## Mathematics Education

#### Department of - Mathematics, Science & Technology

#### Contact Information

(212) 678-3381

(212) 678-8319

Professor Alexander Karp

### Program Description

Over its long and distinguished history, the Program in Mathematics Education has stressed the preparation of leaders in education. These leaders are successful scholars in their discipline, as well as educators. Faculty and staff are committed to leadership training through a variety of courses, workshops, and research experiences and through domestic and international study offerings. Many of the local learning experiences are performed in collaboration with private, public, and parochial schools in the tri-state metropolitan region.

Master’s-level offerings in Mathematics Education are appropriate for both initial and professional teachers. Advanced master’s and doctoral programs complete preparation for a variety of positions including: teaching, supervisory, and research roles spanning the elementary through college levels of instruction. Some courses offered through these programs are intended especially for students from other areas of study at Teachers College who need to acquire knowledge and skills in mathematics but who do not wish to earn a degree in this area.

A hallmark of Teachers College Mathematics Education program is a strong emphasis on mathematics content and the role of mathematical ways of thinking in the teaching and learning of mathematics. Our graduates take positions in college teaching of mathematics, in addition to pre-college professional roles.

**Master of Arts**

Emphasis is placed on those competencies necessary for effective mathematics teaching as a means of enhancing professional growth of initial and professional teachers. Conceptual issues in teaching are translated into practice through group and individualized instruction in special methods courses. Master of Arts requirements include a culminating scholarly project.

A minimum of 32 points of coursework is required, along with a final essay or project. No transfer credit for graduate courses completed elsewhere can be applied to the M.A. degree. Courses taken through these programs and elsewhere at Teachers College in mathematics, mathematics education, and professional education to meet individual needs may be supplemented with permission by courses taken in other faculties of Columbia University.

**Master of Science and Master of Education**

Both programs require a minimum of 60 points, a formal essay or integrative project, and involve extensive preparation in mathematics, as well as education. For the Master of Science degree, the college requires that a minimum of 32 points with an integrative project be completed under the auspices of Teachers College. Master of Science and Master of Education students who choose to do a formal essay may apply a maximum of 30 semester hours of graduate credit toward their degree requirement. Please refer to the Degree Requirements section of this bulletin for college-wide minimum point requirements. For the M.S. degree, there is greater emphasis on preparation in mathematics content. In the Ed.M. program, there is greater emphasis on preparation in professional education. Programs are arranged in consultation with the major professor to meet both program and college requirements.

Applicants for the M.S. and Ed.M. degrees must also prepare a written integrative project.

**Doctoral Degrees**

The department provides programs for both the Ed.D. and the Ph.D. degrees. In general, the Ed.D. degree places emphasis on breadth of professional coursework with a focus on educational practice. All candidates are required to be competent in statistical research methodology and computing and to have knowledge of the epistemology of mathematics and of psychology sufficient to be an informed scholar-practitioner. All doctoral candidates must have a written program plan approved by their advisor. The approved plan then must be approved by the Office of Doctoral Studies. Following submission of a statement of total program, the student normally completes doctoral coursework and engages in doctoral research and writing. Refer to the Ph.D. and Ed.D. Requirements Bulletin, prepared by the Office of Doctoral Studies, for a fuller description of degree requirements.

In planning a program of study, it should be noted that doctoral students are required to complete a minimum of 20 points after taking the certification examination for the first time, including points taken during the term in which that examination is taken.

**Specializations:**

*Elementary School Mathematics*

The Elementary School Mathematics Specialist specialization is designed for those who are preparing for positions of leadership in elementary schools or in the training of elementary school teachers. Programs for elementary school specialists emphasize knowledge of subject matter, methodologies, and curricula of mathematics and include appropriate field experiences with elementary school students and teachers. In addition to program offerings, students have access to courses in related departments and institutions.

*Secondary School Mathematics*

The Secondary School Teaching specialization includes an in-service component for experienced teachers and preservice education for students entering the profession. Programs are designed individually in consultation with a faculty advisor to reflect each teacher’s background and goals. The program stresses the direct application of theory to practice with particular emphasis on experiences with teaching strategies that match classroom activities to student characteristics, that examine teacher and student interpersonal interaction, and that reflect the historical and philosophical roots of the discipline. The final project for the degree should include evidence that these components have been fulfilled.

*Supervision in Schools*

Students interested in mathematics supervision in schools may elect to develop individual programs that reflect their specific background and interests and that draw on the resources of the department and college, or they may work as part of the staff of the field-based teacher education programs. School and university faculty work with graduate students in a collaborative effort where teaching, preservice, and supervision training and education research are intimately related.

*Teacher Education in Mathematics*

The Teacher Education in Mathematics specialization is designed to prepare scholars for educational leadership roles as education professors in colleges and universities. Participants in the program have opportunities to build their mathematics content background through content courses in the department and the offerings of Columbia University. There are opportunities also for professional experiences in the initial and professional teacher education programs.

*College Teaching of an Academic Subject*

Teachers College offers a doctorate in college teaching that emphasizes preparation in content supplemented by a program of professional education. Field experiences can be pursued in mathematics, computing, and several related disciplines. The course content and sequence are especially organized to meet the unique needs and career goals of each candidate within the general requirements of the Ed.D. degree at Teachers College.

### Degree Summary

Initial Certification Master of Arts degree students and applicants should direct admissions and certification questions to Dr. Stuart Weinberg - (212) 678-3717, saw29@columbia.edu.

MATHEMATICS EDUCATION (MATH)

Degrees offered:

- Master of Arts (M.A.)
- Master of Science (M.S.)
- Master of Education (Ed.M.)
- Doctor of Education (Ed.D.)
- Doctor of Education in the College Teaching of an Academic Subject (Ed.D.C.T.)
- Doctor of Philosophy (Ph.D.)

MATHEMATICS EDUCATION-INITIAL CERTIFICATION (MATH-INIT)

Degree offered:

- Master of Arts (M.A.)

MATHEMATICS EDUCATION-PROFESSIONAL CERTIFICATION (MATH-PROF)*

Degree offered:

- Master of Arts (M.A.)

* Program not currently accepting applications

MATHEMATICS EDUCATION-TRANSITIONAL B (MATH-TRAN)

Degree offered:

- Master of Arts (M.A.)

For a complete listing of degree requirements, please click the "Degrees" tab above

For a complete listing of degree requirements, please continue on to this program's "Degrees" section in this document

### Degree Requirements

### General

Programming competencies in at least one computer language and further computer science training equivalent to at least 6 points of graduate study ordinarily are required of all students seeking degrees beyond the Master of Arts. These points either can be included in the mathematics/mathematics education requirement or can be taken as electives.

In addition to content courses in mathematics, students should enroll in at least two professional courses in mathematics education such as MSTM 4019, MSTM 4020, MSTM 5012, or MSTM 5520.

### Master of Arts

Normally students complete 24 points in courses in mathematics and mathematics education including MSTM 4019 and selected courses in related disciplines such as statistics and computing. The remaining 8 points (3 courses) are reserved for electives chosen from professional areas such as psychology, philosophy, curriculum, etc. Programs for specialists in the teaching of elementary school mathematics should include MSTM 5010. Secondary school specialists should enroll in MSTM 5023, MSTM 5032, and MSTM 5037.

Prospective community college teachers should select courses in at least three mathematical areas such as analysis, algebra, and computing, in preparation for study beyond the master’s level. Preparation in computing is recommended for all specializations. Initial certification students should refer to the program brochure for information on additional requirements for state certification. All applicants for the M.A. degree must prepare a written project as a culminating integrative experience.

### Master of Science

Normally the program of studies for the Master of Science (M.S.) degree should include 42 points in courses in mathematics and mathematics education. Preparation in mathematics content should be of sufficient depth in two or three areas to communicate content effectively at the freshman and sophomore college levels. Algebra and analysis are recommended as areas of concentration. Content courses can be selected from courses offered by the department or from courses offered by the Graduate School of Arts and Sciences of Columbia University. Preparation in computing and statistics is also recommended.

### Master of Education

Typically, the program of studies for the Master of Education (Ed.M.) degree should include 42 points in courses in mathematics and mathematics education. Preparation in mathematics content should be of sufficient depth to provide leadership to elementary and secondary school teachers. Content courses can be selected from courses offered by the department or from courses offered by the Graduate School of Arts and Sciences of Columbia University. Students interested in developing research competencies for further graduate study should elect at least 6 points in statistics. HUDM 4122, Probability and statistical inference, and HUDM 5123, Linear models and experimental design, are recommended.

### 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 include MSTM 4019/4020, MSTM 6037, and 6000-level mathematics content courses.

Students must demonstrate acceptable proficiency in at least three of the following six mathematics content areas: algebra, analysis, computer 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 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 Education

A program of study for the Doctor of Education (Ed.D.) degree must include a minimum of 90 semester hours of approved graduate credit, at least 45 points of which must be taken under Teachers College registration. In order to permit the acquisition of broad basic scholarship, each program of study should include at least 70 points in mathematics and mathematics education. At least 24 points should be at an advanced level. Ordinarily, points in mathematics and mathematics education should include at least 45 points in mathematics content courses, 12 points in mathematics education courses, and 12 points of research preparation including MSTM 6500 and MSTM 7500.

Professional courses taken outside the program of Mathematics Education normally should include 15 points in the curricular, psychological, and social foundations of education. Students specializing in teacher education are encouraged to select elective courses related to higher education programs and practices. Preparation in computing and statistics is also 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 dissertations involve statistical analysis are required to include appropriate statistics courses in their programs. These points can be included either in the mathematics/mathematics education requirement or can be taken as electives.

The Ed.D. culminates in a dissertation contributing 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 courses and pertinent advanced study to enable efficient preparation of the dissertation. Dissertations in mathematics education can be (1) experimental studies in learning, (2) design and formative evaluation of mathematics curricula, or (3) analytical studies in policy theory in mathematics education.

### Doctor of Education in the College Teaching of an Academic Subject

The Program in Mathematics Education at Teachers College offers a program of study leading to the Doctor of Education Degree in the College Teaching of Mathematics (Ed.D.C.T.) to prepare students for positions as teachers of mathematics in two- and four-year colleges.

This degree program is designed to develop both the depth and breadth in the students’ knowledge of mathematics but is intended to prepare graduates for careers in teaching rather than in mathematics research. For further details concerning general degree requirements, students should consult the bulletin, “Requirements for the Degree of Doctor of Education in the College Teaching of an Academic Subject” available in the Office of Doctoral Studies.

A program of study for the Ed.D.C.T. degree must include a minimum of 90 semester hours of approved graduate credit, at least 45 points of which must be taken under Teachers College registration. In order to permit the acquisition of broad and basic scholarship, each program of study should include at least 75 points in mathematics and mathematics education, with at least 30 points in advanced courses and 15 points in professional educational disciplines and including at least two courses related to higher education programs and practices.

Ordinarily, points in mathematics and mathematics education should include at least 50 points in mathematics content courses, three points in either MSTM 5012 or MSTM 5520 and 12 points of research preparation including MSTM 6500 and MSTM 7500. Preparation in mathematics content should be of sufficient depth in three areas to communicate content effectively at the freshman and sophomore college levels. Algebra and analysis are recommended as initial areas of concentration. Content courses can be selected from courses with the department or from courses offered by the Graduate Faculties of Columbia University.

Candidates for the Ed.D. in College Teaching who have not completed the equivalent of at least one year of full-time service as a college teacher of mathematics/computing/statistics are required to include MSTM 6400 within their doctoral programs. Interns will teach college mathematics courses under the supervision of experienced college teachers for a period of at least one semester. Incoming doctoral candidates should register for Professional Seminar in Mathematics during the first year of doctoral studies.

Candidates for the Ed.D.C.T. are required to demonstrate competency in one language chosen from among French, German, and Russian. Students who require other languages for the preparation of their dissertation may petition the department to request substitution. Students in mathematics may not use computer languages to satisfy the language requirement. The Ed.D.C.T. degree requirements include a dissertation contributing 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 courses and pertinent advanced study to enable efficient preparation of the dissertation. Doctoral dissertations in the college teaching of mathematics can be (1) experimental studies in adult learning, (2) design and formative evaluation of college mathematics curricula, or (3) analytical studies in policy theory in mathematics post-secondary education.

### Doctor of Philosophy in Mathematics Education

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.

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.

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. program.

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 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.

### Application Information

Applications are reviewed on an ongoing basis. Preference in scholarship awards will be given to applicants who meet the early deadline.

Mathematics education students seeking Master of Arts, Master of Science, and Master of Education degrees are expected to have completed at least 24 credits of undergraduate mathematics.

Applicants who wish to receive Initial New York State teaching certification should apply to the Master of Arts degree program.

Mathematics education students seeking Doctor of Education or Doctor of Education in the College Teaching of an Academic Subject degrees are expected to have completed an undergraduate major in mathematics. Mathematics education students seeking a Doctor of Philosophy degree should have both undergraduate and master’s degrees in their specialization.

### Faculty List

#### Faculty

#### Lecturers

#### Visiting Faculty

#### Adjunct

#### Full-Time Instructors

#### Instructors

Adjunct Professor

Visiting Professor

Professor of Mathematics Education

Adjunct Professor

Adjunct Professor

Visiting Professor of Mathematics Education

Acting Program Director, Math Education

Clifford Brewster Upton Professor of Mathematical Education

Professor of Mathematics and Education

Assistant Professor of Mathematics Education

Lecturer

For up to date information about course offerings including faculty information, please visit the online course schedule.

### Course List

**MSTC 5001 Qualitative methods in science education research**

Permission required from the instructor. Introduction to qualitative research methods and completion of pilot studies. Designed largely for doctoral students and advanced masters students.

**MSTC 5155 Critical voices in teacher education**

This course is designed for doctoral students and advanced master's students interested in teacher education and becoming teacher educators. The course consists of elements of theory, practice, and research within a broad or interdisciplinary field of education with an emphasis on the preparation of selves as teachers.

**MSTM 4005 Teaching mathematics in diverse cultures**

Principles, techniques, and issues in the teaching of mathematics in other cultural and national settings. Study tour of schools and institutions in various nations.

**MSTM 4019 Mathematics teaching and learning I**

Cognitive development and learning strategies for teaching and the use of instructional materials. Current research in mathematics education. Required for pre-service students.

**MSTM 4020 Mathematics teaching and learning II**

Historical/comparative study of mathematical education programs in the United States and abroad. Current research in mathematics education.

**MSTM 4023 Mathematics for exceptional students**

Content, methods, and instructional models for teaching exceptional students, including LED, LD, and MT students.

**MSTM 4025 Teaching Mathematics Using Technology**

A review of teaching methods and curricular innovations in computing and computer mathematics.

**MSTM 4026 Teaching applied mathematics**

The role of applications in mathematics curriculum. Mathematical models, use of calculators and computers. Applications in the natural and social sciences.

**MSTM 4031 Number theory**

Primes, composites, divisibility and factorization, congruence, historical topics.

**MSTM 4034 Exploring secondary school mathematics**

For students who are preparing to teach in secondary school. The mathematical content of advanced secondary school mathematics and the development and application of fundamental ideas in mathematics.

**MSTM 4038 Finite mathematics**

Statements, propositions, and sets; vectors and matrices; probability. Applications: finite Markov chains, game theory.

**MSTM 4760 Student teaching in mathematics**

Permission required. Prerequisite: MSTM 5011. Open only to students enrolled in the pre-service program. Students do supervised teaching in metropolitan area schools.

**MSTM 4901 Guided study in mathematics education**

Permission required from the instructor with whom the student wishes to work. Independent study in selected areas.

**MSTM 5010 Mathematics in the elementary school**

Problems, issues, and methods in the teaching and supervision of elementary school mathematics.

**MSTM 5011 Mathematics in the secondary school**

Problems, issues, and methods in the teaching and supervision of secondary school mathematics. Includes field experiences. Required for preservice students.

**MSTM 5019 Mathematics in Popular Culture and Media**

**MSTM 5020 Mathematics and multicultural education**

Survey of mathematical topics and methods appropriate for multicultural and bilingual programs.

**MSTM 5022 Mathematics curriculum development**

Principles, strategies, and techniques for curriculum development and textbook preparation in mathematics.

**MSTM 5023 Problem solving**

Theories and methods of mathematical problem solving with applications to classroom instruction.

**MSTM 5030 Topics in probability theory**

Simple, compound, and conditional probabilities and applications. Doctoral students should register for MSTM 6030.

**MSTM 5031 Topics in the foundations of mathematics**

Propositional and predicate calculi, set theory, axiomatics, order types, the linear continuum, and Goedel's theorem.

**MSTM 5032 Topics in geometry/ topology**

Foundation of geometry/topology. Emphasis upon the relationship between topology and geometry and other mathematical areas.

**MSTM 5033 Topics in algebra**

Groups, rings, fields. Doctoral students should register for MSTM 6033.

**MSTM 5034 Topics in analysis**

Real or complex functions and their properties. Doctoral students should register for MSTM 6034.

**MSTM 5035 Topics in mathematical modeling**

Simulation, information theory and coding, stochastic models, probabilistic systems, simple harmonic motion. Topics vary between natural sciences and behavioral sciences.

**MSTM 5036 Topics in discrete mathematics**

Discrete mathematics, combinatorics, graph theory.

**MSTM 5037 History of mathematics**

Historical development of major ideas in mathematics. Contributions of noteworthy mathematicians. Analysis of mathematical classics.

**MSTM 5038 Topics in mathematical logic**

Prepositional calculus, Church-Turing thesis, Goedel's incompleteness theorem.

**MSTM 5039 Comparative mathematics education**

A review and comparison of mathematics education in other nations.

**MSTM 5061 Research, Evaluation, and Policy in Mathematics Education**

Theory and methods of evaluating pupils and programs in the cognitive and affective domains. The roles of research and policy in evaluation of mathematics outcomes.

**MSTM 5126 Mathematical foundations of statistics**

Prerequisite: MSTM 5030 or MSTM 6030. Estimation, hypothesis testing, and tests based on the chi-square distribution. The normal distribution and its applications. Analysis of variance and regression. Doctoral students should register for MSTM 6126.

**MSTM 5264 Guided supervision of student teaching in mathematics**

Permission required. Open only to doctoral students. Guided field experience in supervising student teachers.

**MSTM 5520 Seminar in the college teaching of mathematics**

Current issues in undergraduate mathematics. Examination of relations between elementary and advanced mathematics.

**MSTM 5800 Mathematics colloquium**

Lecture series featuring presentations by distinguished guest speakers.

**MSTM 5801 Mathematics colloquium**

Lecture series featuring presentations by distinguished guest speakers.

**MSTM 6030 Advanced topics in probability theory**

Open only to doctoral students. Emphasis on proof and advanced applications.

**MSTM 6032 Advanced topics in geometry/topology**

Foundation of geometry/topology. Emphasis upon the relationship between topology and geometry and other mathematical areas.

**MSTM 6033 Advanced topics in algebra**

Open only to doctoral students. Advanced study of groups, rings, and fields.

**MSTM 6034 Advanced topics in analysis**

Open only to doctoral students. Advanced study of real or complex functions.

**MSTM 6035 Advanced topics in mathematical modeling**

Open only to doctoral students. Advanced study of mathematical modeling**.**

**MSTM 6036 Advanced topics in discrete mathematics**

Open only to doctoral students. Advanced study of discrete mathematics, combinatorics, and graph theory.

**MSTM 6037 Advanced selected topics and issues in mathematics education**

Topics will vary

**MSTM 6039 Advanced comparative mathematics education**

A review and comparison of mathematics education in other nations.

**MSTM 6126 Advanced topics in the mathematical foundations of statistics**

Open only to doctoral students. Prerequisite: MSTM 5030 or MSTM 6030. Advanced topics including hypothesis testing, distribution theory, and analysis of variance and regression.

**MSTM 6400 Internship in mathematics education**

Permission required. Supervised intern service in a variety of field settings including classroom teaching at various levels, supervision, curriculum development, and inservice education.

**MSTM 6500 Research seminar in mathematics education**

Permission required. Research oriented seminars dealing with a variety of issues and leading to preparation of preliminary proposals for the doctoral dissertation. Required for doctoral students.

**MSTM 6501 Research seminar in mathematics education**

Permission required. Research oriented seminars dealing with a variety of issues and leading to preparation of preliminary proposals for the doctoral dissertation. Required for doctoral students.

**MSTM 6901 Research and independent study in mathematics education**

Permission required. Guided independent study leading to the preparation of a major project or paper. May be taken repeatedly by doctoral candidates engaged in research.

**MSTM 7500 Dissertation seminar in mathematics education**

Development of final doctoral dissertation proposals and presentation of proposals for departmental review.

**MSTM 8900 Dissertation advisement in mathematics education**

Individual advisement on doctoral dissertations. Fee to equal 3 points at current tuition rate for each term. For requirements, see section in catalog on Continuous Registration for Ed.D./Ph.D. degrees.