Department of Mathematics Bachelor of Science in ...websupport1.citytech.cuny.edu/faculty/adouglas/proposal_10_11.pdf · Bachelor of Science in Mathematics Education 3. Needs Assessment

New York City College of Technology, CUNY

CURRICULUM MODIFICATION PROPOSAL

Department of Mathematics

Bachelor of Science in Mathematics Education

October 12, 2010


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Department of Mathematics Bachelor of Science in Mathematics Education

Proposal

October 12, 2010 Table of Contents:

1. Curriculum Modification Form 2. Description of Curriculum Modification:

Bachelor of Science in Mathematics Education 3. Needs Assessment 4. Proposed Curriculum:

A. Introduction B. Pedagogy Core C. Mathematics Core D. Mathematical Applications Core E. Liberal Arts and Science Core F. Summary of Degree Credit Requirements G. Curriculum by Semester

5. State Requirements for Teacher Preparation Programs 6. National Council for Accreditation of Teacher Education

& National Council of Teachers of Mathematics 7. Prospective Students 8. Faculty 9. Student Views 10. Cost Assessment 11. Articulation Agreements 12. Consultation with affected Departments

A. Career and Technology Teacher Education B. Architecture C. Computer Systems D. Electrical & Telecommunication Engineering Technology

13. Relevant Minutes from Department Curriculum Committee Meeting 14. Relevant Minutes from Department Meetings 15. Letter for Dean Brown 16. Library Resource and Information Literacy Form 17. Curriculum Modification Questions 18. References

Appendix A. Detailed Course Syllabi for Proposed Pedagogy Courses Appendix B. Detailed Course Syllabi for Proposed Math Courses Appendix C. State Requirements for Teacher Preparation Programs Appendix D. NCATE and NCTM Accreditation Standards Appendix E. Certification and Licensing of Teachers in New York State


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New York City College of Technology, CUNY

CURRICULUM MODIFICATION PROPOSAL Please refer to the Curriculum Modification Guide before submitting a proposal.

Title of Proposal Date

Bachelor of Science in Mathematics Education October 12, 2010

Department Chairperson / Coordinator Department/Program

Professor Henry Africk Mathematics

Brief Description

The Mathematics Department of the New York City College of Technology is proposing to sponsor a Bachelor of Science Degree in Mathematics Education. The program will prepare students to teach Middle School and High School mathematics (grades 7 to 12) in New York State. The proposed curriculum is comprised of 4 components: A pedagogy core (25 credits), a mathematics core (41 credits), a required liberal arts core (43-45 credits), and a mathematical applications core (9-11 credits). Courses within the mathematical applications core may be chosen from architecture, electrical and computer engineering technology, computer systems, and/or applied mathematics. The proposal includes 8 new pedagogy courses and 7 new mathematics courses.

Indicate the specific change or changes desired.

MAJOR:

X new course(s)

__experimental courses

__Continuing Education courses for credit

X addition or elimination of programs or certificates

__changes in entrance requirements for matriculation or admission to a specific degree program

__a change which would affect the educational objective of a department and/or of the college

MINOR:

__change in course number and/or title

__change in course description

__change in sequence of courses

__change in prerequisites or corequisites for individual course

__substitution of one course for another of similar hours and credits

__substitution of required course(s) for the degree

__course(s) withdrawn or reinstated

Supporting Documents Checklist:

MAJOR:

Complete description of MAJOR modifications and rationale

All course proposals (see Course Proposal Document Checklist)

Catalog course description specifying hours and credits for lecture and labs, prerequisites and/or corequisites

Relevant minutes from department meetings Completed Curriculum Modification

MINOR:

Description of MINOR modifications and rationale Department minutes with record of the approval Memo or email from the Dean approving the change Evidence of consultation with all affected departments Completed Curriculum Modification Questions


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Questions Documentation of needs assessment Documentation of student views Documentation of Advisory Commission

views (if applicable). Evidence of consultation with all affected

departments Projected headcounts (fall/spring and

day/evening) for each new or modified course. Memo or email from the academic dean to the

Curriculum Committee chairperson with a recommendation for or against adopting the proposed change(s) and reasons for the recommendation.

Completed Library Resources and Information Literacy Form

A memorandum from the VP for Finance and Administration with written comments regarding additional and/or new facilities, renovations or construction (if applicable).

Comparative charts, specifying differences in class hours, lab hours and credits, including course titles and codes.

Documentation indicating core curriculum requirements have been met for New Programs/Options or Program Changes. (if applicable)

Plan and process for evaluation of Curricular Experiments (if applicable)

Established time limit for Curricular Experiments (if applicable)

Submitted by

Department of Mathematics, NYCCT

Contact: Professor Andrew Douglas

Email: [email protected]

Email this form along with all supporting documents to the Chair of the College Council Curriculum Committee. Professor Jill Bouratoglou

Email: [email protected]


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2. Description of Curriculum Modification: Bachelor of Science in Mathematics Education

The Mathematics Department of the New York City College of Technology is proposing to sponsor a Bachelor of Science Degree in Mathematics Education. The program will prepare students to teach Middle School and High School mathematics (grades 7 to 12) in New York State. The proposed curriculum is comprised of 4 components: A pedagogy core (25 credits), a mathematics core (41 credits), a required liberal arts core (43-45 credits), and a mathematical applications core (9-11 credits). Courses in the pedagogy core are linked to mathematics content and are specifically focused on the teaching of mathematics. The mathematics core will provide students with a solid foundation needed to teach mathematics with rigor and self-confidence. Program graduates will have the math background necessary to enter Master’s degree programs in either Mathematics Education or pure Mathematics. Courses within the mathematical applications core may be chosen from architecture, electrical and computer engineering technology, computer systems, and/or applied mathematics. The electives are designed to provide a broad foundation in the application of mathematical principles. The proposal includes 8 new pedagogy courses and 7 new mathematics courses. Catalogue descriptions of the new courses are included in Section 4. Detailed course outlines are included in Appendices A and B.

3. Needs Assessment Substantial employment opportunities exist for highly qualified mathematics teachers According to the 2010-2011 Occupational Outlook Handbook published by the Bureau of Labor Statistics, this trend will continue for the foreseeable future, especially in urban and rural areas with underserved populations. “Currently, many school districts have difficulty hiring qualified teachers in some subject areas—most often mathematics, science (especially chemistry and physics), bilingual education, and foreign languages. Increasing enrollments of minorities, coupled with a shortage of minority teachers, should cause efforts to recruit minority teachers to intensify.” To quote NEA President Dennis Van Roekel, “There is a clear understanding that our nation’s prosperity is tied to innovation spurred on by our students’ engagement in science, engineering, and mathematics.” According to federal sources, a substantial STEM teacher shortage exists today. Overall, up to one million teachers will need to be recruited over the next five years, and vacancies in math and science are often the hardest to fill.


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In addition, searches of relevant jobs listings consistently show a significant number of positions available for mathematics instructors.


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4. Proposed Curriculum 4. A. Introduction The proposed curriculum is comprised of 4 components: A pedagogy core (25 credits), a mathematics core (41 credits), a required liberal arts core (43-45 credits), and a mathematical applications core (9-11 credits). 4. B. Pedagogy Core The Pedagogical Core has been designed to provide students with a solid grasp of teaching and learning theory as it applies to mathematics education. It will endow students with a wealth of knowledge and experience in the methods of instruction in the mathematics classroom. The core consists of 25 credits of required coursework as reflected in the table below. The catalog course descriptions may be found below. Detailed course syllabi may be found in Appendix A. Course Credits MEDU 2901 Peer Leader Training in Mathematics 1 *MEDU 1010 Foundations of Education 2 *MEDU 1020 Teaching and Learning Strategies 2 *MEDU 2010 Assessment Techniques in Mathematics 2 *MEDU 2020 Pedagogy of Mathematics Applications 2 *MEDU 3010 Methods of Teaching Middle School and High School Mathematics I

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*MEDU 3020 Methods of Teaching Middle School and High School Mathematics II

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*MEDU 4010 Supervised Student Teaching and Seminar in Middle School Mathematics

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*MEDU 4020 Supervised Student Teaching and Seminar in High School Mathematics

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EDU 4600 Professional Development Seminar 2 Total Credits 25 *Indicates a new course. The Pedagogy Core provides an extensive sequence of courses focused on teaching and learning and the examination of effective instructional methods. These courses have been designed to support and complement the students’ field experiences and cover a broad range of pre-service essentials, such as: the psychological underpinnings of adolescent behavior, instructional methods, and issues pertinent to urban populations. The Pedagogy Core will immerse students in rich and diverse field experiences in both middle school and secondary school classrooms. Under the supervision of mathematics faculty, students will spend 120 hours of pre-service classroom teaching, where they will


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observe experienced classroom teachers, participate in lessons, and work with small groups of students. After successful completion of pre-service teaching, students will enter the supervised teaching practicum. Here students spend more than 200 hours teaching in both middle and secondary school classrooms. Students will apply their acquired pedagogical knowledge and skills, and be observed and receive feedback from mathematics faculty and skilled classroom teachers. A unique feature of the proposed program is the focus on enhancing and enriching teacher candidates' understanding of how fundamental mathematics is in every aspect of our society. This will be addressed in a specially designed course entitled "Pedagogy of Mathematics Applications." In essence, The Pedagogy Core seeks to facilitate the development of prospective teacher candidates into reflective educators, well trained in the best practices of mathematics education, and instilled with a commitment to lifelong growth in their future career as math educators.

Catalogue Descriptions of Proposed Pedagogy Courses Course: MEDU 2901 Title: Peer Leader Training in Mathematics Credit Hours: 1 cl hr, 1 cr Catalogue Description: Training students to be peer leaders for a mathematics workshop is the objective for this course. Peer leaders learn to lead a group of students by focusing on communication, group dynamics, motivation, learning styles and other process issues, to help participants actively engage with course material. Reflective journals revealing the development of workshop practices will be required. Prerequisite: ENG 1101, MAT 1275 and Permission by the Mathematics Department. Course: MEDU 1010 Title: Foundations of Education Catalogue Description: This course examines the historical, philosophical, and sociological foundations underlying the development of American educational institutions. The role of the schools, the aims of education, diverse learners, the mathematics curriculum in New York State, legal principles that affect education, and the role of state, local, and federal agencies will be emphasized. Prerequisites: CUNY proficiency in reading, writing and mathematics. Course: MEDU 1020 Title: Teaching and Learning Strategies Credit Hours: 1 cl hr, 2 lab hours, 2 cr Catalogue Description: Students explore a wide variety of teaching and learning strategies used in mathematics. These strategies include oral and written communication, quantitative literacy, soft competencies, collaborative learning, critical thinking, library research and use of technology. Students will also explore theories of teaching and learning processes and motivation. Strategies to address students' learning difficulties in mathematics will be developed based on emotional intelligence, learning styles and other


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theories. Active learning through the arts of observing, listening and questioning will be explored. Teacher candidates will examine ways in which students' previous knowledge can be used to stimulate intellectual curiosity. Prerequisites: MAT 1375, CUNY proficiency in reading and writing. Course: MEDU 2010 Title: Assessment Techniques in Mathematics Credit Hours: 1 cl hours, 2 lab hours, 2 cr Catalogue Description: Students will explore essential classroom assessment concepts and major assessment issues including those pertaining to district, state and national assessment. A variety of assessment techniques will be examined in theory and practice, including affective assessment, portfolio assessment, and formative and summative performance-based assessment. The distinction between assessment and evaluation will be discussed. Test and rubric construction, designing questions to promote thinking, and the role of standardized tests will also be included. Prerequisites: MEDU 1020, ENG 1101 Course: MEDU 2020 Title: Pedagogy of Mathematical Applications Credit Hours: 1 cl hour, 2 lab hours, 2 cr Catalogue Description: Students will examine effective pedagogical approaches to teaching mathematical applications. Applications will be used to motivate and explore the use of problem solving and writing in the teaching and learning of mathematics. Technology will be used as a tool to pursue problems, and its effective use in the classroom will be analyzed. Students will develop activities consistent with state curriculum that are enriched with mathematical applications. Applications will be selected from a wide variety of fields in science, technology, and engineering, and may include mathematical modeling. Prerequisites: MEDU 1020, MEDU 2010, MAT 1475 Course: MEDU 3010 Title: Methods of Teaching Middle School Mathematics Credit Hours: 3 cl hours, 6 field hours/week, 3 cr Catalogue Description: Students will examine the development of curriculum for grades 7-‐9, aligning with state and national standards and incorporating appropriate teaching and learning strategies and assessment techniques. Focus and analysis will be on the needs of individual learners, and small and large group instruction techniques (i.e. learning communities), the various roles of the teacher in the classroom, planning individual lessons, and long-‐range curriculum planning. Topics will include differentiation of instruction to meet the needs of various learners, including students with disabilities and special health-‐care needs, as well as strategies for the development of listening, speaking, reading and writing skills of all students. Includes 6 hours per week for 10 weeks of preservice field experience in middle schools. Pre/Corequisite: MEDU 2020, ENG 1121


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Course: MEDU 3020 Title: Methods of Teaching High School Mathematics Credit Hours: 3 cl hours, 6 field hours/week, 3 cr Catalogue Description: Students will examine the development of curriculum for grades 10-‐12, aligning with state and national standards and incorporating appropriate teaching and learning strategies and assessment techniques. Focus and analysis will be on the needs of individual learners including English language learners and those with disabilities and special health needs, small and large group instruction techniques (i.e. learning communities), the development of literacy in the mathematics classroom, the various roles of the teacher in the classroom, planning individual lessons, and long-‐range curriculum planning. Includes 6 hours per week for 10 weeks of preservice field experience in high schools. Prerequisite: MEDU 3010 Course: MEDU 4010 Title: Supervised Student Teaching and Seminar in Middle School Mathematics Credit Hours: 1 cl hr, 1 cr Catalogue Description: The field experience is designed to prepare students for teacher certification in mathematics. The course involves a supervised student teaching experience in grades 7 through 9 mandated in state standards for preparing classroom teachers. Emphasis is placed on preparing student teachers to teach towards diversity, implement different teaching strategies, refine classroom management skills, develop assessment practices, and incorporate technological resources to facilitate instruction. The seminar component provides a forum on reflective practice in the concurrent field placement. Students are expected to complete a minimum of 20 days or 120 hours of supervised student teaching in a Middle School mathematics classroom. Prerequisite: MEDU 3010 and permission of department. Course: MEDU 4020 Title: Supervised Student Teaching and Seminar in High School Mathematics Credit Hours: 9 field hrs/week, 3 cr Catalogue Description: The field experience is designed to prepare students for teacher certification in mathematics. The course involves a supervised student teaching experience in grades 10 through 12 mandated in state standards for preparing classroom teachers. Students design lesson plans appropriate for the high school mathematics curriculum. Topics in mathematics pedagogy include problem solving, connections between mathematics and other disciplines, assessment in the contexts of New York State and national standards. Students develop and analyze lessons that incorporate appropriate technology to meet the needs of diverse student populations. Students are expected to complete a minimum of 20 days or 120 hours of supervised student teaching in a high school mathematics classroom. Prerequisite: MEDU 3020 and permission of department.


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Course: EDU 4600 Title: Professional Development Seminar Credit Hours: 2 cl hrs, 2 cr Catalogue Description: A series of seminars that accompany the student teaching experience. Seminar topics focus on both the student teaching experience and a broad range of educational issues which form the basis for student reports and reflective essays. The course provides the forum for instruction on special topics mandated in the Regents standards for preparing classroom teachers including identifying and reporting suspected child abuse or maltreatment; preventing child abduction; preventing alcohol, tobacco and other drug abuse; providing safety education; and providing instruction in fire and arson prevention. Prerequisite: MEDU 3020 Corequisite: MEDU 4010 4. C. Mathematics Core The mathematics core of the proposed program will provide future middle school and high school math teachers with the solid foundation needed to teach mathematics with rigor and self-confidence. Program graduates will have the math background necessary to enter Master’s degree programs in either Mathematics Education or pure Mathematics, which is required of teacher in New York State. The mathematics core consists of 41 credits of required mathematics coursework listed in the table below. In addition to these 41 credits of mathematics, MAT 1475 Calculus I, and MAT 1575 Calculus II are part of the Liberal Arts and Science Core Requirements, which brings the total required credits in mathematics to 49. Additional mathematics courses may be taken within the mathematical applications core described in subsection 4. D.


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Course Credits MAT 2675 Calculus III 4 MAT 1476L Calculus Laboratory 1 MAT 2580 Linear Algebra 3 MAT 2630 Applied Mathematics Technology 3 MAT 2572 Probability and Statistics I 4 MAT 2672 Probability and Statistics II 4 *MAT 2070 Introduction to Proofs and Combinatorics 3 *MAT 3020 Number Theory 3 *MAT 3050 Geometry I 3 *MAT 3075 Introduction to Analysis 4 *MAT 3080 Modern Algebra 3 *MAT 4050 Geometry II 3 *MAT 4030 History of Mathematics 3 Total Credits in the Math Core 41 **MAT 1475 Calculus I 4 **MAT 1575 Calculus II 4 Total Required Math Credits in the Proposed Program 49 * Indicates a new course ** Indicates a mathematics course included in the Liberal Arts and Science Core Requirements.

The mathematics requirements at New York City College of Technology are designed so graduates are proficient in the use of current technology. To this end, we include non-traditional courses, Calculus Lab and Applied Mathematics Technology. In the Calculus Lab majors learn how to use computer applications to solve problems involving calculus while students in the Applied Mathematics Technology course study why and when errors occur from computations utilizing computer technology and they learn how to avoid them. Another unique feature of the proposed program is the coordination of the pedagogical coursework with the math content courses. This infuses the program’s mathematics courses with the latest and most relevant pedagogy, demonstrating and reinforcing effective teaching methods across the spectrum of mathematics. Pedagogy is not presented separately from mathematics, as often occurs in more traditional education programs.


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Catalogue Descriptions of Proposed Mathematics Courses

Course: MAT 2070 Title: Introduction to Proofs and Combinatorics Credit Hours: 3 cl hrs, 3 cr Catalogue Description: The course is designed to prepare students for an advanced mathematics curriculum by providing a transition from Calculus to abstract mathematics. The course focuses on the processes of mathematical reasoning, argument, and discovery. Topics include propositional and first order logic, learning proofs through puzzles and games, axiomatic approach to group theory, number theory, and set theory, abstract properties of relations and functions, elementary graph theory, sets of different cardinalities, and the construction and properties of real numbers. Pre/Corequisite: MAT 1575 Course: MAT 3020 Title: Number Theory Credit Hours: 3 cl hrs, 3 cr Catalogue Description: This course is an introduction to number theory. Topics include Divisibility (Division algorithm, GCD, etc), primes, congruences, the fundamental theorem of arithmetic, quadratic reciprocity, number theoretic functions and Fermat’s little theorem. Some applications will be done, which can be computer based, to encourage students to propose and test conjectures. Prerequisite: MAT 2070 Course: MAT 3050 Title: Geometry I Credit Hours: 3 cl hrs, 3cr Catalogue Description: This course will cover Euclidean geometry in two dimensions from a synthetic point of view. It will cover classical theorems as well as groups of transformations. Prerequisites: MAT 2070 Pre/Co-requisites: MAT 3080 Course: MAT 3075 Title: Introduction to real analysis Credit Hours: 4 cl hrs, 4 cr Catalogue Description: This course is an introduction to analysis of real functions of one variable with a focus on proof. Topics include the real number system, limits and continuity, differentiability, the mean value theorem, Riemann integral, fundamental theorem of calculus, series and sequences, Taylor polynomials and error estimates, Taylor series and power series. Prerequisites: MAT 1575, MAT 2070


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Course: MAT 3080 Title: Modern Algebra Credit Hours: 3 cl hrs, 3 cr Catalogue Description: An introductory course in modern algebra covering groups, rings and fields. Topics in group theory include permutation groups, cyclic groups, dihedral groups, subgroups, cosets, symmetry groups and rotation groups. In ring and field theories topics include integral domains, polynomial rings, the factorization of polynomials, and abstract vector spaces. Prerequisites: MAT 2580, MAT 3075 Course: MAT 4030 Title: History of Mathematics Credit Hours: 3 cl hrs, 3 cr Catalogue Description: The course examines the historical development of mathematical concepts from the origins of algebra and geometry in the ancient civilizations of Egypt and Mesopotamia through the advent of demonstrative mathematics of ancient Greeks to the discovery of Calculus, non-Euclidian geometries, and formal mathematics in the 17-20th century Europe. Topics include a historical examination of the development of number systems, methods of demonstration, geometry, number theory, algebra, Calculus, and non-Euclidean geometries. Prerequisites: MAT 2070, MAT 3020. Course: MAT 4050 Title: Geometry II Credit Hours: 3 cl hrs, 3 cr Catalogue Description: This course will cover Euclidean and hyperbolic geometry in two dimensions including group actions on these spaces by groups of transformations. The complex plane will be introduced in rectangular and polar coordinates and classical theorems of geometry will be covered in this setting. Prerequisites: MAT 3050, MAT 3080. 4. D. Mathematical Applications Core Mathematics Education majors will be exposed to an array of applied mathematics experiences. Taking advantage of the unique offerings at City Tech, majors can select 9-11 credits from two or more of the following areas: Architecture, Electrical Engineering Technology, Computer Systems, and Applied Mathematics. These electives provide teacher candidates with a deeper understanding of the application and importance of mathematics. For example, in architecture students will apply mathematics to orthographic projection, creation of three-dimensional models and site planning. In the electrical engineering


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elective courses students apply math to the analysis of electric circuits and systems and to computer technology. Students will enhance their problem solving skills using computer programming with electives in computer systems and the electives in applied mathematics will illustrate the use of differential equations, optimization, and dynamic models to solve problems from industry. Architecture Credits Computer Systems Credits ARCH CST 1111 Foundations I 3 1101 Intro Programming 3 1211 Foundations II 2 2403 C++ Programming I 3 1250 Site Planning 2 3503 C++ Programming II 3 Electrical & Telecommunication Engineering Technology

Applied Mathematics

EET MAT 1102 Electrical Tech 2 2680 Diff Equations 3 1122 Circuits I 4 3770 Math Modeling I 3 1150 Circuits II 5 4880 Math Modeling II 3 Note: The Department of Architectural Technology is planning curricular changes to ARCH 1111, ARCH 1211 and ARCH 1250. These changes will not affect their inclusion into the mathematical Applications Core. 4. E. Liberal Arts and Science Core Requirements The liberal arts core requirements satisfy both College and the State requirements for the baccalaureate degree and are designed so students can acquire a broad knowledge base, crucial skills, and an awareness of ethical and aesthetic values. The core course requirements are illustrated in the table below.


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Liberal Arts & Science Core Requirements

Competency Requirement Credits Communication Skills Oral: Speech (SPE 1330

Effective Speaking or higher) Written: English Composition I and II, Literature (ENG 2, PRS 2 or AFR 2), elective (ENG 1121 or higher) 12

Scientific Reasoning A two semester sequence in a lab science*: Physics: PHY 1441, 1442, Biology: BIO 1101, 1201 or Chemistry: CHEM 1110, 1210 8-10

Mathematics Calculus I and II 8 Appreciation for Inquiry PSY 1101 Introduction to

Psychology, and PSY 2501 Child and Adolescent Development. Two electives from literature, aesthetics or philosophy 15

Total 43-45 credits * The physics sequence is 10 credits. The biology and chemistry sequences are each 8 credits. 4. F. Summary of Degree Credit Requirements Pedagogy Core 25 Credits Mathematics Core 41 Credits Liberal Arts and Science Core 43-45 Credits Mathematical Applications Core 9-11 Credits (to make 120 credits) Total 120 Credits


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4. G. Curriculum by Semester Scheduling of the Pedagogy and Mathematics courses by semester is outlined in the tables below. Mathematics faculty, in consultation with each student, will determine the scheduling of courses within the Liberal Arts and Science Core, and the mathematical application core.

Scheduling of Pedagogy Courses by Semester

Semester Pedagogy Core Courses I MEDU 2901 Peer Leader Training in Mathematics II MEDU 1010 Foundations of Mathematics

MEDU 1020 Teaching and Learning Strategies III MEDU 2010 Assessment Techniques in Mathematics IV MEDU 2020 Pedagogy of Mathematics Applications V MEDU 3010 Methods of Teaching Middle School Mathematics VI MEDU 3020 Methods of Teaching High School Mathematics VII EDU 4600 Professional Development Seminar

MEDU 4010 Supervised Student Teaching and Seminar in Middle School Mathematics VIII MEDU 4020 Supervised Student Teaching and Seminar in High School Mathematics

Scheduling of Mathematics Courses by Semester Semester Math Core Course I MAT 1475 Calculus I

MAT 1476L Calculus Lab II MAT 1575 Calculus II

MAT 2580 Introduction to Linear Algebra III MAT 2675 Calculus III

MAT 2070 Introduction to Proofs and Combinatorics IV MAT 2630 Applied Mathematics Technology

MAT 3075 Introduction to Analysis V MAT 2572 Probability and Mathematical Statistics I

MAT 3020 Number Theory VI MAT 2672 Probability and Mathematical Statistics II

MAT 3080 Modern Algebra MAT 3050 Geometry I

VII MAT 4050 Geometry II VIII MAT 4030 History of Mathematics


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5. State Requirements for Teacher Preparation Programs Teacher preparation programs must be registered with the New York State Education Department (NYSED). The program described in the current proposal meets or exceeds the NYSED pedagogical requirements for adolescence teacher education programs (grades 7-12). In Appendix C we explicitly list the NYSED pedagogical requirements. This list is accompanied by justification that the proposed program meets these requirements. 6. National Council for Accreditation of Teacher Education & National Council

of Teachers of Mathematics We intend to seek national accreditation within 5 years of starting the proposed program. The agency responsible for such accreditation is the National Council for Accreditation of Teacher Education (NCATE). NCATE has 6 standards that must be met for accreditation. The first standard relating to content knowledge and pedagogical content knowledge is tied to criteria defined by the National Council of Teachers of Mathematics (NCTM). In Appendix D we describe both the NCATE and NCTM standards. The program described in the current proposal meets or exceeds the standards set out by NCATE and NCTM for mathematics teacher education programs. 7. Prospective Students Based on program offerings at the College, we fully expect that the students who will be attracted to and enroll in this program will reflect the rich cultural diversity present in the College’s student population which is 35% Black, 31% Hispanic, 18% Asian, and approximately 52% male and 48% female. The expected enrollment growth for the program over the first five years is projected in the table below. Y ear 1 2 3 4 5 Full Time 15 34 57 79 87 Part Time 5 10 19 28 37 Total 20 43 76 107 123 We make the assumption that the retention rate is 95% from years 1 through 4. In year 1 we anticipate 15 full time and 5 part time students. For year 2 we expect 20 new full time and 5 new part time students. For the following years we assume 25 new full time and 10


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new part time students. In computing the full time students in year 5,we used a 90% graduation rate. 8. Faculty The Mathematics Department at New York City College of Technology has 46 full time faculty – 38 with doctorates including scholars in the field of mathematics education. The Department of Mathematics, along with consultation from the Career and Technical Education Department, is fully capable of delivering and supporting this program.


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9. Student Views In the fall 2010, a survey was distributed to students enrolled in MAT 1375, MAT 1475, MAT 1575, MAT 2675 and students involved in the Peer Leader program. The survey form and results follow. Student Survey of Interest in B. S. Degree in Secondary School Mathematics Education

Completing this form is voluntary and has no bearing on your course grades. 1. What mathematics course(s) are you currently taking? 2. When are you taking these math courses? Day Evening 3. Are you a part-‐time or full-‐time student? Part-‐time Full-‐time 4. Please indicate your current major program: 5. Are you planning to complete a baccalaureate degree? Yes No 6. Are you a member of the Math Peer Leader Program? Yes No To meet the strong demand for highly qualified teachers of secondary school mathematics, the college is preparing to offer a Bachelor of Science Degree in Mathematics Education. This program, offered by the Mathematics Department, will prepare students for entry-‐level certification as teachers of middle and high school mathematics. The program will include a wide range of mathematics courses, instruction in teaching pedagogy and assessment, supervised practice teaching, and elective courses involving applications of mathematics in several of the college's mathematics and technology programs. 7. How interested would you be in enrolling in a B. S. degree program in

Mathematics Education, if such a program were offered at New York City College of Technology?

(Your response to this question does not commit you to any course of action.) Very interested Somewhat interested Not interested 8. If you have an interest in this program, check when you would prefer to take

your classes: I prefer day classes I prefer evening classes I prefer weekend classes ________


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Comments: Results of Student Survey The results for the following question are listed in the table below: How interested would you be in enrolling in a B. S. degree program in Mathematics Education, if such a program were offered at New York City College of Technology?

Course Very Interested

Somewhat Interested

Not Interested No Answer Total Surveyed

MAT 1375 63 274 336 4 677 MAT 1475 62 166 178 0 362 MAT 1575 31 72 54 0 157 MAT 2675 7 20 14 0 41 Peer Leaders 6 4 0 0 10 Total 169 536 582 4 1291


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10. Cost Assessment No additional faculty are required and no additional expenses are anticipated. The following table shows our projected expenses for the first five years of our program.

Year 1 2 3 4 5

I. Additional Personnel

$0.00 $0.00 $0.00 $0.00 $0.00

2. OTPS $0.00 $0.00 $0.00 $0.00 $0.00

11. Articulation Agreements The College has reached out to the Borough of Manhattan Community College, which has expressed interest in articulating with this program. Due to the uniqueness of the proposed program, we anticipate interest from other community colleges as well. 12. Consultation with affected Departments

12. A. Career and Technology Teacher Education Dear Prof. Douglas: This email confirms that you consulted with me in connection with your department's proposed B.S. in Education degree program in Mathematics Education. The faculty of the Department of Career and Technology Teacher Education considered your proposal during our faculty meeting of September 22, 2010 and was very supportive of the proposal. We welcome the prospect of having other teacher programs at City Tech. My department supports the inclusion of our course, EDU 4600 Professional Development Seminar in the proposed Mathematics Education curriculum. We will, at some point in the future, modify the current pre- and co-requisities of EDU 4600 to match the courses in your proposed program. Let me know if I can be of further assistance. Best regards, Godfrey Nwoke


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12. B. Architecture Hello Andrew, We support the inclusion of Architectural Technology courses among the mathematical applications choices in the proposed new Mathematics Education curriculum. Given the extent of mathematical applications in architecture, we believe this will be of mutual benefit to students in both programs. Best of luck with the proposal, Shelley Professor Shelley E. Smith Department of Architectural Technology New York City College of Technology The City University of New York 300 Jay Street, Voorhees 818 Brooklyn NY 11201 718.260.4993 718.260.8547 fax [email protected] 12. C. Computer Systems

Hi Andrew, Have you submitted the letter of intent? We support your proposal of a Mathematical Education B.S. degree. Let me know if you need anything else from me. Thanks, Candido ___________________________ Andrew Douglas wrote: Dear Professor Cabo, In October 2010, the Department of Mathematics is planning on submitting a proposal for a new Bachelor of Science in Mathematics Education. Attached is the proposal for the program. The proposal affects your department because we would like to include CST 1101, CST 2403, and CST 3503 into a group of courses from which students will select electives. We are hoping that you and your faculty will support our proposal for a new program Best regards,


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Andrew Douglas Assistant Professor Department of Mathematics New York City College of Technology City University of New York ____________________________ Candido Cabo, Ph.D. Associate Professor and Chairman Department of Computer Systems New York City College of Technology City University of New York 300 Jay Street Brooklyn, NY 11201 718-260-5170 (voice) 718-254-8659 (fax) [email protected]

12. D. Electrical & Telecommunication Engineering Technology September 20, 2010 From: Andrew Douglas <[email protected]> To: [email protected] Cc: Henry Africk <[email protected]> Dear Professor Razani, In October 2010, the Department of Mathematics is planning on submitting a proposal for a new Bachelor of Science in Mathematics Education. Attached is the proposal for the program. The proposal affects your department because we would like to include EET 1102, EET 1122, and EET 1150 into a group of courses from which students will select electives. We are hoping that you and your faculty will support our proposal for a new program Best regards, Andrew Douglas Assistant Professor Department of Mathematics New York City College of Technology City University of New York


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13. Relevant Minutes from Department Curriculum Committee Meeting Department of Mathematics Curriculum Committee Minutes Meeting date: October 7, 2010 Present: H. Carley, P. Deraney, A. Douglas, L. Ghezzi, , M. Harrow, N. Katz, J. Natov, B.

Kostadinov, A. Mayeli, M. Munn, E. Rojas, A. Taraporevala (Chair), L. Zhou Guest: D. Kahrobaei, D. Desantis, Z. Chen, A. Rozenblyum, T. Johnstone, J.

Greenstein, G. Klimi Absence/Excused: M. Ajoodanian, N. Benakli, S. Han, J. Liou-‐Mark, S. Singh

1. The meeting was called to order at 12:50pm in N 718.

2. Prof. Douglas gave an updated report on the proposal for the new program: Bachelor of Science in Mathematics Education. Motion: Approve the proposal for the new program: Bachelor of Science in Mathematics Education Action: Carried.

3. The meeting was adjourned at 1:05pm.

Respectfully submitted, Lin Zhou


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14. Relevant Minutes from Department Meetings Mathematics Department Meeting (Minutes) Date: October 7, 2010 Present: Profs. Africk (Chair), Benakli, Bonanome, Carley, Cermele, Chen, Chosid,

Deraney, Desantis, Douglas, ElHitti, Ghezzi, Gitman, Greenstein, Han, Harrow, Johnstone, Kahrobaei, Katz, Klimi, Kostadinov, Liou-Mark, Mayeli, Mukhin, Munn, Natov, Niezgoda, Reitz, Rojas, Rozenblyum, Schoutens, Taraporevala, Yuce, Zhou.

Absence/Excused: Profs: Ajoodanian, Beheshti, (Celikler), Colucci, Ellner, Gelbwasser,

Ghosh-Dastidar, Halleck, Hill, Kramer, Singh, Tradler.

• The meeting was called to order at 1:00 p.m. in N 717. • Motion: Approval of the minutes of the department meeting of September 2,

2010, as amended. Action: Carried.

• Chairperson’s report:

Dates to remember: • 10/8: Two talks at the Graduate Center: Prof. Ghezzi in the algebra

colloquium at 10:30am in Rm. 3209; Prof. Reitz in the set theory seminar at 10:00am in Rm. 6417

• 10/12-10/15: Elections (Prof. Ghezzi runs for alternate delegate at large to college council)

• 10/12-10/14: First week of MAT 1175&1275 review workshops. Sessions will be held the weeks of 10/11, 11/8, and 12/6. Sign-up in Atrium Learning Center AG-18 for one, two, or three sets of two 2 1/2 hr sessions

• 10/14: LAS General meeting 12:45-2:00pm Atrium Amphitheater. • 10/14: Math club: “Visualizing math with Maple” , Prof. Taraporevala • 10/17: Proposals due for Annual Poster Session on November 18, 2010 • 10/21: Math club: “Logic Puzzle Solving”, Profs. Gitman and Reitz • 10/28: Math club: “Internships and Careers for Applied Mathematics Major”,

Prof. Natov • 10/28: Curriculum committee meeting • 11/04: Math club: student presentations • 11/04: Next mathematics department meeting

Chairperson’s announcements: • A report of President Hotzler’s announcements at the recent P & B meeting:

Budget news is worse TAP will be cut further: each student award will be reduced by $100;

each new student will have to pay $150 deposit before being allowed to


26

register; minimum number of credits required for TAP may be raised for Spring 2011 (situation is unclear and college will advise)

Chancellor will request a 4% tuition increase for Spring 2011 CUNY proficiency exams (CPE) may be eliminated starting January

2011 Discussions at CUNY on new limitations on admission of remedial

students and how many times a student may repeat a remedial course

• Curriculum Committee Action items:

Prof. Taraporevala introduced Profs. Natov and Douglas to report recent curriculum committee agenda. • Prof. Natov presented minor changes for some applied math courses.

– Motion: Change the prerequisites of MAT 2572 from MAT 1475 to MAT 1575. Action: Carried. – Motion: Change the prerequisites of MAT 2672 from MAT 2572 and MAT 2580 to MAT

2572, MAT 2580 and MAT 2675; change the course number from MAT 2672 to MAT 3672.

Action: Carried. – Motion: Change the prerequisites of MAT 3772 from MAT 2672 to MAT

2572. Action: Carried. – Motion: Change the prerequisite of MAT 4872 from MAT 3772 to MAT 3672 (formerly MAT 2672). Action: Carried. – Motion: Change the name of MAT 2630 from “Numerical Methods” to “Applied Mathematics Technology - Numerical Methods”. Action: Carried.

• Prof. Douglas gave a computer-aided presentation of the proposal for the Bachelor of Science in Mathematics Education. Motion: Accept this proposal for the Bachelor of Science in Mathematics Education. Action: Carried. Prof. Douglas thanked the twenty members of the mathematics education committee for their assistance.

• Profs. Africk and Taraporevala thanked Prof. Douglas for his efforts in creating the proposal for the Bachelor of Science in Mathematics Education, and they also thanked the other members of the mathematics education committee for their contributions. The proposal will be submitted to the college council curriculum committee on October 12, 2010.


27

• Prof. Cermele reminded us to submit our requests to the budget and supplies committee by Oct. 17, 2010, if we want to order books related to our research. He also reminded us that fellowship award applications and scholar incentive award applications for 2011/12 are now being accepted until November 12.

• Prof. Rozenblyum reported that the final examination committee is working on creating new final exams in MAT 1175 and MAT 1375, since the respective curricula were recently changed in these courses.

• Prof. Han distributed and discussed hand-outs illustrating the current, difficult situation concerning TAP awards for students. For instance, from the third semester on, students must pass at least 15 credits each semester and are not allowed to ever fall behind schedule, in order to receive any TAP awards. We should take these strict requirements into account when advising students at registration.

• The meeting was adjourned at 2 pm.

Respectfully submitted, Thomas Johnstone


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15. Letter from Dean Brown NEW YORK CITY COLLEGE OF TECHNOLOGY The City University of New York Pamela Brown, PhD, PE Dean of the School of Arts and Sciences 300 Jay Street, Namm 805 Brooklyn, NY 11201-‐2983 Ph: (718) 260 – 5008 Fax: (718) 260 – 5012 [email protected]

October 8, 2010 To: Prof. Jill Bouratoglou, Chair of the Curriculum Committee From: Pamela Brown, Dean of the School of Arts and Sciences Subject: Letter of Support – Proposed BS in Mathematics Education It is my pleasure to write a letter of support for the proposed BS in Mathematics Education. Research has shown that the most important factor in students’ learning is the teacher – what the teacher knows and can do (Sanders, 1997). The design of this program is based on the findings of educational research on how to most effectively prepare K-‐12 teachers. “Measures of teacher preparation and certification are by far the strongest correlates of student achievement in reading and mathematics, both before and after controlling for student poverty and language status.” (Darling-‐Hammond (2000)). The proposed program boasts a strong foundation in mathematics, pedagogy, general education, and mathematical applications. The mathematics core and mathematical application requirements far exceed those of most mathematics education programs. It is for these reasons that I support this proposal.


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16. Library Resource and Information Literacy Form CURRICULUM PROPOSAL – NEW COURSES AND PROGRAMS

LIBRARY RESOURCES & INFORMATION LITERACY Please complete this form for new courses/programs and major changes to existing courses/programs. Library resources will be assessed to see if adequate for the course(s) and if additional materials should be acquired. Consult with library faculty subject selectors early in the planning of course proposals. This will ensure enough time for collection assessment/selection, and budget allocations/requests if materials need to be purchased. Library faculty subject selectors are listed at: http://library.citytech.cuny.edu/research/subjectguides/subjectSpecialists/index.html Course proposer: please complete boxes 1-5. Library faculty subject selector: please complete box 6. #1 Title of proposal Bachelor of Science in Mathematics Education

Department/Program Mathematics

Department Chairperson/Coordinator Henry Africk

Expected date course will be offered # of students Fall 2011 Each new course is projected to have 20 students the first time it is offered.

Proposed by Department of Mathematics Contact: Andrew Douglas [email protected] 718.260.4964

Date September 20, 2010

#2 Brief description of course The Mathematics Department of the New York City College of Technology is proposing to sponsor a Bachelor of Science Degree in Mathematics Education. The program will prepare students to teach Middle School and High School mathematics (grades 7 to 12) in New York State. The proposed curriculum is comprised of 4 components: A pedagogy core (25 credits), a mathematics core (41 credits), a required liberal arts core (43-45 credits), and a mathematical applications core (9-11 credits). Courses within the mathematical applications core may be chosen from architecture, electrical and computer engineering technology, computer systems, and/or applied mathematics. The proposal includes 8 new pedagogy courses and 7 new mathematics courses.


30

#3 Are City Tech library resources sufficient for this course/program? Please explain. The resources are currently sufficient, but the library will need to acquire the recommended books listed under #4. Students will use the library resources including electronic databases for research and course assignments. #4 Are additional resources needed? Specific books / journals / indexes in print Databases and other electronic resources Multi-media (dvds, cds, cd-roms, etc.) Other Optional resources Please include author, title, publisher, edition, date and price. • Teaching and Learning Mathematics: Translating Research for Secondary School

Teachers, http://www.nctm.org/catalog/product.aspx?ID=13775, $18.95. • W.J. Popham, Classroom Assessment: What Teachers Need to Know, Pearson,

2010. $84.15. • Rubenstein, R. N., Beckman, C. E., & Thompson, D. R. (2004). Teaching and

learning middle grades mathematics. Emeryville, CA: Key Curriculum Press. $112.15

• Brumbaugh, et. al. Teaching Secondary School Mathematics, 3rd Edition. Lawrence

Erlbaum Publishers, 2006, $51.36. • Carol Schumacher, Chapter zero: fundamental notions of abstract mathematics, 2nd

edition, Addison Wesley, 2000. $66.89. • David M. Burton, Elementary Number Theory, 7th Ed. McGraw-Hill, 2011.

$130.70. • G. E. Martin, The Foundations of Geometry and the Non-Euclidean Plane, Springer

1975, New York. $52.47. • J. A. Gallian, Contemporary Abstract Algebra, 7th Ed. Brooks/Cole Cengage

Learning, 2010. $140.71. • Victor Katz, History of Mathematics, 3rd edition, Addison Wesley, 2008. $92.52. • Lian-shin Hahn, Complex numbers and geometry, The Mathematical Association of America, 1994. $39.95


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• Kauchak, Eggen, and Carter, Introduction to Teaching: Becoming a

Professional 3rd Ed, 2008, Merril-Prentice Hall. $90.34 • Mathematics: Modeling Our World (MMOW) Course 1, the

Consortium for Mathematics and its Applications, 2nd edition. ($15)

• Mathematics: Modeling Our World (MMOW) Course 2, the Consortium for Mathematics and its Applications, 2nd edition. ($21)

#5 Library faculty members are available to confer with instructors regarding development and enrichment of assignments, papers and projects that foster research and information seeking, critical thinking about sources, and integration of research into student work. Do you plan to consult with the library faculty subject specialist for your area? Yes Please give details. Help may be sought for assisting students with researching journals, books and electronic databases. #6 Library Faculty Subject Selector ______Songqian Lu___ Comments and Recommendations The proposal for Bachelor of Science Degree in Mathematics Education and the related library resources have been reviewed. The current library collection is adequate to support the required liberal arts and mathematics courses for the proposed program, which include required liberal arts core, mathematics core, and mathematical applications core courses. The library will need to acquire the recommended books listed under #4 and additional material for the proposed pedagogy core courses and career education. City Tech library in recent years has expanded its electronic collections. Students and instructors can take advantage of the rich databases and e-book collections, especially the ones focusing on education. In addition to City Tech resources, students have access via CLICS (CUNY Libraries Inter-Campus Services) to books at other CUNY colleges, and now have access to interlibrary loan for journal articles.


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Date September 22, 2010 Library Department October 4, 2006


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17. Curriculum Modification Questions For all Curriculum Modifications

• Has the department approved the modification and recorded the approval in the minutes? Yes

• Has the department consulted with the academic dean?

Yes

• Has documentation of consultation with affected areas been received?

Yes

• Have potential staff space and budget impacts been addressed?

Yes

• Have all legal issues and/or restrictions been addressed?

NA

• Is renovation or new construction required?

No

• Does new space need to be made available?

NA

• If applicable, has the VP for Finance and Administration submitted written comments regarding additional and/or new facilities, renovations or construction?

NA

For New Courses

• Has the form Library Resources and Information Literacy form been completed by proposer and library faculty subject selector?

Yes

• Is this course unique in that the content does not significantly overlap with other

courses?


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Yes • If the proposed modification affects other departments or curricula, have they

been consulted?

Yes

• Are more instructional hours required?

No

• How many full-time and part-time faculty members are qualified to teach this course?

There are 46 full-time faculty qualified to teach the mathematics courses within the proposed program. There are 46 full-time faculty qualified to teach the pedagogy courses. There are also numerous part-time faculty who are current or former high school mathematics teachers who may be qualified to teach pedagogy courses.

• Does new equipment need to be acquired?

No

• Is external funding anticipated?

NA

• Have you surveyed students to determine their interest in the course and learn why they would be interested in taking the course? Are these results included?

Yes/Yes

Role of the course in the curriculum • Is it a stand-alone course or part of a sequence?

All of the new courses in the proposal are required courses for the proposed new Bachelor of Science in Mathematics Education.

• Will this course replace or be an alternative to another course in the curriculum.

If a replacement, will another course be removed from the curriculum? NA

• Does this course have a prerequisite? If so, how often is that course offered?


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Each new course has one or more prerequisites. Prerequisite courses will offered at least once per academic year.

• For which majors will this be a required course? For which majors will this be an

elective?

The new courses are required courses within the proposed Bachelor of Science in Mathematics Education.

• Will you submit this proposal to the Arts and Sciences Core Curriculum

Committee for inclusion in the core? NA

Enrollment needs assessment • When is it expected that this course will this course be offered – spring, summer,

fall, day, evening?

It is intended that each course will be offered once per year, either in the spring or fall. These courses will be offered in the day, but some of the proposed courses could be offered in the evening depending on student demand.

• Each semester, approximately how many students are enrolled in programs where

this course is required or an elective?

NA

• What is your estimate of the number of students that would enroll in this course each semester it is offered? How many sections do you anticipate offering each semester it is offered? How were these value determined? Projected student enrolment and rationale for this projection is presented in Section 7. We will have one section per course initially with the number of sections increasing as the number of students increases.

For New Programs or Program Changes

• Based on the Core Curriculum Checklist, have core curriculum requirements been met? Yes

For Experimental Courses

• Has a time line for the experiment, not to exceed one year, been established? NA


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• After consultation with the director of assessment, have plans for evaluation been

submitted? NA

• Who is responsible for the proposal?

The Department of Mathematics.


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18. References [1] National Council for Accreditation of Teacher Education, Professional Standards

for the Accreditation of Teacher Preparation Institutions, 2008. [2] National Council of Teachers of Mathematics, Principles and Standards for

School Mathematics, 2000. [3] National Council of Teachers of Mathematics, Program Standards for Initial

Preparation of Mathematics Teachers, 2003. [4] New York State Education Department, Pedagogical Core Requirements for

Programs Leading to Certification in Teacher Education, http://www.highered.nysed.gov/ocue/aipr/register.html#Teacher.


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Appendix A. Detailed Course Syllabi for Proposed Pedagogy Courses


39

New York City College of Technology

The City University of New York

DEPARTMENT: Mathematics PREPARED BY: Professor Janet Liou-Mark and Professor A.E. Dreyfuss COURSE: MEDU 2901 TITLE: Peer Leader Training in Mathematics COURSE DESCRIPTION: Training students to be peer leaders for a mathematics workshop is the objective for this course. Peer leaders learn to lead a group of students by focusing on communication, group dynamics, motivation, learning styles and other process issues, to help participants actively engage with course material. Reflective journals revealing the development of workshop practices will be required. TEXT: Roth, V., Goldstein, E., Marcus, G., Peer-Led Team Learning: Handbook for Team Leaders, 2001, Upper Saddle River, NJ: Prentice Hall. CREDITS HOURS: 1cl hr, 1 cr PREQUISITES: ENG 1101, MAT 1275 and Permission by the Mathematics Department LEARNING OUTCOMES: Upon completing this course students should be able to:

1. Implement pedagogical techniques to use in workshops.

2. Communicate effectively in a workshop setting.

3. Reflect on their practice as workshop leaders.

4. Write about their workshop experience and their role as peer leaders with

respect to learning theories covered in this course.

5. Support practice as peer leaders with learning theory.


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6. Understand the emphasis on students’ learning in a collaborative setting.

7. Research a learning theory.

8. Present the results of their research in a poster presentation.

INSTRUCTIONAL OBJECTIVES AND ASSESSMENT:

Instructional Objectives

For the successful completion of this course, students should be able to:

Assessment

Instructional Activity, Evaluation Methods and Criteria

Use facilitation skills in leading workshop

Discussion in class; Reading contents of weekly journals on Discussion Forum; Feedback on in-‐class questionnaires

Write a weekly journal integrating class activities and readings in practice

Discussion in class; Reading contents of weekly journals on Discussion Forum

Write comments on other leaders’ journals to share experiences

Reading contents of Discussion Forum

Read from Handbook, other assigned readings to learn about learning theories applicable to workshop

Reading contents of weekly journals on Discussion Forum; Finding appropriate literature; Feedback on in-‐class questionnaires

Prepare a poster including researching literature

Research skills Understanding what is appropriate literature; Using APA citations; Using PowerPoint; Designing and writing poster content

GRADING PROCEDURE

• Writing Assignments 63% • Research Poster 22% • Attendance, Punctuality, and Classroom Participation 15%

WRITING ASSIGNMENTS Percent of Grade: 63% Nine assignments – 7 points each Please read all directions very carefully each week under “Assignments” on Blackboard. Assignment description: Your writing assignments are an important document in regard to your own learning process and should reflect your learning, thoughts and questions in regard to course and workshop activities, and your ideas about the reading assignments, combining the three elements:


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1) your experience that week leading workshop or tutoring; 2) what you learned from the reading; and 3) what you gained from the Peer Leader Training class. Your writing assignment must be posted before the next class. The earlier you post after your workshop, the better your recollection and the more opportunity there is for feedback from your classmates. Post your assignments to the Discussion Board - each week there will be a new forum. There will be nine assignments and each one is worth seven points. You are asked to read at least two of your classmates' journals each week, and comment on their reflections. Please note: an "assignment" may also take the form of annotated research.

RESEARCH POSTER Percent of grade: 22% Final project Assignment Description: Identify a topic that interests you in regard to learning. Submit your topic to the Discussion Forum set up for this. Research the topic: Identify an area that applies to the Workshop model or tutoring, review the literature for suggested learning interventions, observe your students before and after, discuss the results in light of the learning theory chosen, identifying how we can incorporate your research into the Workshop model. Further guidelines for the poster presentation (content and methodology) and referencing are listed on the Blackboard site. Your presentation will include a summary of the research in your selected area, practical aspects toward the Workshop model, a conclusion and a bibliography. Poster presentations present the ideas (with possible illustration) in bullet form.

ATTENDANCE, PUNCTUALITY, AND CLASSROOM PARTICIPATION Percent of grade: 15% Class is one hour. If you cannot be on time or present for any reason, send an email to the instructor before class starts. Since this class is designed to support your practice as a Peer Leader, it is your obligation to be present so you can help the students in your workshop group to learn from you and each other.

TEACHING AND LEARNING METHODS:

• Facilitation of workshops • Practice using facilitation techniques • Discussion in groups • Brief lectures • Writing journals


42

• Research learning theories and annotate contents of site information • Readings after class sessions to reinforce class activities • Reflecting on practice through discussion, writing, comments • Preparation of poster for presentation: observation of workshop practice; research;

writing; designing and formatting • Use of Blackboard: Discussion Forums

WEEKLY COURSE OUTLINE

Session Topic Assignments 1-5

5 hours (Prior to the start of class)

Peer-‐Led Team Learning Full Day Orientation

Assignments (Reading and Writing) are posted on Blackboard site, under “Assignments”)

6 Communication Skills and Pair Problem-‐Solving

• Write: How did you implement the ideas we discussed in the Education class and you read about? Post your journal on Blackboard, under the Discussion Forum.

• Read: (after the Orientation and prior to first workshop) In Handbook (Roth, Goldstein, Marcus (2001)) Chapters One, Two, and Three (pp. 1-‐22); p. 82, Epstein: How Do I Handle...; p. 79, Kukafka: The First Day; Chapter Five: Basic Learning Principles (pp. 31-‐38).

7 Mattering & Marginality and Jigsaw

• Read: In Handbook: Chapter 7: Race, Class, Gender, and the Workshop; Chapter 8: Students with Disabilities and the Workshop; Gallos, J., "Gender and Silence..." pp. 106-‐114; Ramirez, F., "Addressing Homophobia..." p. 149; Woods, M., "William Shawinski." pp. 150-‐154; Roth, V., "Some Common Myths About Disabilities." pp. 155-‐156; Burg: Reflections on Leader Training, p. 95.

8 Learning Styles (Felder, Kolb, & McCarthy)

• Read: In Handbook: Learning Styles: Ch. 4, pp. 24-‐30; Ch. 5, pp. 35-‐38; Felder, R., pp. 83-‐90; Nakleh, M. pp. 91-‐94. Smith and Kolb (documents handed out in class). In Progressions Newsletter (www.pltl.org): Spring 2001 issue (V. 2, No. 3,) pp. 11-‐12. Algorithmic Problem Solvers Or Conceptual Thinkers? by Okason Morrison (a Peer Leader who graduated from CCNY in May 2005); Progressions Newsletter, Winter 2000, V. 1, No. 2 , pp. 10-‐11 An Application of Learning Theories by Nardia McFarlane; Spring 2004, V.5, No. 3, p. 7. Do Introductory Physics Tests Disadvantage Some Learning Styles More Than Others? By Mark Dentico-‐Olin.

9 Stages of Group Formation (Tucker & Stetson)

• Read:. In Progressions Newsletter (www.pltl.org): Summer 2000 (v. 1, #4) Dixon, L.J., Stages in Group Dynamics, Implications for PLTL, p. 3; Rice, C., Relationship Leadership and Its Usefulness to the Workshop Model, p. 5; Look under "Course Documents" for an article on Relationship Leadership.

• Read: In Handbook: Towns, M.H., How Do I Get My Students To Work Together? Getting Cooperative Learning Started, pp. 74-78; Rosser, S. V., Consequences of Ignoring Gender and Race in Group Work, pp.


43

136-148; Rekuski, R., Helping a Group That Won't Talk Much, pp. 80-81.

10 Feedback Mechanisms (Angelo & Cross)

• Feedback: Miah, W. (2004). Would a five-‐minute paper improve understanding in a workshop? Progressions, V. 5, #3, p. 15. Go to: http://www.league.org/gettingresults/web/module6/assessing/ and click on Formative Assessment. Are there other links on this page that might be useful as tools for helping to assess student learning? Find at least one other link on this site.

• Motivation: Read: In Handbook: Chapter 6, pp. 44-‐46, Deci and Ryan; In Progressions Newsletter (www.pltl.org) V. 2, No. 3, pp. 8-‐10. Motivation in the Workshop by Chris Richard (Peer leader at University of Rochester); V. 4, #1&2, p. 4, Building an Emotional Bond, by Arleann Santoro (Peer leader at University of Montana, Missoula);

• Research: Two sites that discuss Deci and Ryan's Self-‐Determination Theory. Be sure to note the URL (web address) and the date you downloaded the materials.

11 Assumptions & Misconceptions (Argyris & Schon)

• Search: Find two sites on Chris Argyris' and Donald Schon's theory, Action Science (use the Google (Scholar) Search Engine: http://www.google.com). Remember to enclose the words in double quotes to keep them together. Key words you might use are those listed in the class handout and:

Chris Argyris and Donald Schon Action Science Single-‐loop learning Double-‐loop learning Important: be sure to cite the URL (web address) and the date you downloaded the materials.

12 Developmental Stages (Perry & Belenky)

• Read: In Handbook: "The Student's Experience" by William Perry, pp. 115-‐123; Chapter 6 -‐ Learning Theory and the Workshop Leader, pp. 39-‐43; In Progressions Newsletter (www.pltl.org): Summer 2001 issue: "The Answer Key" (V. 2, #4), (written by David Gosser) ; Spring 2000, "Where do answers come from?" (V. 1, #3). Written by peer leaders.

• Research: Find two sites dealing with William Perry and/or Mary Belenky (your choice); be sure to note the URL (web address) and the date you downloaded the materials.

13 Language, Scaffolding, Zone Proximal Development (Vygotsky)

• Read: In Handbook: pp. 43-‐44 re: Vygotsky;

In Progressions Newsletter (www.pltl.org): Winter 2000, V. 1 #2, Vygotsky's Zone of Proximal Development Research: two sites on Lev Vygotsky's theories. Be sure to note the URL (web address) and the date you downloaded the materials, as well as any cited author(s). An interesting diagram is from: http://www.ncrel.org/sdrs/areas/issues/students/learning/lr1zpd.htm.

14 PowerPoint Training – creating a (virtual) poster

• Meet with Instructor.

15 Poster Presentation


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DEPARTMENT: Mathematics PREPARED BY: Professor Andrew Douglas COURSE: MEDU 1010 TITLE: Foundations of Education DESCRIPTION: This course examines the historical, philosophical, and sociological foundations underlying the development of American educational institutions. The role of the schools, the aims of education, diverse learners, the mathematics curriculum in New York State, legal principles that affect education, and the role of state, local, and federal agencies will be emphasized. TEXT: Kauchak, Eggen, and Carter, Introduction to Teaching: Becoming a Professional

4th Ed, 2011, Merril. CREDIT HOURS: 2 cl hrs, 0 lab hrs, 2 cr PREREQUISITE: CUNY proficiency in reading and writing. LEARNING OUTCOMES: Upon successful completion of the course, students should be able to:

1. Identify knowledge and skills necessary to become an effective teacher. 2. Describe historical, philosophical and sociological foundations underlying the

development of American educational institutions. 3. Explain how schools are financed. 4. Identify the legal principles that affect public education. 5. Trace the steps in becoming a licensed teacher.


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INSTRUCTIONAL OBJECTIVES AND ASSESSMENT: INSTRUCTIONAL OBJECTIVES For successful completion of the course, students should be able to:

ASSESSMENT Instructional Activity, Evaluation Methods and Criteria

Identify knowledge and skills necessary to become an effective teacher.

Classroom Discussion, Essays, Group Presentation, Final Exam

Identify the characteristics of effective instruction.


Provide an overview of the historical development of American education.


Describe various general philosophies and philosophers of education; give their philosophy of education and relate it to a formal philosophy.


Identify social problems affecting children and youths and explain how these problems challenge schools and teachers.


Explain how schools are financed. Classroom Discussion Identify the legal principles that affect public education.


Trace the steps in becoming a licensed teacher in New York State.

Classroom Discussion

GRADING PROCEDURE:

• Class participation and Attendance 5% • Short Essays 10% • Group Presentations and Project 50% • Final Exam 35%

TEACHING AND LEARNING METHODS:

• Guided Discussion and Short Lecture • Homework Reading Assignments • Group Project and Presentation • Co-Operative/Group Learning


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WEEKLY COURSE OUTLINE: WEEK TOPIC CHAPTERS

1 Do I Want to Become a Teacher? Developing as a Professional

1 2

2-3 Student Diversity: Culture, Language and Gender Student Diversity: Development, Ability and Exceptionalities

4 5

4-6 Philosophical, Historical and Sociological Foundations of American Education

3, 6, 7

7 The Organization of American Schools Governance and Finance: Regulating and Funding Schools

8 9

8-9 School Law: Ethical and Legal Influences on Teaching 10 10-11 The School Mathematics Curriculum, NCTM Standards 11

12 Creating Productive Learning Environments: Classroom Management

12

13 Instruction in Today’s Schools Assessment, Standards and Accountability

13 14

14 Student Presentations 15 Final Exam


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DEPARTMENT: Mathematics PREPARED BY: Arnavaz Taraporevala , Estela Rojas, and Peter Deraney COURSE: MEDU 1020 TITLE: Teaching & Learning Strategies DESCRIPTION: Students explore a wide variety of teaching and learning strategies used in mathematics. These strategies include oral and written communication, quantitative literacy, soft competencies, collaborative learning, critical thinking, library research and use of technology. Students will also explore theories of teaching and learning processes and motivation. Strategies to address students' learning difficulties in mathematics will be developed based on emotional intelligence, learning styles and other theories. Active learning through the arts of observing, listening and questioning will be explored. Teacher candidates will examine ways in which students' previous knowledge can be used to stimulate intellectual curiosity. TEXTS: 1. Teaching and Learning Mathematics: Translating Research for Secondary School Teachers (a 2010 National Council for Teachers of Mathematics publication) 2. http://www.nctm.org/uploadedFiles/Math_Standards/FHSM_Executive_Summay.pdf CREDIT HOURS: 1 cl hours, 2 lab hours, 2 cr PREREQUISITES: MAT 1375, CUNY proficiency in reading and writing LEARNING OUTCOMES: Upon successful completion of the course, students should be able to:

• Explore a wide variety of teaching and learning strategies used in mathematics.

• Explore theories of teaching and learning processes and motivation.


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• Develop strategies to address students' learning difficulties in mathematics based on emotional intelligence, learning styles and other theories.

• Explore active learning through the arts of observing, listening and questioning.

• Examine ways in which students' previous knowledge can be used to stimulate intellectual curiosity.



Explore teaching and learning strategies used in mathematics

Discussion and student presentation

Explore theories of teaching and learning processes and motivation


Develop strategies to address students' learning difficulties in mathematics based on emotional intelligence, learning styles and other theories


Explore active learning through the arts of observing, listening and questioning


GRADING PROCEDURE:

• In class presentations 25% • Written report of class presentations 20% • Daily Reflections 10% • Project presentation 25% • Written report of the project 20%

TEACHING AND LEARNING METHODS: Discussion and student presentation of daily readings and projects


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WEEKLY COURSE OUTLINE:

WEEK TOPIC CHAPTERS/SECTIONS 1 NY State, NCTM, and NCATE Standards 2 Secondary School Students’ Proportional

Reasoning Chapter 1

3 Role of Problem Solving in the Secondary School Mathematics Classroom

Chapter 2

4 Learning and Teaching Algebra in Secondary School Classrooms

Chapter 3

5 Geometry and Proofs in Secondary School Classrooms

Chapter 4

6 Probability and Statistics in Secondary School Classrooms

Chapter 5

7 The Role of Curricular Materials in Secondary School Mathematics Classrooms

Chapter 6

8 The Influence of technology on Secondary School Students’ Mathematics learning

Chapter 7

9 Secondary School Mathematics Teachers’ Classroom Practices

Chapter 8

10 Qualities of Effective Secondary School Mathematics teachers

Chapter 9

11 How Teachers’ Actions Affect What Students learn in Secondary School Mathematics Classrooms

Chapter 10

12 Formative Assessment in Secondary School mathematics Classrooms

Chapter 11

13 Language, Culture, and Equity in Secondary School mathematics Classrooms

Chapter 12

14 Project Presentation 15 Project Presentation


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DEPARTMENT: Mathematics PREPARED BY: Professor Andrew Douglas, Professor Estela Rojas COURSE: MEDU 2010 TITLE: Assessment Techniques in Mathematics DESCRIPTION: Students will explore essential classroom assessment concepts and major assessment issues including those pertaining to district, state and national assessment. A variety of assessment techniques will be examined in theory and practice, including affective assessment, portfolio assessment, and formative and summative performance-based assessment. The distinction between assessment and evaluation will be discussed. Test and rubric construction, designing questions to promote thinking, and the role of standardized tests will also be included. TEXTS: W.J. Popham, Classroom Assessment: What Teachers Need to Know, Pearson,

2010. ADDITIONAL RESOURSES:

• Trends in International Mathematics and Science Study (TIMSS): http://nces.ed.gov/timss/index.asp

• National Assessment of Educational Progress (NAEP): http://nces.ed.gov/nationsreportcard/

• Office of Assessment Policy, Development and Administration (APDA): http://www.emsc.nysed.gov/osa/math/

CREDIT HOURS: 1 cl hrs, 2 lab hrs, 2 cr PREREQUISITES: ENG 1101, MEDU 1020


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LEARNING OUTCOMES: Upon successful completion of the course, students will demonstrate the following:

1. Knowledge of assessment issues related to the mathematics classroom, including the use of rubrics and alternative forms of assessment.

2. Knowledge of state-level tests in mathematics and their influence on the curriculum.

3. Knowledge of major national and international assessments related to mathematics.

4. Knowledge of assessment issues in mathematics in technology-rich environments.



Discuss reliability and validity and their importance to mathematics classroom assessment.

Guided discussion, learning logs, homework assignments, student portfolio, final exam.

Construct mathematics tests including question items that measure concept understanding, high-level cognition and problem solving.

Guided discussion, learning logs, homework assignments, student portfolio, classroom group work/activities, final exam.

Create mathematics assessment rubrics. Guided discussion, learning logs, homework assignments, student portfolio, classroom group work/activities.

Plan and construct alternative measures of assessment in the mathematics classroom including performance assessment, learning logs and student portfolios.

Guided discussion, learning logs, homework assignments, student portfolio, classroom group work/activities, final exam.

Discuss the effects of state-level, national and international mathematics assessment on classroom teaching.

Guided discussion, learning logs, homework assignments, student portfolio, classroom group work/activities.

GRADING PROCEDURE:

• Student Portfolio 10% • Learning Log 10% • Class Attendance and Participation 10% • Final Exam 25% • In class and homework Assignments 25%

(Including the creation of assessment measures) • Journal Article Review 20%


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Description of Journal Article Review: This is a two-part assignment. 1. Students will be required to review one journal article dealing with

mathematics classroom assessment. Students will be required to review and critique a scholarly research article (peer reviewed) involving mathematics classroom assessment. The review should be approximately 2-3 pages in length and should include both a summary of the article as well as your own thoughts and comments about the article.

2. Students will briefly present their article and review to the class. TEACHING AND LEARNING METHODS:

• Guided Discussion and Short Lecture • Learning Log • Homework Reading Assignments • Group Project and Presentation • Co-Operative/Group Learning

WEEKLY COURSE OUTLINE: WEEK TOPIC CHAPTERS

1 Introduction: Why Do We Test? Assessment vs. Evaluation

1

2-3 Reliability of Assessment Validity of Assessment

2 3

4 Absence of Bias Deciding what to Assess and How, rubrics

4 5,8

5-6 Math Test Construction Instructor Provided Document, Samples of Quizzes, Tests, Exams

7-10 Alternative Assessment in Mathematics, Learning Logs, Student Portfolios, Performance Assessment, Affective Assessment, Formative Assessment, assessment issues in a Technology rich environment.

8,9,10,12

11-12 State-Level Assessments in Mathematics (APDA) National Assessments in Mathematics (NAEP) International Assessment in Mathematics (TIMSS, PISA)

13 NAEP Documents TIMSS Documents APDA Documents

13 Student Presentations 14 Student Presentations 15 Final Exam


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DEPARTMENT: Mathematics PREPARED BY: Peter Deraney and Arnavaz Taraporevala COURSE: MEDU 2020 TITLE: Pedagogy of Mathematics Applications DESCRIPTION: Students will examine effective pedagogical approaches to teaching mathematics applications and mathematical modeling. Applications will be used to motivate and explore the use of problem solving and writing in the teaching and learning of mathematics. Technology will be used as a tool in problem solving, and its effective use in the classroom will be analyzed. Students will develop activities consistent with state curriculum requirements and NCTM guidelines that are enriched with mathematics applications. Applications will be selected from a wide range of topics in science, social science, business, engineering, and technology. TEXT: 1. Mathematics: Modeling Our World (MMOW) Course 1, the Consortium for Mathematics and its Applications, 2nd edition. Additional references: 2. Mathematics: Modeling Our World (MMOW) Course 2, the Consortium for Mathematics and its Applications, 2nd edition. 3. Teaching Mathematics and Its Applications, Oxford Journals. CREDIT HOURS: 1 cl hrs, 2 lab hrs, 2 cr PREREQUISITES: MEDU 1020, MAT 1475 LEARNING OUTCOMES: Upon successful completion of the course, students should be able to: 1. evaluate and develop model lessons that are enriched with mathematics


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applications and are consistent with state curriculum curriculum requirements and NCTM standards.

2. demonstrate effective pedagogical approaches for teaching mathematics

applications. 3. develop activities which incorporate collaborative work and writing in the

application of mathematics to problems in science, social science, business, engineering, and technology.

4. use appropriate technology in the solution of problems involving mathematics applications. INSTRUCTIONAL OBJECTIVES AND ASSESSMENT:

INSTRUCTIONAL OBJECTIVES For successful completion of the course, students should be able to:


Evaluate instructional models appropriate to the secondary school curriculum which incorporate mathematics applications.

Working collaboratively in small groups, complete model lessons from the text , Evaluate the effectiveness of these lessons in writing and in oral presentation.

Construct a model lesson incorporating mathematics applications.

As a term project, construct a new model lesson incorporating mathematical applications. Provide a written report which describes and evaluates the lesson. Present an oral summary of this project to the class.

Incorporate and evaluate the use of technology in the instructional models reviewed in class and developed for the term project.

In the written summary of each model lesson, discuss the appropriate use of technology in clarifying and facilitating the solution of the problem.

GRADING PROCEDURE:

• Term Project: Written project report: 25% Oral Presentation of project: 15%

• Collaborative work on 5 class projects: 25% (Contribution to group activities, written summaries, and group presentations.)

• Effective use of technology: 15%


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• Midsemester Test 20% TEACHING AND LEARNING METHODS: The course will provide teacher led examples and small group collaborative exploration of model lessons involving mathematics applications. Class and home work will be evaluated by means of written assignments and oral presentation. The course will culminate in an individual project in which each student will construct a lesson which applies topics from the secondary school curriculum to real world situations. WEEKLY COURSE OUTLINE:

Week Topics Assignments 1 Introduction to Course;

Application: Basic Mathematics Chapter O: Pick a Winner: Decision Making in a Democracy

Purchase Textbook and Supplies Text: Chapter 0: Lessons 1 and 2

2 Application: Algebra and Functional Notation Chapter 1: Secret Codes and the Power of Algebra (Part 1)

Text: Chapter 1: Lessons 1 – 3

3 Application: Algebra and Functional Notation Chapter 1: Secret Codes and the Power of Algebra (Part 2)


4 Application: Geometry Chapter 2: Scene from Above


5 Application: Graphing and Statistics Chapter 3: Prediction


6 Application: Graphical Representation of Functions Chapter 4: Animation/Special Effects


7 Review of weeks 1 – 6 Midterm Exam

Midterm Exam Review Exercises

8 Application: Functions; Parametric Equations Chapter 5: Wildlife (Part 1)


9 Application: Exponential Growth and Decay Chapter 5: Wildlife (Part 2)

Text: Chapter 5: Lessons 3 – 5 Submit topic and outline for term project


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10 Application: Probability Chapter 6: Imperfect Testing


11 Application: Probability; Curve Fitting Chapter 7: Testing 1, 2, 3 (Part 1)

Text: Chapter 7: Lessons 1 –3 Submit draft of term project

12 Application: Quadratic Functions and Equations Chapter 7: Testing 1, 2, 3 (Part 2)


13 Review; Work on Term Project Complete Term Project; Prepare Presentation 14 Presentation of Term Projects Prepare presentation 15 Presentation of Term Projects


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DEPARTMENT: Mathematics PREPARED BY: Jonas Reitz COURSE: MEDU 3010 TITLE: Methods of Teaching Middle School Mathematics DESCRIPTION: Students will examine the development of curriculum for grades 7-‐9, aligning with state and national standards and incorporating appropriate teaching and learning strategies and assessment techniques. Focus and analysis will be on the needs of individual learners, and small and large group instruction techniques (i.e. learning communities), the various roles of the teacher in the classroom, planning individual lessons, and long-‐range curriculum planning. Topics will include differentiation of instruction to meet the needs of various learners, including students with disabilities and special health-‐care needs, as well as strategies for the development of listening, speaking, reading and writing skills of all students. Includes 6 hours per week for 10 weeks of preservice field experience in middle schools. TEXT: Rubenstein, R. N., Beckman, C. E., & Thompson, D. R. (2004). Teaching and

learning middle grades mathematics. Emeryville, CA: Key Curriculum Press CREDIT HOURS: 3 cl hrs, 6 field hours/week, 3 cr PRE/COREQUISITES: MEDU 2020, ENG 1121 LEARNING OUTCOMES: Upon successful completion of the course, students should be able to:

1. Plan for teaching a middle school mathematics course on a long range (year), medium range (unit), and short range (lesson) basis, incorporating state and national standards.

2. Identify and implement effective instructional strategies appropriate to a variety of mathematical abilities and learning styles, including a variety of


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disabilities and special health-‐care needs, with a focus on developmental and content issues specific to middle school mathematics.

3. Effectively incorporate manipulatives, technology and other materials in the classroom.

4. Assess student progress and assign grades to students in a fair and equitable manner.



Plan for teaching middle school mathematics.

Develop and implement course, unit and lesson outlines both in the classroom and in the field.

Implement effective instructional strategies at the middle school level.

Develop and carry out lesson plans incorporating instructional strategies and reflect on their effectiveness.

Implement instructional strategies to support students with disabilities and special needs.


Incorporate manipulatives, technology and other materials.

Create lesson plans incorporating various materials.

Assess student progress. Design and implement assessment tools in the classroom and in the field.

GRADING PROCEDURE: Grades will be assigned based on exams, development of course outlines, lesson plans, and other assignments, reflective writing, and practical implementation of teaching methods through the field experience. TEACHING AND LEARNING METHODS:

• Lecture/Discussion 10% • Group Work 10% • Blackboard 20% • Field Experience* 40% • Assignments 20%

*Observation of and participation in middle school mathematics instruction under the guidance of an experienced teacher.


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WEEKLY COURSE OUTLINE: WEEK TOPIC CHAPTERS/SECTIONS

1 Introduction Teaching in Middle School: An Overview

Introduction

2 Problem Solving Chp 1.1-1.3 3-5 Teaching and Learning Techniques

Manipulatives and other Materials Use of Technology Literacy in the Mathematics Classroom Math Topics: Number Sense and Operations

Unit One introduction Chp 1.4-1.7

6-8 Theories of Learning Students with Disabilities and Special Needs Math Topics: Rational Numbers & Proportions

Chp 2.1-2.5

9-10 Lesson Planning Math Topics: Geometry and Measurement

Chp 3.1-3.6

11-13 Assessment Techniques Math Topics: Probability and Statistics

Chp 4.1-4.5

14-15 Curriculum Development State and National Standards Professional Development

Chp 5.1-5.3


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DEPARTMENT: Mathematics PREPARED BY: Jonas Reitz COURSE: MEDU 3020 TITLE: Methods of Teaching High School Mathematics DESCRIPTION: Students will examine the development of curriculum for grades 10-‐12, aligning with state and national standards and incorporating appropriate teaching and learning strategies and assessment techniques. Focus and analysis will be on the needs of individual learners including English language learners and those with disabilities and special health needs, small and large group instruction techniques (i.e. learning communities), the development of literacy in the mathematics classroom, the various roles of the teacher in the classroom, planning individual lessons, and long-‐range curriculum planning. Includes 6 hours per week for 10 weeks of preservice field experience in high schools. TEXT: Brumbaugh, et. al. Teaching Secondary School Mathematics, 3rd Edition.

Lawrence Erlbaum Publishers, 2006. CREDIT HOURS: 3 cl hrs, 6 field hours/week, 3 cr PREREQUISITES: MEDU 3010 - Methods of Teaching Middle School Mathematics LEARNING OUTCOMES: Upon successful completion of the course, students should be able to:

1. Plan for teaching a high school mathematics course on a long range (year), medium range (unit), and short range (lesson) basis, incorporating state and national standards.

2. Identify and implement effective instructional strategies appropriate to a variety of mathematical abilities and learning styles, including the full range of disabilities and special health-‐care needs, with awareness of developmental and content issues specific to high school mathematics.


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3. Support language acquisition and literacy development for native English speakers as well as English language learners.

4. Effectively incorporate problem solving and technology in the classroom. 5. Assess student progress and assign grades to students in a fair and

equitable manner. INSTRUCTIONAL OBJECTIVES AND ASSESSMENT: INSTRUCTIONAL OBJECTIVES For successful completion of the course, students should be able to:


Plan for teaching high school mathematics. Develop and implement course, unit and lesson outlines both in the classroom and in the field.

Implement effective instructional strategies for a variety of students, including students with disabilities and special needs.


Implement instructional strategies to support language acquisition and literacy development.


Incorporate problem solving and technology.

Create lesson plans incorporating problem solving and technology.

Assess student progress. Design and implement assessment tools in the classroom and in the field.

GRADING PROCEDURE: Grades will be assigned based on exams, development of course outlines, lesson plans, and other assignments, reflective writing, and practical implementation of teaching methods through the field experience. TEACHING AND LEARNING METHODS:

• Lecture/Discussion 10% • Group Work 10% • Blackboard 20% • Field Experience* 40% • Assignments 20%

*Observation of and participation in middle school mathematics instruction under the guidance of an experienced teacher.


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WEEK TOPIC CHAPTERS/SECTIONS 1 - 2 Teaching in a High School: An Overview

Professional Responsibilities Ethical Behavior Leadership Structures Professional Development Opportunities

Chp 1

3 - 5 Learning Theories and Curriculum A review of competing theories of learning as applied to mathematics Students with disabilities and special needs Overall views of curriculum The establishment of mathematics curriculum

Chp 2

6 Knowledge of Mathematics The need of the Teacher to have a solid background in Mathematics Competency testing

Chp 9

7 Assessment Issues Chp 2 8-10 Lesson Planning

Long Range Planning – (whole course) Unit Planning – (a couple of weeks) Detailed Daily Lesson Plans - (daily)

Chp 3 Chp 10-15 (selections)

11-13 Instructional Models Questioning Skills Language acquisition and literacy development Inductive and deductive models Presenting mathematics lessons Appropriate uses of technology in teaching lessons

Chp 4, 5, 7

14 Problem solving issues Chp 6 15 Proofs Chp 8


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DEPARTMENT: Mathematics PREPARED BY: Professor Andrew Douglas, Professor Janet Liou-Mark COURSE: MEDU 4010 TITLE: Supervised Student Teaching and Seminar in Middle School Mathematics DESCRIPTION: The field experience is designed to prepare students for teacher certification in mathematics. The course involves a supervised student teaching experience in grades 7 through 9 mandated in state standards for preparing classroom teachers. Emphasis is placed on preparing student teachers to teach towards diversity, implement different teaching strategies, refine classroom management skills, develop assessment practices, and incorporate technological resources to facilitate instruction. The seminar component provides a forum on reflective practice in the concurrent field placement. Students are expected to complete a minimum of 20 days or 120 hours of supervised student teaching in a Middle School mathematics classroom. TEXT: Selected readings/documents to be provided by the instructor CREDITS HOURS: 1class hours, 9 field hours/week, 4 credits PREREQUISITES: MEDU 3010 and permission of department.

LEARNING OUTCOMES: For successful completion of the course, students should be able to:

1. Demonstrate mastery of the 7 through 9 grades middle school mathematics curriculum.

2. Create and implement educationally meaningful and relevant lesson plans. 3. Effectively apply verbal, nonverbal and technology-based techniques to foster

active inquiry and collaboration. 4. Effectively implement formal and informal assessment strategies.


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INSTRUCTIONAL OBJECTIVES


ASSESSMENT


Plan and implement curriculum and instruction

Supervisor’s Evaluation for Student Teachers Cooperating Teacher’s Evaluation for Student Teachers Portfolio

Manage the classroom learning environment Supervisor’s Evaluation for Student Teachers Cooperating Teacher’s Evaluation for Student Teachers

Interact with students using different teaching methodologies

Cooperating Teacher’s Evaluation for Student Teachers

Apply teaching and learning theories in practical situations

Cooperating Teacher’s Evaluation for Student Teachers Discussion in seminar Portfolio

Evaluate assessment strategies Cooperating Teacher’s Evaluation for Student Teachers Discussion in seminar

Develop student activities to foster literacy and communication skills.

Field logs Discussion Forum - Blackboard Discussion in seminar

Identify strengths, and individualize instruction for students with disabilities and special needs.

Field logs Discussion Forum - Blackboard

GRADING PROCEDURE:

• Student teaching portfolio 8% • Field logs 5% • Seminar: attendance, punctuality, and classroom participation 3% • Three written assignments on classroom management, 3%

each lesson and unit planning, and meeting the needs of all learners • Lesson observations by cooperating teacher and faculty member* 75%

* 50% of the final grade will come from observation reports of the cooperating teacher, and 25% of the final grade will be observations from a faculty member. TEACHING AND LEARNING METHODS:

• Preparation of lesson plans • Practice of facilitation techniques • Development of a portfolio • Discussion in groups • Brief lectures • Reflection on practice through field logs and discussions • Use of Blackboard: discussion forum


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WEEKLY SEMINAR OUTLINE: For each seminar, students are required to bring an issue, topic or idea to share and discuss with the class. This subject should reflect the mathematical content in relation to the teaching and learning of mathematics and the student dimension that impinge on maintaining and executing a conducive learning environment. The class, under the supervision of the instructor, will address these issues. In addition to the class discussions initiated from student teaching, the topics outlined in the table below will be examined.

Seminar Session Topic Assignments

1

Overview of Supervised Student Teaching

-Sign Student Teaching Contract with cooperating teacher. -Design an activity to collect student information. -Design an introduction letter to students’ parents/guardians.

2 Identify strengths, and individualize instruction for students with disabilities and special needs.

-Discuss the variety of disabilities and special needs that teacher are likely to encounter. -Prepare lesson plans and activities consistent with foster the growth of students with the discussed special needs and disabilities.

3,4 Lesson Planning -Review the principles of creating lesson plans. -Group activity: Construct mathematics lesson plans appropriate for high school students.

5 Classroom Management -Design student responsibility policy. -Discuss classroom management issues at the high schools that students encountered in their placements and management techniques resolving these situations.

6 Literacy and Communication skills Development.

-Discuss ways to develop literacy and communication skills in the mathematics classroom (e.g., written assignments, writing math in words, learning logs)

7,8,9 Teaching with Technology -Create activities using graphing calculators, computer algebra systems, and the Geometer’s Sketchpad applicable to the high school mathematics curriculum. -Prepare and demonstrate a mini lesson involving technology.

10 Designing Exams -Analyze exams from students’ classroom placements. -Group activity: Create a quiz and a test appropriate for high school mathematics class. Present an assessment measure.

11,12,13,14

Alternative assessment: learning logs, portfolio assessment,

-Group Activity: Create a learning log to be used in a high school mathematics class.


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performance assessment - Group Activity: Design a lesson plan with a performance assessment. -Create (or update) a student teaching portfolio under the guidance of the instructor.

15 Final Class -Submit student teaching portfolio and field logs.


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DEPARTMENT: Mathematics PREPARED BY: Professor Andrew Douglas, Professor Janet Liou-Mark COURSE: MEDU 4020 TITLE: Supervised Student Teaching and Seminar in High School Mathematics DESCRIPTION: The field experience is designed to prepare students for teacher certification in mathematics. The course involves a supervised student teaching experience in grades 10 through 12 mandated in state standards for preparing classroom teachers. Students design lesson plans appropriate for the high school mathematics curriculum. Topics in mathematics pedagogy include problem solving, connections between mathematics and other disciplines, assessment in the contexts of New York State and national standards. Students develop and analyze lessons that incorporate appropriate technology to meet the needs of diverse student populations. Students are expected to complete a minimum of 20 days or 120 hours of supervised student teaching in a high school mathematics classroom. TEXT: Selected readings/documents to be provided by the instructor CREDITS HOURS: 1class hours, 9 field hours/week, 4 credits PREREQUISITES: MEDU 3020 and permission of department.

LEARNING OUTCOMES: For successful completion of the course, students should be able to:

1. Demonstrate mastery of the 10 through 12 grades high school mathematics curriculum.

2. Create and implement educationally meaningful and relevant lesson plans. 3. Effectively apply verbal, nonverbal and technology-based techniques to foster

active inquiry and collaboration in a high school mathematics classroom. 4. Effectively implement formal and informal assessment strategies in a high school

mathematics classroom.


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INSTRUCTIONAL OBJECTIVES


ASSESSMENT


Plan and implement curriculum and instruction

Supervisor’s Evaluation for Student Teachers Cooperating Teacher’s Evaluation for Student Teachers Portfolio

Manage the classroom learning environment Supervisor’s Evaluation for Student Teachers Cooperating Teacher’s Evaluation for Student Teachers

Interact with students using different teaching methodologies

Cooperating Teacher’s Evaluation for Student Teachers

Apply teaching and learning theories in practical situations


Evaluate assessment strategies Cooperating Teacher’s Evaluation for Student Teachers Discussion in seminar

Develop student activities to foster literacy and communication skills.


Identify strengths, and individualize instruction for students with disabilities and special needs.


GRADING PROCEDURE:

• Student teaching portfolio 8% • Field logs 5% • Seminar: attendance, punctuality, and classroom participation 3% • Three written assignments on classroom management, 3%

lesson and unit planning, and meeting the needs of all learners • Lesson observations by cooperating teacher and faculty member* 75%

* 50% of the final grade will come from observation reports of the cooperating teacher, and 25% of the final grade will be observations from a faculty member. TEACHING AND LEARNING METHODS:

• Preparation of lesson plans • Practice of facilitation techniques • Development of a portfolio • Discussion in groups • Brief lectures • Reflection on practice through field logs and discussions • Use of Blackboard: discussion forum


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WEEKLY SEMINAR OUTLINE: For each seminar, students are required to bring an issue, topic or idea to share and discuss with the class. This subject should reflect the mathematical content in relation to the teaching and learning of mathematics and the student dimension that impinge on maintaining and executing a conducive learning environment. The class, under the supervision of the instructor, will address these issues. In addition to the class discussions initiated from student teaching, the topics outlined in the table below will be examined.

Seminar Session Topic Assignments

1

Overview of Supervised Student Teaching

-Sign Student Teaching Contract with cooperating teacher. -Design an activity to collect student information. -Design an introduction letter to students’ parents/guardians.

2 Identify strengths, and individualize instruction for students with disabilities and special needs.

-Discuss the variety of disabilities and special needs that teacher are likely to encounter. -Prepare lesson plans and activities consistent with foster the growth of students with the discussed special needs and disabilities.

3,4 Lesson Planning -Review the principles of creating lesson plans. -Group activity: Construct mathematics lesson plans appropriate for high school students.

5 Classroom Management -Design student responsibility policy. -Discuss classroom management issues at the high schools that students encountered in their placements and management techniques resolving these situations.

6 Literacy and Communication skills Development.

-Discuss ways to develop literacy and communication skills in the mathematics classroom (e.g., written assignments, writing math in words, learning logs)

7,8,9 Teaching with Technology -Create activities using graphing calculators, computer algebra systems, and the Geometer’s Sketchpad applicable to the high school mathematics curriculum. -Prepare and demonstrate a mini lesson involving technology.

10 Designing Exams -Analyze exams from students’ classroom placements. -Group activity: Create a quiz and a test appropriate for high school mathematics class. Present an assessment measure.


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11,12,13,14

Alternative assessment: learning logs, portfolio assessment, performance assessment

-Group Activity: Create a learning log to be used in a high school mathematics class. - Group Activity: Design a lesson plan with a performance assessment. -Create (or update) a teaching portfolio under the guidance of the instructor.

15 Final Class -Submit student teaching portfolio and field logs.


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Appendix B. Detailed Course Syllabi for Proposed Math Courses


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DEPARTMENT: Mathematics PREPARED BY: Professor Victoria Gitman, Professor Yalin Celikler COURSE: MAT 2070 TITLE: Introduction to Proofs and Combinatorics DESCRIPTION: The course is designed to prepare students for an advanced mathematics curriculum by providing a transition from Calculus to abstract mathematics. The course focuses on the processes of mathematical reasoning, argument, and discovery. Topics include propositional and first order logic, learning proofs through puzzles and games, axiomatic approach to group theory, number theory, and set theory, abstract properties of relations and functions, elementary graph theory, sets of different cardinalities, and the construction and properties of real numbers. TEXT: 1) Carol Schumacher, Chapter zero: fundamental notions of abstract

mathematics, 2nd edition, Addison Wesley, 2000 2) Dave Witt Morris and Joy Morris, Proofs and Concepts, Open Source

CREDIT HOURS: 3 cl hrs, 0 lab hrs, 3 cr PRE- or COREQUISITES: MAT 1575 LEARNING OUTCOMES:

1. Students will be able to evaluate truth of statements in propositional and first order logic.

2. Students will be able to understand and use formal reasoning methods. 3. Students will be able to recognize the role of sets in mathematics.


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Evaluate truth of statements in propositional and first-order logic

Lecture, group work, homework assignments, examinations

Reason in accordance with laws of propositional and first-order logic


Use the axiomatic method in establishing the truth of mathematical statements


Analyze and prove elementary statements about group theory, number theory, set theory, and graph theory


View mathematics from the perspective of its constituent blocks – sets


Construct real numbers and derive their properties starting from the natural numbers


GRADING PROCEDURE:

• Homework assignments and oral presentations 30% • Midterm 35% • Final Exam 35%

TEACHING/LEARNING METHODS:

• Lecture and guided discussion • Student presentations • Use of online resources • Writing intensive assignments


WEEK TOPIC CHAPTERS/SECTIONS 1 Introduction to logic assertions and deductions,

deductive validity, truth, logic puzzles

2 Propositional logic logical connectives, truth tables, tautologies, contradictions

3 First-order logic quantifiers, uniqueness, bounded variables, counterexamples


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4 Proofs, games, and puzzles methods of proof, examples and counterexamples, proving theorems and solving puzzles, existence theorems and uniqueness theorems

5 Proofs, games, and puzzles continued

proofs using induction and strong induction, the axiomatic approach: group theory

6 Axiomatic number theory Peano axioms, proving properties of numbers

7 Midterm 8 Set theory sets in mathematics,

operations on sets, combinatorics of finite sets, set existence and Russell’s paradox, axioms of set theory and the axiom of choice

9 Relations and functions relations, relations as sets, orderings, equivalence relations, functions, bijections, isomorphisms

10 Elementary graph theory relations as graphs, planar, Eulerian and Hamiltonian graphs

11 Graph theory continued directed graphs, matrices and graphs

12 Cardinality Galileo’s paradox and cardinality of infinite sets, countable sets and uncountability of the reals, different sizes of infinity, Continuum hypothesis

13 Real numbers construction of rationals, arithmetic and order on the rationals, construction of reals, arithmetic and order on reals

14 Real numbers continued Least Upper Bound axiom and convergence of sequences, dense orderings, well-orderings

15 Final exam


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DEPARTMENT: Mathematics PREPARED BY: Prof. Satyanand Singh COURSE: MAT 3020 TITLE: Number Theory DESCRIPTION: This course is an introduction to number theory. Topics include Divisibility (Division algorithm, GCD, etc), primes, congruences, the fundamental theorem of arithmetic, quadratic reciprocity, number theoretic functions and Fermat’s little theorem. Some applications will be done, which can be computer based, to encourage students to propose and test conjectures. TEXT: David M. Burton, Elementary Number Theory, 7th Ed. McGraw-Hill, 2011 CREDIT HOURS: 3 class hrs, 3 credits PREREQUISITE: MAT 2070 LEARNING OUTCOMES:

1. Students will have a solid foundation and greater understanding of algebra, arithmetic and subject presentation.

2. Students will be able to state, apply and provide proofs to basic theorems in number theory.

3. Students will appreciate the deceptively simple nature of some of the problems in

number theory and be able to test conjectures, provide counterexamples and proofs in simple cases.


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State the hypothesis and apply basic theorems such as the Division algorithm, the Euclidean algorithm, the fundamental theorem of arithmetic, Fermat’s little theorem and Wilson’s theorem.

class discussion, written assignments, class presentations and in class examinations

Offer a simple proof of the infinitude of primes.


Understand the properties of congruences, be able to prove simple properties and apply them to solve problems


Be able to test conjectures and provide proofs in simple cases.


GRADING PROCEDURE:

• 3 Term Tests 15% each (45%) • Final Exam 35% • Problem Sets 14% • Class project and writing assignment 6%


• Lecture and guided discussion in class • Homework, written assignments • Discussion outside class • In class presentations


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WEEK TOPIC CHAPTERS 1-2 Divisibility theory in the integers 2 3-4 Primes and their distribution 3 5-6 The theory of congruences 4 7-8 Fermat’s Theorem 5 9-10 Number theoretic functions 6 11-12 Euler’s generalization of Fermat’s theorem 7 13-14 Primitive roots and indices 8

14 The quadratic reciprocity law 9 15 Review and final exam


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DEPARTMENT: Mathematics PREPARED BY: Prof. H. Carley, Prof. F. Celikler, Prof. N. Katz, Prof. A. Mayeli COURSE: MAT 3050 TITLE: Geometry I DESCRIPTION: This course will cover Euclidean geometry in two dimensions from a synthetic point of view. It will cover classical theorems as well as groups of transformations. TEXT: G. E. Martin, The Foundations of Geometry and the Non-Euclidean Plane,

Springer 1975, New York. CREDIT HOURS: 3 cl hrs, 3 cr PREREQUISITES: MAT 2070 PRE/COREQUISITE: MAT 3080 LEARNING OUTCOMES:

1. Students will be able to present an axiomatic description of Euclidean geometry. 2. Students will be able to present proofs in Euclidean geometry from an axiomatic

point of view.


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state a consistent set of axioms for Euclidean geometry and apply them in proofs


state the hypotheses and conclusions of basic theorems in synthetic Euclidean geometry and apply them in proofs


apply the group of rigid transformations of the Euclidean plane in proofs


use ruler and protractor constructions to produce examples in synthetic Euclidean geometry


GRADING PROCEDURE:

• 3 Term Test 45% • Homework, presentations, written assignments 20%

and class participation • Final Examination 35%




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WEEK TOPIC CHAPTERS 1 equivalence relations, mappings, the real numbers 1,2,3 2 axiom systems 4 3 models 5 4 incidence axiom, ruler postulate 6 5 ordering points on a line, taxicab geometry 7 6 segments, rays, convex sets 8 7 angles, triangles 9 8 Pasch's postulate, plane separation postulate 12 9 crossbar, quadrilaterals 13 10 measuring angles, the protractor postulate 14 11 reflection and symmetry 16 12 congruence 17 13 perpendiculars and related inequalities 18 14 isometries 19 15 Review and final exam


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DEPARTMENT: Mathematics PREPARED BY: Prof. H. Carley, Prof. F. Celikler, Prof. N. Katz, Prof. A. Mayeli COURSE: MAT 3075 TITLE: Introduction to real analysis DESCRIPTION: This course is an introduction to analysis of real functions of one variable with a focus on proof. Topics include the real number system, limits and continuity, differentiability, the mean value theorem, Riemann integral, fundamental theorem of calculus, series and sequences, Taylor polynomials and error estimates, Taylor series and power series. TEXT: M. Spivak, Calculus 4th Ed., Publish or Perish Press, Houston Texas, 2008. CREDIT HOURS: 4 cl hrs, 4 cr PREREQUISITES: MAT 1575, MAT 2070 LEARNING OUTCOMES:

1. Students will be able to formulate key concepts in real analysis with mathematical precision.

2. Students will be able to state the hypothesis and conclusions of basic theorems in real analysis and apply them in proofs.


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list limit and order properties of real numbers and use those properties to prove results about subsets of real numbers


prove that a limit does or does not exist class discussion, written assignments, class presentations and in class examinations

prove continuity or uniform continuity of a function


formulate the construction of the Reimann integral and prove basic facts about its properties.


find approximation of functions using Taylor polynomials including estimation of error


check a sequence of functions for point-wise and uniform convergence


GRADING PROCEDURE:

• 3 Term Tests 45% • Homework, presentations, written assignments 20%

and class participation • Final Exam 35%




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WEEK TOPIC CHAPTERS 1 the real number system 1, 2 2 functions of one real variable, graphs of functions 3, 4 3 limits 5 4 continuity of functions of one real variable 6 5 properties of continuous functions of one real variable 7 6 least upper bounds and uniform continuity 8 7 differentiable functions 9 8 calculating derivatives, critical points, extremal values,

l'Hôpital's rule 10, 11

9 mean value theorem, inverse functions 11, 12 10 the Riemann integral, fundamental theorem of calculus 13, 14 11 trigonometric, logarithmic and exponential functions 15, 17 12 Taylor polynomials 19 13 infinite sequences and infinite series 21, 22 14 uniform convergence and power series 23 15 student presentations and final exam


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DEPARTMENT: Mathematics PREPARED BY: Professor Andrew Douglas, Professor Delaram Kahrobaei COURSE: MAT 3080 TITLE: Modern Algebra DESCRIPTION: An introductory course in modern algebra covering groups, rings and fields. Topics in group theory include permutation groups, cyclic groups, dihedral groups, subgroups, cosets, symmetry groups and rotation groups. In ring and field theories topics include integral domains, polynomial rings, the factorization of polynomials, and abstract vector spaces. TEXT: J. A. Gallian, Contemporary Abstract Algebra, 7th Ed. Brooks/Cole Cengage

Learning, 2010. CREDITS HOURS: 3 cl hrs, 0 lab hrs, 3 cr PREREQUISITES: MAT 2580, MAT 3075 LEARNING OBJECTIVES: For successful completion of the course, students should be able to:

1. Define the terms group, ring and field and be able to give examples of each of these kinds of algebraic structures.

2. Define terms (such as homomorphism, subgroup and integral domain) and state theorems (such as Lagrange’s Theorem) of modern algebra.

3. Apply concepts, terminology and theorems to solve problems and prove simple propositions in modern algebra.

4. Describe applications and relationships of group theory to geometry.


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Define the terms group, ring and field and be able to give examples of each of these kinds of algebraic structures.

Class and Blackboard discussion, Tests, Final Exam.

Define the concept of a subgroup and determine (prove or disprove), in specific examples, whether a given subset of a group is a subgroup of the group.

Graded Homework, Group Work, Tests, Final Exam.

Solve problems and prove simple propositions involving concepts, terms and theorems of group theory.

Graded Homework, Group Work, Tests, Exam.

Compare rings, fields and integral domains. Class and Blackboard Discussion, Graded Homework.

Solve problems and prove simple propositions involving concepts, terms and theorems of ring theory.


Apply the reducibility and the irreducibility tests for polynomials.


Describe applications and relationships of group theory to geometry

Graded Homework, Class and Blackboard discussion, Tests, Exam.

GRADING PROCEDURE:

• Homework Assignments 20% • In Class Tests 10% Each (3 tests) • Final Exam 35% • Projects 10% • Presentations 5%


• Lecture and guided discussion • Blackboard discussion • Homework assignments • Group project and group work • Technology: A computer algebra system such as MAPLE will be used to facilitate

the exploration of mathematical concepts.


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WEEK TOPIC CHAPTERS 1 Preliminaries: Properties of Integers, Modular Arithmetic,

Mathematical Induction, Equivalence Relations. 0

2 Motivation and Introduction: Symmetries of a Square, the Dihedral Group, applications of the Dihedral group (e.g., Designing a Zip code reader)

1

3 Groups: Definition, Examples, Elementary Properties of Groups. Subgroups: Terminology and Notation, Subgroup Test, Examples.

2 3

4 Cyclic Groups and Permutation Groups: Definitions and Basic Properties.

4,5

5 Normal Subgroups: Definitions, examples, applications. Homomorphism: Definitions, examples, properties.

9 10

6-8 Cosets and Lagrange’s Theorem: Properties of Cosets, Lagrange’s Theorem, the Rotation Group of a Cube. Symmetry Groups: Isometries, Finite Plane Symmetry Groups, Finite Groups of Rotation in R3, the groups of rotation of the platonic solids, the Euclidean Group in R2 and R3.

7

29

9 Introduction to Rings: Definitions and Motivation, Examples of Rings, Properties of Rings, Subrings.

12

10 Integral Domains: Definition and Examples, Fields. 13 11-13 Polynomial Rings: Notation and Terminology, The Division Algorithm

and Consequences. Factorization of Polynomials: Reducibility Tests, Irreducibility Tests, Factorization in Z[x].

16

17

14 Vector Spaces: Definitions and examples of vector spaces, subspaces, linear independence.

19

15 Final Exam


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DEPARTMENT: Mathematics PREPARED BY: Professor William Colluci, Professor Victoria Gitman COURSE: MAT 4030 TITLE: History of Mathematics DESCRIPTION: The course examines the historical development of mathematical concepts from the origins of algebra and geometry in the ancient civilizations of Egypt and Mesopotamia through the advent of demonstrative mathematics of ancient Greeks to the discovery of Calculus, non-Euclidian geometries, and formal mathematics in the 17-20th century Europe. Topics include a historical examination of the development of number systems, methods of demonstration, geometry, number theory, algebra, Calculus, and non-Euclidean geometries. TEXTS: 1) Victor Katz, History of Mathematics, 3rd edition, Addison Wesley, 2008.

2) William Dunham, Journey through Genius, Penguin Books, 1990 CREDIT HOURS: 3 cl hrs, 0 lab hrs, 3 cr PREREQUISITES: MAT 2070, MAT 3020. LEARNING OUTCOMES:

1. Students will be able to trace the historical development of mathematical disciplines including number theory, algebra, geometry, and calculus from ancient to modern times.

2. Students will learn where crucial mathematical concepts came from and how they fit together.

3. Students will improve their oral and written communications skills in the context of mathematics.

4. Students will be able to understand how mathematics was shaped by and in turn shaped its cultural environment.


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Trace the development of mathematical disciplines through history

Lecture, reading assignments, homework assignments, examinations, term paper

Analyze where key mathematical concepts came from and how they fit together


Prove key mathematical theorems Lecture, group work, homework assignments, examinations

Improve their oral and written communications skills in the context of mathematics.

Reading assignments, homework assignments, examinations, term paper

Understand how culture and mathematics influence each other


Learn about the contributions of female and non-western mathematicians


GRADING PROCEDURE:

• Homework assignments and oral presentations 20% • Midterm 25% • Term Paper 20% • Final Exam 35%


• Lecture and guided discussion • Student presentations • Use of online resources • Writing intensive assignments


WEEK TOPIC CHAPTERS/SECTIONS 1 Egypt and Mesopotamia Number systems, linear and

quadratic equations, degree measurement of angles, Pythagorean theorem

2 Early Greek Mathematics Thales (proof), Pythagoras (commensurability), Hippocrates (quadrature of lune), Eudoxus (method of exhaustion)


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3 Euclid’s Elements postulates, propositions, straight edge and compass constructions through Pythagorean theorem, infinitude of primes, irrational magnitudes

4 Later Greek Mathematics Archimedes (method of exhaustion, sums of series, approximation of pi), Ptolemy (early trigonometry), Heron (area of triangle), Diaphantus (Diophantine equations)

5 China and India systems of linear equations, Chinese remainder theorem, Chinese triangle, Hindu-Arabic place-value system and arithmetic, quadratic formula

6 Islamic World Midterm

decimal arithmetic, al-Khwarizmi’s algebra, algebra of polynomials (negative exponents), induction

7 Medieval Europe and Renaissance

Fibonacci numbers, Cardano (cubic equations), Bombeli (complex numbers), algebraic symbolism, fundamental theorem of algebra

8 Renaissance continued Descartes (analytic geometry), Pascal (probability), Fermat (number theory)

9 Calculus Newton (fluxions, fluents), Leibniz (fundamental theorem of calculus)

10 Calculus continued Bernoulli (differential equations), Euler (infinite sums)

11 Number Theory Euler, Gauss, Galois (unsolvability of quintic, group theory)

12 Geometry parallel postulate and non-Euclidian geometry

13 Formal Mathematics Cantor (non-denumerability


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of the continuum, infinite cardinals) Russell (Russell’s Paradox, set theory axioms)

14 Women in Mathematics Hypatia, Germain, Kovalevskaya, Noether, Robinson

15 Final Exam


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DEPARTMENT: Mathematics PREPARED BY: Professor Holly Carley, Professor Firat Celikler, Professor Neil Katz COURSE: MAT 4050 TITLE: Geometry II DESCRIPTION: This course will cover Euclidean and hyperbolic geometry in two dimensions including group actions on these spaces by groups of transformations. The complex plane will be introduced in rectangular and polar coordinates and classical theorems of geometry will be covered in this setting. TEXTS:

1. Lian-shin Hahn, Complex numbers and geometry, The Mathematical Association of America, 1994.

2. G. E. Martin, The Foundations of Geometry and the Non-Euclidean Plane, Springer 1975, New York.

CREDIT HOURS: 3 cl hrs, 3 cr PREREQUISITES: MAT 3050, MAT 3080 LEARNING OUTCOMES:

1. Students will be able to state the hypothesis and conclusions of basic theorems in in analytic Euclidean geometry and apply them in proofs using analytic techniques.

2. Students will be able show basic understanding of complex numbers and apply Mőbius transformations to the complex plane.

3. Students will be familiar with basic properties of hyperbolic geometry and the Poincaré disc.


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state the hypotheses and conclusions of the Ptlolemy-Euler, Clifford, Simson's, Cantor, Feuerbach, and Morley theorems and apply them in proofs


make geometric proofs using analytic techniques


apply stereographic projection and Mőbius transformations to figures in the plane


compare and contrast non-Euclidean geometry with the Euclidean plane


GRADING PROCEDURE:

• 3 Term Test 45% • Homework, presentations, written assignments 20%

and class participation • Final Examination 35%




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WEEKLY COURSE OUTLINE: Topics and sections in regular text are from (1). Topics and sections in italics are from (2).

WEEK TOPIC SECTIONS 1 complex numbers, quadratic equations 1.1—1.5 2 triangle inequality, the complex plane, polar representation

of the complex plane 1.6—1.8

3 roots of unity and complex exponentiation, triangles in the complex plane

1.9—1.10, 2.1

4 Ptolemy-Euler and Clifford theorems 2.2, 2.3 5 the nine point circle, Simson's theorem 2.4, 2.5 6 generalizations of Simson's theorem, Cantor theorem 2.6, 2.7 7 Feuerbach theorem and the Morley theorem 2.8, 2.9 8 stereographic projection and Mőbius transformations 3.1, 3.2 9 cross ratios and symmetry under Mőbius transformations 3.3, 3.4 10 circles under Mőbius transformations 3.5, 3.6 11 classification of Mőbius transformations, inversions 3.7, 3.8 12 the Poincaré model 3.9 13 parallel lines in the hyperbolic plane 26 14 isometries of the hyperbolic plane 29 15 presentations and final exam


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Appendix C. State Requirements for Teacher Preparation Programs Below we list the state pedagogical requirements outlined by the NYSED for accreditation of Adolescence Teacher Preparation Programs (grades 7-12) [4]. These standards are divided into two groups: General Pedagogical Core Requirements, and Program-Specific Requirements. Following each list, we present a table indicating required courses that meet each of these standards. I. General Pedagogical Core Requirements The program shall include the following: (i) human developmental processes and variations, including but not limited to: the impact of culture, heritage, socioeconomic level, personal health and safety, nutrition, past or present abusive or dangerous environment, and factors in the home, school, and community on students’ readiness to learn -- and skill in applying that understanding to create a safe and nurturing learning environment that is free of alcohol, tobacco, and other drugs and that fosters the health and learning of all students, and the development of a sense of community and respect for one another;

(ii) learning processes, motivation, communication, and classroom management -- and skill in applying those understandings to stimulate and sustain student interest, cooperation, and achievement to each student’s highest level of learning in preparation for productive work, citizenship in a democracy, and continuing growth;

(iii) the nature of students within the full range of disabilities and special health-care needs, and the effect of those disabilities and needs on learning and behavior -- and skill in identifying strengths, individualizing instruction, and collaborating with others to prepare students with disabilities and special needs to their highest levels of academic achievement and independence;

(iv) language acquisition and literacy development by native English speakers and students who are English language learners -- and skill in developing the listening, speaking, reading, and writing skills of all students;

(v) curriculum development, instructional planning, and multiple research-validated instructional strategies for teaching students within the full range of abilities -- and skill in designing and offering differentiated instruction that enhances the learning of all students in the content area(s) of the certificate;

(vi) uses of technology, including instructional and assistive technology, in teaching and learning -- and skill in using technology and teaching students to use technology to acquire information, communicate, and enhance learning;

(vii) formal and informal methods of assessing student learning and the means of analyzing one’s own teaching practice -- and skill in using information gathered through assessment and analysis to plan or modify instruction, and skill in using various resources to enhance teaching;

(viii) history, philosophy, and role of education, the rights and responsibilities of teachers and other professional staff, students, parents, community members, school administrators, and others with regard to education, and the importance of productive


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relationships and interactions among the school, home, and community for enhancing student learning -- and skill in fostering effective relationships and interactions to support student growth and learning, including skill in resolving conflicts;

(ix) means to update knowledge and skills in the subject(s) taught and in pedagogy;

(x) means for identifying and reporting suspected child abuse and maltreatment, which shall include at least two clock hours of coursework or training regarding the identification and reporting of suspected child abuse or maltreatment, in accordance with the requirements of section 3004 of the Education Law;

(xi) means for instructing students for the purpose of preventing child abduction, in accordance with Education Law section 803-a; preventing alcohol, tobacco and other drug abuse, in accordance with Education Law section 804; providing safety education, in accordance with Education Law section 806; and providing instruction in fire and arson prevention, in accordance with Education Law section 808; and

(xii) means for the prevention of and intervention in school violence, in accordance with section 3004 of the Education Law. This study shall be composed of at least two clock hours of course work or training that includes, but is not limited to, study in the warning signs within a developmental and social context that relate to violence and other troubling behaviors in children; the statutes, regulations and policies relating to a safe nonviolent school climate; effective classroom management techniques and other academic supports that promote a nonviolent school climate and enhance learning; the integration of social and problem solving skill development for students within the regular curriculum; intervention techniques designed to address a school violence situation; and how to participate in an effective school/community referral process for students exhibiting violent behavior.


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General Pedagogical Core Requirements (GPCR)

Required Courses that Address Each GPCR

(i) PSY 2501, EDU 4600, MEDU 1010 (ii) MEDU 1020, MEDU 3010, MEDU 3020, MEDU

4010, MEDU 4020 (iii) PSY 2501, MEDU 1010, MEDU 3010, MEDU

3020, MEDU 4010, MEDU 4020 (iv) Required Communication Skills Electives

including ENG 1101, SPE 1330, MEDU 3010, MEDU 3020, MEDU 4010, MEDU 4020

(v) MEDU 1010, MEDU 1020, MEDU 2010, MEDU 1020, MEDU 3010, MEDU 3020, MEDU 4010, MEDU 4020

(vi) MEDU 1020, MEDU 2020, MEDU 3010, MEDU 3020, MEDU 4010, MEDU 4020

(vii) MEDU 1010, MEDU 2010, MEDU 3010, MEDU 3020, MEDU 4010, MEDU 4020

(viii) MEDU 1010 (ix) MEDU 1010, MEDU 2010, MEDU 3010, MEDU

3020, MEDU 4010, MEDU 4020 (x) EDU 4600 (xi) EDU 4600 (xii) EDU 4600

II. Program-Specific Requirements Coursework The program shall include the following: (i) study in the processes of growth and development in adolescence and how to provide learning experiences and conduct assessments reflecting understanding of those processes; and

(ii) at least six semester hours of study in teaching the literacy skills of listening, speaking, reading, and writing to native English speakers and students who are English language learners. This six-semester-hour requirement may be waived upon a showing of good cause satisfactory to the Commissioner, including but not limited to a showing that the program provides adequate instruction in language acquisition and literacy development through other means.

Field experiences, student teaching and practica (iii) The program shall include at least 100 clock hours of field experiences related to coursework prior to student teaching and at least two college-supervised student-teaching experiences of at least 20 schools days each.


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(iv) Student teaching shall include both adolescence education settings, grades 7 through 9 and grades 10 through 12.

(v) For candidates holding another classroom teaching certificate or for candidates who are simultaneously preparing for another classroom teaching certificate and completing the full field experience for that other certificate, the programs shall require such candidates to complete at least 50 clock hours of field experiences, practica, or student teaching with students in adolescence, including experiences in both adolescence education settings, grades 7 through 9 and grades 10 through 12.

Program Specific Requirements (PSR)

Required Courses that Address Each PSR

(i) PSY 2501, MEDU 1010, MEDU 2010, MEDU 3010, MEDU 3020, MEDU 4010, MEDU 4020

(ii) Required Communication Skills Electives including ENG 1101, SPE 1330, MEDU 3010, MEDU 3020, MEDU 4010, MEDU 4020

(iii) MEDU 3010, MEDU 3020 (iv) MEDU 4010, MEDU 4020 (v) Not Applicable


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Appendix D. NCATE and NCTM Accreditation Standards NCATE lists 6 standards [1] that teacher preparation programs must meet for accreditation. These standards are as follows: NCATE Standard 1: Candidate Knowledge, Skills, and Professional Dispositions.

Candidates preparing to work in schools as teachers or other school professionals know and demonstrate the content knowledge, pedagogical content knowledge and skills, pedagogical and professional knowledge and skills, and professional dispositions necessary to help all students learn. Assessments indicate that candidates meet professional, state, and institutional standards.

NCATE Standard 2: Assessment System and Unit Evaluation.

The unit has an assessment system that collects and analyzes data on applicant qualifications, candidate and graduate performance, and unit operations to evaluate and improve the performance of candidates, the unit, and its programs.

NCATE Standard 3: Field Experiences and Clinical Practice

The unit and its school partners design, implement, and evaluate field experiences and clinical practice so that teacher candidates and other school professionals develop and demonstrate the knowledge, skills, and professional dispositions necessary to help all students learn.

NCATE Standard 4: Diversity

The unit designs, implements, and evaluates curriculum and provides experiences for candidates to acquire and demonstrate the knowledge, skills, and professional dispositions necessary to help all students learn. Assessments indicate that candidates can demonstrate and apply proficiencies related to diversity. Experiences provided for candidates include working with diverse populations, including higher education and P–12 school faculty, candidates, and students in P–12 schools.

NCATE Standard 5: Faculty Qualifications, Performance, and Development

Faculty are qualified and model best professional practices in scholarship, service, and teaching, including the assessment of their own effectiveness as related to candidate performance. They also collaborate with colleagues in the disciplines and schools. The unit systematically evaluates faculty performance and facilitates professional development.


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NCATE Standard 6: Unit Governance and Resources

The unit has the leadership, authority, budget, personnel, facilities, and resources, including information technology resources, for the preparation of candidates to meet professional, state, and institutional standards.

NCATE Standard 1 is tied to standards defined by the National Council of Teacher of Mathematics (NCTM) [3]. The NCTM standards must be met to satisfy NCATE Standard 1. The NCTM standards are grouped into three areas: process standards, content standards, pedagogy standards, and field-based experience standards. A brief description of each group of standards follows: NCTM Process Standards: The process standards are based on the belief that mathematics must be approached as a unified whole. Its concepts, procedures, and intellectual processes are so interrelated that, in a significant sense, its “whole is greater than the sum of the parts.” This approach would best be addressed by involvement of the mathematics content, mathematics education, education, and field experience faculty working together in developing the candidates’ experiences. Likewise, the response to the disposition standard will require total faculty input. This standard addresses the candidates’ nature and temperament relative to being a mathematician, an instructor, a facilitator of learning, a planner of lessons, a member of a professional community, and a communicator with learners and their families. Process standards include problem solving, reasoning and proof, mathematical communication, mathematical connections, mathematical representation, technology, and dispositions. NCTM Content Standards: Candidates’ comfort with, and confidence in, their knowledge of mathematics affects both what they teach and how they teach it. Knowing mathematics includes understanding specific concepts and procedures as well as the process of doing mathematics. Content standards include knowledge of number and operation; different perspectives on algebra; geometries; calculus; discrete mathematics; data analysis, statistics, and probability; and measurement. NCTM Pedagogy Standards: In addition to knowing students as learners, mathematics teacher candidates should develop knowledge of and ability to use and evaluate instructional strategies and classroom organizational models, ways to represent mathematical concepts and procedures, instructional materials and resources, ways to promote discourse, and means of assessing student understanding. The pedagogy standard section of each set includes only one standard, but has multiple indicators that must be addressed. NCTM Field-Based Experiences: The development of mathematics teacher candidates should include opportunities to examine the nature of mathematics, how it should be taught and how students learn mathematics; observe and analyze a range of approaches to mathematics teaching and learning, focusing on the tasks, discourse, environment and assessment; and work with a diverse range of students individually, in small groups, and in large class settings. Experiences should cover the range of grade levels included in the


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program such as middle and high school experiences for secondary mathematics programs. Full-time student teaching experience should be supervised by a highly qualified teacher and a university or college supervisor with mathematics teaching experience at the appropriate level.


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Appendix E. Certification and Licensing of Teachers in New York State The initial certification of a mathematics teacher candidate in New York State requires the following:

• Completion of a NYS Registered Program - Mathematics 7-12 • Institutional Recommendation - Mathematics 7-12 • New York State Teacher Certification Exam - Liberal Arts & Science Test

(LAST) • New York State Teacher Certification Exam - Secondary Assessment of

Teaching Skills (ATS-W) • Content Specialty Test (CST) - Mathematics

For more detail on the certification and licensing procedure visit http://eservices.nysed.gov/teach/certhelp/CertRequirementHelp.do.