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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!

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_Sep_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) 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.

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=Non-TC+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 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 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.