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Mathematics Education
Department of Mathematics, Science & Technology
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 tristate metropolitan region.
Master’slevel degree offerings in Mathematics Education are appropriate for both initial and professional teacher certification in New York State. Advanced master’s and doctoral degree 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 precollege professional roles.
Master of Arts
Emphasis is placed on those competencies necessary for effective mathematics teaching as a means of enhancing 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 degree 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 requirements. Courses taken at Teachers College in mathematics, mathematics education, and professional teacher certification 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 extensive preparation in mathematics, as well as education. For the Master of Science degree program, 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 Collegewide 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 teacher 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 the Ed.D., Ed.DCT, and the Ph.D. degrees. In general, the Ed.D. degree program 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 scholarpractitioner. 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 (ODS). The student then 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.
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 inservice 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 fieldbased 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 mathematics 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 teacher education degree programs leading to initial and professional teacher certification.
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, 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.CT degree program at Teachers College.
Degrees

Master of Arts

Mathematics Education
Master of Arts  Initial Cert: Math 712Points/Credits: 36
Entry Terms: Spring/Summer/Fall
Certification:
 NY State Initial: Mathematics 712
Degree Requirements
Master of Arts With Initial Certification
This program requires 36 points (4 points in Student Teaching). Initial Teacher Certification Master of Arts degree students and applicants should direct admissions and certification questions to Dr. Sian Zelbo at (212) 6783747 or sez2105@tc.columbia.edu.
Normally students complete 24 points in courses in mathematics and mathematics education including MSTM 4019, MSTM 5011, and History of Mathematics Education and Multiculturalism. At least 12 points in mathematics must be taken. Additionally, 4 points should be completed in Student Teaching. The remaining points are reserved for courses in Human development, English language acquisition, Inclusive education, and History of Education and Multiculturalism.Initial teacher certification students should refer to the program brochure for information on additional requirements for New York State initial teacher certification. All applicants for the M.A. degree must prepare a written project as a culminating integrative experience.

Mathematics Education
Master of Arts  NonCertificationPoints/Credits: 32
Entry Terms: Spring/Summer/Fall
Certification:
 NonCertification Track
Degree Requirements
General
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 5011, or MSTM 5520.
Master of Arts
Normally students complete 24 points in courses in mathematics and mathematics education including MSTM 4019 and and at least 12 points in mathematics.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 5011, or for example, 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. Initial teacher certification students should refer to the program brochure for information on additional requirements for New York SState certification. All applicants for the M.A. degree must prepare a written project as a culminating integrative experience.

Mathematics Education (Peace Corps)
Master of Arts  Transitional B Cert: Math 712Points/Credits: 34
Entry Terms: Summer Only
Certification:
 NY State Transitional B: Mathematics 712
Degree Requirements
This program is specifically designed for students admitted to the college as returning Peace Corps Fellows volunteers, and leads to a New York State initial certificate for teaching secondary school mathematics (grades 712). It requires 34 points (including a 2point teaching seminar). Applicants should direct admissions and certification questions to Dr. Alexander Karp at 2126783842 or apk16@tc.columbia.edu.
Master of Arts
Normally students complete 24 points in courses in mathematics and mathematics education including MSTM 4019, MSTM 5011 and with at least 12 points in mathematics. Additionally, a 2point studentteaching seminar should be completed. The remaining 8 points (3 courses) are reserved for classes chosen outside of the Program in Mathematics and should include a course in human development; a course in the nature of students within the full range of disabilities and inclusive education; and a course in language acquisition and literacy development. All applicants for the M.A. degree must prepare a written project as a culminating integrative experience.
The Master of Arts degree – Transitional B – The program of study for the degree is designed to increase the teacher’s knowledge of mathematics and prepare them for the profession of teaching. The program can be completed in one calendar year through fulltime study during an academic year and a dual summer session, or spread across two academic years.
Prerequisite Requirements
Admission to the program requires evidence of ability to be prepared for certification to teach secondary school mathematics. Normally, (i) strong undergraduate preparation with a minimum of 24 semester hours in mathematics content courses, including two semesters of calculus, and (ii) one year of college level study, or its equivalent, of a language other than English. Students are referred to the Admission Bulletin of the Teachers College Catalog for general information concerning admission and degree requirements (https://www.tc.columbia.edu/catalog/admission/).
Minimum Point Requirement
The program of study for the M.A. Transitional B degree must include 34 points of graduate study under Teachers College auspices. Normally students complete at least 24 points in mathematics and mathematics education courses.
Course Requirements
Courses offered within the Program in mathematics (MSTM) tend to be either mathematics content or mathematics education courses. The program of study has certain requirements (see the Table below) – though there are few specific courses that are required. Students’ precise program of study should be determined in consultation with their program advisor.
1. Mathematics Content
Breadth in mathematics content to enrich student’s undergraduate preparation. Students will need to provide documentation that their composite undergraduate and graduate mathematical profile includes coursework in all of the following areas: (i) Number theory/historical topics, (ii) Algebra, (iii) Geometry/topology, (iv) Calculus/analysis, (v) Discrete mathematics, and (vi) Probability/statistics. Students are also encouraged to include coursework mathematical models/applications.
At least 12 points
2. Mathematics Education
Theory and methods courses in the teaching of mathematics must include the following two required courses: MSTM 4019 Mathematics Teaching and Learning (3 points), which discusses theoretical aspects of teaching and learning, and MSTM 5011 Mathematics in the Secondary School (3 points), which is a methods course dealing with issues of classroom teaching and includes field experiences during the school day. One other professional course in mathematics education must be taken to satisfy a state requirement for understanding history, philosophy, and the role of education. Recommended courses to meet this requirement include MSTM 5020 Mathematics and Multicultural Education, MSTM 4020 Mathematics Teaching and Learning II, , MSTM 4005 Teaching Mathematics in Diverse Cultures, or other methods courses offered by the program.
At least 8 points
3. General Professional Education
Teachers College courses outside the Program in Mathematics related to general educational foundations or broader professional issues, which must meet the following requirements:
 a course in human development (2 or 3 points) which must include at least one of the following required courses: HUDK 4027 Development of Mathematical Thinking, HUDK 4023 Developmental Psychology: Adolescence, or HUDK 5023 Cognitive Development;
 a course in the nature of students within the full range of disabilities and inclusive education (3 points), which must include at least one of the following required courses: C&T 4001 Teaching Students with Disabilities in Inclusive Classrooms, C&T 4046A Multifoundational Approach to Learning Disabilities, or HBSE 4002 Instruction and Curriculum for Students With and Without Disabilities (alternatively, students can enroll in MSTM 4023 Mathematics for Exceptional Students to meet this requirement, but which then does not count towards the General Professional Education requirements).
 a course in language acquisition and literacy development (3 points), which must include either C&T 4137 Literacy and Learning in the Content Areas (3 points) or C&T 4842 Institute: Content Area Literacies (3 points). Based on an analysis of their undergraduate transcripts, students and their advisor should decide whether any more courses in teaching literacy are needed in addition to this one requirement.
At least 8 points
4. Student Teaching
Supervised teaching experiences in metropolitan area secondary schools, fulfilled by completing the required course MSTM 4760 Student Teaching in Mathematics (2 points).
2 points

Mathematics Education (Teaching Residents)
Master of Arts  Initial Cert: Math 712 (TR@TC)Points/Credits: 44
Entry Terms: Spring/Summer
Certification:
 NY State Initial: Mathematics 712
Degree Requirements
Master of Arts With Initial Certification
This program requires 36 points (4 points in Student Teaching). Initial Teacher Certification Master of Arts degree students and applicants should direct admissions and certification questions to Dr. Sian Zelboat (212) 6783747or sez2105@tc.columbia.edu.
Normally students complete 24 points in courses in mathematics and mathematics education including MSTM 4019, MSTM 5011, and History of Mathematics Education and Multiculturalism. At least 12 points in mathematics must be taken. Additionally, 4 points should be completed in Student Teaching. The remaining points are reserved for courses in Human development, English language acquisition, Inclusive education, and History of Education and Multiculturalism..
Initial teacher certification students should refer to the program brochure for information on additional requirements for New York State teacher certification. All applicants for the M.A. degree must prepare a written project as a culminating integrative experience.


Master of Science

Mathematics Education
Master of SciencePoints/Credits: 60
Entry Terms: Spring/Summer/Fall
Degree Requirements
Master of Science
Normally the program of studies for the Master of Science (M.S.) degree should include 42 points of courses in mathematics and mathematics education within the minimum requirement of 60 points.
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, geometry, analysis, and discrete mathematics are recommended as areas of concentration. Content courses can be selected from courses offered by theDepartment or from courses offered by the Graduate School of Arts and Sciences of Columbia University.
Preparation in statistics is also recommended.


Master of Education

Mathematics Education
Master of EducationPoints/Credits: 60
Entry Terms: Spring/Summer/Fall
Degree Requirements
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 within the minimum requirement of 60 points. Preparation in mathematics content should be of sufficient depth to provide leadership to elementary and secondary school teachers. Content courses may 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.


Doctor of Education

Mathematics Education
Doctor of EducationPoints/Credits: 90
Entry Terms: Spring/Summer/Fall
Degree Requirements
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 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 6500/6501 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.
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. degree culminates in a dissertation contributing knowledge to the field and should be planned early in the doctoral degree 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. The website of the Program offers a list of Topic study groups which doctoral students are recommended to join.


Doctor of Education in College Teaching

Mathematics Education
Doctor of Education in College TeachingPoints/Credits: 90
Entry Terms: Spring/Summer/Fall
Degree Requirements
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 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 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 fouryear 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 (ODS).
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, mathematics education and research in 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; courses in mathematics education should include MSTM 5520. Also, 12 points of research preparation including MSTM 6500/6501 and MSTM 7500 should be taken. Preparation in mathematics content should be of sufficient depth in three areas to communicate content effectively at the freshman and sophomore college levels. Algebra geometry, analysis, and discrete mathematics 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 fulltime service as a college teacher of mathematics/computing/statistics are recommended 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 MSTM 6037 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 postsecondary education. The website of the Program offers a list of Topic study groups which doctoral students are recommended to join.


Doctor of Philosophy

Mathematics Education
Doctor of PhilosophyPoints/Credits: 75
Entry Terms: Spring/Summer/Fall
Degree Requirements
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 teachinglearning 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 graduatelevel 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.

Faculty
Faculty
 Alexander P. Karp Professor of Mathematics Education
 Irina Lyublinskaya Professor of Mathematics and Education
 Erica Walker Clifford Brewster Upton Professor of Mathematical Education
 Nicholas Henning Wasserman Associate Professor of Mathematics Education
Visiting Faculty
 Daniel L. Goroff
 Neil Grabois
 J Philip Smith Visiting Professor
Lecturers
 Chaya R Flint Lecturer
 Stuart Allan Weinberg Lecturer
Adjunct Faculty
 Joseph Peter Garrity Adjunct Professor
Instructors
 Joseph Malkevitch
 Henry O Pollak
Courses
 MSTM 4005  Teaching mathematics in diverse culturesPrinciples, 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 ICognitive development and learning strategies for teaching and the use of instructional materials. Current research in mathematics education. Required for preservice students.
 MSTM 4020  Mathematics teaching and learning IIHistorical/comparative study of mathematical education programs in the United States and abroad. Current research in mathematics education.
 MSTM 4023  Mathematics for exceptional studentsContent, methods, and instructional models for teaching exceptional students, including LED, LD, and MT students.
 MSTM 4025  Teaching mathematics using technologyA review of teaching methods and curricular innovations in computing and computer mathematics.
 MSTM 4026  Teaching Applied MathematicsThe role of applications in mathematics curriculum. Mathematical models, use of calculators and computers. Applications in the natural and social sciences.
 MSTM 4031  Number theoryPrimes, composites, divisibility and factorization, congruence, historical topics.
 MSTM 4034  Exploring Secondary School MathematicsFor 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 mathematicsStatements, propositions, and sets; vectors and matrices; probability. Applications: finite Markov chains, game theory.
 MSTM 4760  Student teaching in mathematicsPermission required. Prerequisite: MSTM 5011. Open only to students enrolled in the preservice program. Students do supervised teaching in metropolitan area schools.
 MSTM 4901  Guided study in mathematics educationPermission required from the instructor with whom the student wishes to work. Independent study in selected areas.
 MSTM 5010  Mathematics in the Elementary SchoolProblems, issues, and methods in the teaching and supervision of elementary school mathematics.
 MSTM 5011  Mathematics in the secondary schoolProblems, issues, and methods in the teaching and supervision of secondary school mathematics. Includes field experiences. Required for preservice students.
 MSTM 5017  Mathematical game theoryTaxonomy of games, twoperson zerosum games, transferable and nontransferable utility, equilibrium concepts, twosided markets, elections and voting, bankruptcy, apportionment, combinatorial games. Game theory and the K12 curriculum.
 MSTM 5019  Mathematics in popular culture and mediaSurvey of mathematical topics, methods, and issues related to teaching and learning as represented in popular culture and media, including literature, film, art, advertising, and the press.
 MSTM 5020  Mathematics and multicultural educationSurvey of mathematical topics and methods appropriate for multicultural and bilingual programs.
 MSTM 5022  Mathematics curriculum developmentPrinciples, strategies, and techniques for curriculum development and textbook preparation in mathematics.
 MSTM 5023  Problem solvingTheories and methods of mathematical problem solving with applications to classroom instruction.
 MSTM 5030  Topics in probability theorySimple, compound, and conditional probabilities and applications. Doctoral students should register for MSTM 6030.
 MSTM 5031  Topics in the foundations of mathematicsPropositional and predicate calculi, set theory, axiomatics, order types, the linear continuum, and Goedel's theorem.
 MSTM 5032  Topics in geometry / topologyFoundation of geometry/topology. Emphasis upon the relationship between topology and geometry and other mathematical areas.
 MSTM 5033  Topics in algebraGroups, rings, fields. Doctoral students should register for MSTM 6033.
 MSTM 5034  Topics in analysisReal or complex functions and their properties. Doctoral students should register for MSTM 6034.
 MSTM 5035  Mathematical ModelingSimulation, information theory and coding, stochastic models, probabilistic systems, simple harmonic motion. Topics vary between natural sciences and behavioral sciences.
 MSTM 5036  Topics in discrete mathematicsDiscrete mathematics, combinatorics, graph theory.
 MSTM 5037  History of mathematicsHistorical development of major ideas in mathematics. Contributions of noteworthy mathematicians. Analysis of mathematical classics.
 MSTM 5038  Topics in mathematical logicPrepositional calculus, ChurchTuring thesis, Goedel's incompleteness theorem.
 MSTM 5039  Comparative mathematics educationA review and comparison of mathematics education in other nations.
 MSTM 5051  Nature of ProofsLearn how to create mathematics by turning your observations, beliefs and conjectures into formal statements backed by rigorous arguments.
 MSTM 5061  Research, evaluation, and policy in mathematics educationTheory 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 statisticsPrerequisite: MSTM 5030 or MSTM 6030. Estimation, hypothesis testing, and tests based on the chisquare 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 mathematicsPermission required. Open only to doctoral students. Guided field experience in supervising student teachers.
 MSTM 5520  Seminar in the college teaching of mathematicsCurrent issues in undergraduate mathematics. Examination of relations between elementary and advanced mathematics.
 MSTM 5800  Mathematics colloquiumLecture series featuring presentations by distinguished guest speakers.
 MSTM 5801  No Title Found in BannerLecture series featuring presentations by distinguished guest speakers.
 MSTM 6017  Advanced topics in mathematical game theoryOpen only to doctoral students. Advanced study of game theory.
 MSTM 6030  Advanced topics in probability theoryOpen only to doctoral students. Emphasis on proof and advanced applications.
 MSTM 6031  Advanced topics in the foundations of mathematicsOpen only to doctoral students. Advanced study of axiom systems and 19th – 20th century developments in the logical foundations of mathematics.
 MSTM 6032  Advanced topics in geometry/topologyFoundation of geometry/topology. Emphasis upon the relationship between topology and geometry and other mathematical areas.
 MSTM 6033  Advanced topics in algebraOpen only to doctoral students. Advanced study of groups, rings, and fields.
 MSTM 6034  Advanced topics in analysisOpen only to doctoral students. Advanced study of real or complex functions.
 MSTM 6035  Adv Mathematical ModelingOpen only to doctoral students. Advanced study of mathematical modeling.
 MSTM 6036  Advanced topics in discrete mathematicsOpen only to doctoral students. Advanced study of discrete mathematics, combinatorics, and graph theory.
 MSTM 6037  Professional Seminar: Mathematics EducationTopics will vary
 MSTM 6038  Research Methods in Mathematics EducationAn introduction to educational research methods relevant to mathematics education.
 MSTM 6039  Advanced comparative mathematics educationA review and comparison of mathematics education in other nations.
 MSTM 6126  Advanced topics in the mathematical foundations of statisticsOpen 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 educationPermission 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 educationPermission 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 educationPermission 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 educationPermission 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 educationDevelopment of final doctoral dissertation proposals and presentation of proposals for departmental review.
 MSTM 8900  Dissertation advisement in mathematics educationIndividual 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.