems and issues of broad significance in the field.
Certification Requirements and Information
Certification Examination: All candidates for the Ph.D. degree 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 Autumn,
the Spring and the Summer Terms. See Teachers College Bulletin for dates and times. URL:
http://www.tc.columbia.edu/doctoral/index.asp?Id=Forms&Info=Ph.D.+Students#C
Courses recommended as preparation for the mathematics education examination include MSTM
4019/20.
Students must demonstrate acceptable proficiency in three of the following six mathematics
content areas: algebra, analysis, computer mathematics, foundations of mathematics, geometry,
and probability and statistics. Students may sit for the examination in mathematics content
during the regular certification examination times, or, alternatively, students may register for:
MSTM 5036/6036 Topics/Advanced topics in discrete mathematics (3)
MSTM 5031/6031 Topics/Advanced topics in foundations of mathematics (3)
MSTM 5032/6032 Topics/Advanced topics in geometry/topology (3)
MSTM 6030 Advanced topics in probability theory (3)
MSTM 6033 Advanced topics in algebra (3)
MSTM 6034 Advanced topics in analysis (3)
MSTM 5126 Advanced topics in mathematical foundations of statistics (3)
and, with the permission of the Department, sit for the content area certification examination
upon completion of language requirements, all coursework on program plan, and
recommendation.
Dissertation Proposal Approval
Each doctoral student is required to be registered in his/her program’s dissertation seminar
(MSTM 7500) for at least one term. The purpose of this seminar is to develop the dissertation
proposal. This seminar cannot be counted more than once toward the degree unless the program
requires that it be taken a second time. Under no circumstances should a dissertation seminar
course be taken more than twice, even if the candidate has yet to complete the Dissertation
Proposal Hearing. Once a student has an approved dissertation proposal, a student should not
register for the departmental dissertation seminar course. After the candidate’s Dissertation
Committee is approved, the names of the faculty member who serve as the Dissertation
Committee are entered on the report. The candidate then submits the dissertation proposal to IRB
for approval. Once approved, the signed Dissertation Proposal Hearing form, a copy of the IRB
approval letter, and a PDF copy of the dissertation proposal is submitted to the Office of
Doctoral Studies as part of the candidate’s doctoral record.
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Continuous Registration for Dissertation Advisement
Each candidate must register continuously for at least three (3) credits of Teachers College
coursework or the course in dissertation advisement (MSTM 8900) offered by the department in
the term following enrollment in the dissertation seminar course(s) or after receiving
Departmental approval on the dissertation proposal, whichever comes first. Continuous
registration is required in each Autumn Term and Spring Term whether or not the candidate is in
attendance, and in the Summer Term when special permission to schedule a Final Defense has
been granted.
Continuous registration is required up through and including the term in which the oral
dissertation defense is held when registration in MSTM 8900 (Ph.D. Defense) is required. A
candidate has until one month into the following term to deposit the dissertation manuscript to
waive the advisement fee and to stop continuous registration.
The tuition fee for the Teachers College dissertation advisement course, set currently at the rate
of three tuition points for each term, is payable during the registration period of each term.
Dissertation advisement does not carry points of course credit. The fee is necessary in order that
the student may pay an equitable portion of the costs of the expensive process of advisement.
Such factors as the date of admission to doctoral study, or whether an Incomplete was received
in the dissertation seminar, or whether the student has passed the Certification Examination, are
not relevant to the obligation for dissertation advisement. A candidate who still has to develop a
dissertation plan after having been enrolled in the seminar has all the more need for individual
advisement.
Transfer Credit Evaluation
By College policy, as much as 30 points of approved graduate transfer credit can be applied to
the Ph.D. degree. If you have taken graduate courses previously at Teachers College or
Columbia University, additional points of applicable TC credit can be applied to the Ph.D.
degree. Application for transfer credit evaluation is made through the Office of Admission. Prior
TC graduate credit can be applied to the degree with approval of your advisor. The following
website contains general information on policies and procedures:
http://www.tc.columbia.edu/registrar/index.asp?Id=Degree+Information&Info=NonTC+Credit+Limits
Statement on Satisfactory Progress and Academic Performance
Students are expected to make satisfactory progress toward the completion of degree
requirements. Program faculty will review each student’s progress annually. If a student is
performing below expectations he/she may be required to complete additional course work. The
program will provide a plan and timeline for remediation so students know the expectation for
them to continue in the program. If satisfactory progress is not maintained a student may be
dismissed from the program. For additional information about Academic Performance, please
refer to Degree Requirements in the TC Catalog.
An average grade of B or better is expected for satisfactory completion of the degree. According
to the Mathematics Education Program policy, no more than 3 points of C may be credited
toward any degree or diploma. Students completing requirements for more than one degree or
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diploma may count 3 points of C− toward only one such award. A student who accumulates 8
points or more in C− or lower grades will not be permitted to continue study at the College and
will not be awarded a degree or diploma. Ph.D. students are expected to maintain at least a 3.5
grade point average. Please see the statement on policy of grades at Teachers College. URL:
http://catalog.tc.columbia.edu/tc/catalogdetail/policiesproceduresdocuments/grades/
Standard Policies and Procedures
Services for Students with Disabilities: The College will make reasonable accommodations for
persons with documented disabilities. Students are encouraged to contact the Office of Access
and Services for Individuals with Disabilities for information about registration (163 Thorndike
Hall). Services are available only to students who are registered and submit appropriate
documentation.
Statement on Academic Conduct: A Teachers College student is expected to refrain from any
conduct, including cheating, plagiarizing, or purchasing documents submitted for academic
evaluation, that calls into question his/her academic and/or professional probity. Decisions
regarding academic evaluation in all aspects of students’ work at the college, including course
work, certification examinations, clinical or field experiences, and preparation of dissertations,
are within the sole jurisdiction of the faculty concerned, including as appropriate, the department
or program staff members. Disciplinary actions (e.g., reprimand, suspension, or dismissal) in
cases of academic misconduct can be imposed by the Vice Provost or the Committee on Student
Conduct.
Resolution of Student Academic Program Concerns: Any student who has a concern regarding
an academic matter may seek assistance. The procedure for resolving academic program
concerns (see note of grade correction process below) begins with either the faculty member (if
the concern is related to a course) or the student’s advisor. If the student is not satisfied with the
response or resolution achieved at this first level, or if speaking with the faculty member presents
a conflict of interest for the student, the student should proceed to speak with the Program
Coordinator in the area in which the academic concern resides. If the student is not satisfied with
the response or resolution achieved through the Program Coordinator, the student should proceed
to speak with the Chair of the academic department in which the academic concern resides. If
the student is still not satisfied with the response or resolution achieved through the Department
Chair, or if speaking with the Department Chair presents a conflict of interest for the student, the
next step is to contact the Office of the Vice Provost. At any stage of the process, students are
welcome to seek the advice and guidance of the Ombudsman, who is charged with attempting to
informally resolve student dissatisfaction of an academic nature on a completely confidential
basis.
Grade Correction Procedure: The instructor for a course has the responsibility for setting the
requirements for a course and making an evaluation of students’ work. Once a grade has been
given, the instructor is not free to change the grade unless the instructor indicates to the Registrar
that an error was made in the original grade transmitted. If a student believes that an error has
been made, he/she must take the initiative in bringing about the necessary correction prior to the
conclusion of the semester immediately following the semester in which the course was taken.
The normal procedure for effecting a correction would be through direct discussion between the
student and the instructor. If redress cannot be attained through such discussions, the student may
next appeal to the department chairperson of the department offering the course. If resolution
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cannot be attained through appeal, the student may next appeal to the Dean. In situations where
the student feels that such an appeal process might not be in the student’s interest, counsel and
assistance can be sought from the Office of the College Ombudsman and the Office of the Vice
Provost.
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Appendix
Point Allocation Chart
Ph.D. Degree in Mathematics Education (MATH-PHD)
Recommended
Competencies
Points Recommended
1. Breadth in
mathematics content
with depth in three
areas.
Preparation sufficient to
guarantee mathematical
proficiency appropriate
for the university
professional.
Preparation must
include at least 30
points in advanced
courses.
Examples of Appropriate
Courses/Experiences
MSTM 5036/6036: Topics/Advanced topics in
discrete mathematics (3)
MSTM 5031/6031: Topics/Advanced topics in
foundations of mathematics (3)
MSTM 5032/6032: Topics/Advanced topics in
geometry (3)
MSTM 5035/6035: Topics/Advanced topics in
mathematical modeling (3)
MSTM 5037: History of mathematics (3)
MSTM 5038: Topics in mathematical logic (3)
MSTM 6030: Advanced topics in probability
theory (3)
MSTM 6033: Advanced topics in algebra (3)
MSTM 6034: Advanced topics in analysis (3)
MSTM 6126: Advanced topics in
mathematical foundations of statistics (3)
Also Graduate School of Arts and Sciences
courses.
2. Mathematics
education
competencies.
Preparation sufficient to
ensure educational
proficiency appropriate
for the university
professional.
Preparation normally
does not exceed 12
points.
MSTM 4019: Mathematics teaching and
learning I (3)
MSTM 4020: Mathematics teaching and
learning II (3)
MSTM 4025: Teaching computer mathematics
(3)
MSTM 4026: Teaching applied mathematics
(3)
MSTM 5010: Mathematics in the elementary
school (3)
MSTM 5012: Mathematics in 2- and 4-year
colleges (3)
MSTM 5020:Mathematics and multicultural
education (3)
MSTM 5022: Mathematics curriculum
development (3)
MSTM 5023: Problem solving (3)
MSTM 5061: Research, education and policy
in mathematics education (3)
MSTM 5520: Seminar in college teaching of
mathematics (3)
MSTM 6037 Professional seminar (3)
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3. Research
competencies.
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MSTM 6500: Research seminar in
mathematics education (3)
MSTM 7500: Dissertation seminar in
mathematics education (1)
4. Background in
professional education
(including at least 2
courses related to
higher education).
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C&T 4005: Computer applications in special
education (3)
C&T 4052: Diagnosis and remediation of
mathematics learning problems (3)
EDPS 4000: Education and public policy (3)
A&HH 4070: History of education in the U.S.
(3)
A&HF 4081: Philosophies of education (3)
A&HF 4083: Philosophies of science and
human inquiry (2-3)
HUDK 4027: Development of mathematical
thinking (3)
HUDK 5023: Cognitive development (2-3)
A&HB 4021: Foundations of bilingual/
bicultural education (3)
HUDM 4050: Introduction to measurement (3)
ORLD 4010: Purposes and policies of higher
education (3)
ORLD 4040: The American college student
(3)
ORLD 5053: Organization and administration
of adult and continuing education (3)
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