Board Committee Documents Academic Policy

Table of Contents:

1 Abstract 2 2 Description of Curriculum Modification: 2 Bachelor of Science in Mathematics Education 3 Need, Justification and Purpose 2 4 Students A. Interest/Demand 4 B. Enrollment Projections 5 C. Admission Requirements 6 5 Curriculum: A. Introduction 6 B. Pedagogy Component 6 C. Mathematics Component 10 D. Mathematical Applications Component 13 E. Liberal Arts and Science Core Component 14 F. Summary of Degree Requirements 14 6 Cost Assessment 15 7 References 15

Appendices

A Course Syllabi for New Pedagogy Courses 17 B Course Syllabi for New Math Courses 46 C Program Scheduling 69 D Full-Time Faculty Teaching Assignments 72 E Faculty to be Hired 76 F New Resources 77 G Projected Revenue 78 H Supporting Materials for Projected Revenue 79 I Five Year Financial Projection 85 J Articulation Agreements: Bronx Community College, Borough of Manhattan Community 87 College K State Requirements for Teacher Preparation Programs 97 L NCATE and NCTM Accreditation Standards 101 M Certification and Licensing of Teachers in New York State 104 N Correspondence from Professor S. Smith regarding planned 105 Curricular changes in the Department of Architectural Technology O Student Survey Form 106 P Consultation with affected Departments • Career and Technology Teacher Education 107 • Architectural Technology 107 • Computer Systems 108 • Electrical & Telecommunication 109 Engineering Technology Q Relevant Minutes from Department Curriculum Committee Meeting, 110 Relevant Minutes from Department Meetings 111 R Letter of Support from Dean Pamela Brown 114 S External letter of Support 115 T Library Resource and Information Literacy Form 117 U Chancellor’s Report 122

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1. Abstract

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 for certification to teach middle school and secondary school mathematics (grades 7 to 12) in New York State. The proposed curriculum is comprised of 4 components: A pedagogy component (29 credits), a mathematics component (37 credits), a liberal arts and science core component (43-45 credits), and a mathematical applications component (9-11 credits). Courses within the mathematical applications component may be chosen from architecture, electrical and computer engineering technology, computer systems, applied mathematics, and physics. The program hopes to address the shortage of well-trained mathematics teachers in the New York City public school system, particularly among underrepresented groups.

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

The proposed curriculum is comprised of 4 components: A pedagogy component (29 credits), a mathematics component (37 credits), a liberal arts and science core component (43-45 credits), and a mathematical applications component (9-11 credits).

Courses in the pedagogy component are linked to mathematics content and are specifically focused on the teaching of mathematics. The mathematics component 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 component may be chosen from architecture, electrical and computer engineering technology, computer systems, applied mathematics, and physics. 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. Need, Justification and Purpose The proposed Bachelor of Science in Mathematics Education has been designed to meet a pressing need for well-trained mathematics teachers. A well-trained mathematics teacher must not only have a solid pedagogical foundation, but must also have an extensive background in mathematics.

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It is the latter quality that is most lacking among today’s middle school and secondary school mathematics teachers. A recent study of the National Science Foundation (NSF, 2006) found that between 23 and 29 percent of middle school and high school mathematics and science teachers did not have a college major or even a minor in their teaching field. Ingersol (1999) reported that 49 percent of seventh grade U.S. mathematics teachers did not have the equivalent of a minor in mathematics. Milbourne (2002) found that out of the 134,000 secondary school mathematics teachers in the U.S., only 86 percent were certified to teach mathematics. The mathematics background of teachers is strongly correlated to student performance. Hawkins et al. (1998) concluded that “at the eighth grade level, students who were taught by teachers with teaching certificates in mathematics outperformed, on the mathematics National Assessment of Educational Progress test, students whose teachers had certificates in other fields.” Similar results are found in science education, indicating that content background affects student performance across STEM fields: A meta-analysis by Druva and Anderson (1983) determined that “students' ability to understand the essentials of the scientific method was positively correlated with the number of science courses their teachers had taken.” The proposed program will immerse students in an intensive mathematical course of study in addition to providing a solid pedagogical foundation. In fact, our program goes one crucial step further: Our program integrates pedagogy and mathematics content. Integrating mathematics content with pedagogy is made possible by a fundamental characteristic of our proposed program. Our program, unlike most others, is housed in a single department, the Mathematics Department.

Most training programs for mathematics teachers provide pedagogy training in an education department, and mathematics instruction from a separate mathematics department (Graham et al., 2000). “The segregation between the two major components of mathematics education programs may foster a perspective that methods are unrelated to content or that content is more important than method” (Yunas et al., 2008). Unlike most programs, ours will illuminate the interrelations between pedagogy and mathematics.

The strength of the mathematics component of our program is apparent even in comparison to two very prestigious programs for the training of mathematics teachers: New York University’s Bachelor of Science in Mathematics Education, and the Mathematics Secondary School Teacher Preparation Program of SUNY Stony Brook.

NYU’s program includes 36 credits of mathematics. Stony Brook’s program has a very strong mathematics component; it is one of the few programs housed in a mathematics department. Stony Brook’s program includes 39 credits. By comparison with these top programs, our program requires a minimum of 45 credits in mathematics, and students may take more through electives.

The mathematics component of the proposed program is roughly equivalent to that provided by a typical Bachelor of Science in Mathematics, and would prepare students to enter graduate school in pure mathematics. As such, our program is consistent with recommendations of the National Council of Teachers of Mathematics (NCTM). The NCTM holds that secondary school teachers should have completed the equivalent of an undergraduate major in mathematics and that middle school teachers should have the equivalent of an undergraduate minor in mathematics (NCTM, 2005).

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Demand for Mathematics Teachers

Strong demand for effective mathematics teachers has been a consistent trend for well over a decade across the U.S. (Boyd, 2009). Further, the problem of recruiting effective teachers appears to be more acute in schools serving high poverty student populations (Boyd et al., 2008; Boyd et al., 2006; Hunushek, 2004). In a recent study, Boyd (2009) concluded that “even with the creation of the alternative certification route, New York City finds it difficult to recruit sufficient numbers of teachers with substantial math coursework or a math undergraduate major.” The proposed program will help meet the demand for highly qualified math teachers.

Posam and Choppin (2005) cite the No Child Left Behind act (NCLB) as a factor that has contributed to the shortage of math teachers in New York City. The NCLB increased the demand for qualified teachers by requiring that mathematics teachers be fully certified, and have a content knowledge roughly equivalent to an undergraduate major in mathematics (National Comprehensive Center for Teacher Quality, 2006).

The increased demand for highly qualified Math teachers caused by the NCLB is likely to persist as a result of the Common Core State Standards Initiative (CCSS), an initiative that has been adopted by many states including New York State. The CCSS is a state-led effort “to create shared high standards to make sure all American students are ready for college and work” (CCSS, 2010). The CCSS lays out a rigorous set of middle school and high school mathematics standards that participating states plan to adopt.

Certainly the sluggish economy in New York State at present has decreased teacher demand. But, this decrease appears temporary, and a strong demand for qualified mathematics teachers is likely to continue into the future, and should be strengthened as the economy recovers. The long-term outlook for the demand for qualified mathematics teachers looks promising. The 2010-2011 Occupational Outlook Handbook published by the Bureau of Labor Statistics reports substantial employment opportunities for highly qualified mathematics teachers, with this trend continuing for the foreseeable future, especially in urban and rural areas with underserved populations.

4. Students

4. A. Interest/Demand

In the fall of 2010, a survey was distributed to students enrolled in MAT 1375 Precalculus, MAT 1475 Calculus I, MAT 1575 Calculus II, MAT 2675 Calculus III and students involved in the Peer Leader program. The complete survey form may be found in Appendix G. Results from the following item on the survey 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?

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Course Very Interested Somewhat Not Interested No Answer Total Surveyed Interested 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

4. B. Enrollment Projections

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.

YEAR I YEAR II YEAR III YEAR IV YEAR V

New Cont. New Cont. New Cont. New Cont. New Cont. F-T 20 0 35 12 50 28 65 47 70 64

P-T 4 0 8 2 12 6 16 11 20 16

Sub-totals 24 0 43 14 62 34 71 58 90 80

Totals 24 57 97 129 170

The enrollment numbers are estimates based partially on results of the student survey (Subsection 4.A). We anticipate robust enrollment numbers, as reflected in the student survey, due in part to the unique features and strengths of the proposed program, which we believe will attract students. Our program is one of a very small number of programs in New York State that is being run out a Department of Mathematics. Further, to the best of our knowledge, the program is unique in offering a mathematical applications component. The enrollment numbers should additionally be enhanced due to the relative affordability of a City University of New York Education.

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We used a 60% retention rate. For full-time students in their forth year, we assumed 60% would graduate; 20% would not graduate, but would enroll in the program for the next year; and 20% would leave the program without graduating. We also assumed 5 of the new 50 students in year 3 would be transfer students resulting from articulation agreements (this assumption affects the year 5 numbers due to graduation). We assumed no part-time students would graduate in the first four years.

4. C. Admission Requirements

Students may enter the program as freshmen if they meet the general College criteria on pages 8, 34 of the City Tech College Catalog 2009-2011. Alternatively, they may transfer from one of the City Tech AAS programs before or after completing the associate degree. Students from other colleges may also apply for admission as transfer students if they meet College criteria for transfer admission. Students transferring from other colleges or from programs within City Tech will have their academic records evaluated to determine their appropriate placement in the program. A minimum grade point average of 2.5 is required for transfer.

Regardless of the mode of admission, prospective students must meet CUNY proficiency requirements. To be admitted to the program, all applicants must write an essay and must be interviewed by program faculty to determine their eligibility for state certification and potential for success in the program.

5. Proposed Curriculum

5. A. Introduction

5. B. Pedagogy Component

The pedagogical component 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 component consists of 29 credits of required coursework as reflected in the table below. The catalog course descriptions may also be found below. Detailed course syllabi may be found in Appendix A.

The pedagogy component 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.

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The pedagogy component 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 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 veteran 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 and Technology." In essence, the pedagogy component 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 careers as math educators.

Course Credits MEDU 2901 Peer Leader Training in Mathematics 1 *MEDU 1010 Foundations of Mathematics Education 3 *MEDU 1020 Teaching and Learning Strategies for 2 Mathematics Teachers *MEDU 2010 Pedagogy of Mathematics Applications and 2 Technology *MEDU 3010 Methods of Teaching Middle School 3 Mathematics *MEDU 3020 Methods of Teaching Secondary School 3 Mathematics *MEDU 3030 Assessment Techniques in Mathematics 2 *MEDU 4010 Supervised Student Teaching and Seminar in 4 Middle School Mathematics *MEDU 4020 Supervised Student Teaching and Seminar in 4 Secondary School Mathematics EDU 2455 Methods and Materials for Special Needs 3 Students EDU 4600 Professional Development Seminar 2 Total Credits 29 *Indicates a new course.

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Catalogue Descriptions of Proposed Pedagogy Courses

Course: MEDU 1010 Title: Foundations of Mathematics Education Credit Hours: 3 cl hr, 3 cr. 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 for Mathematics Teachers 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 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: Pedagogy of Mathematical Applications and Technology 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, 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 will be on the needs of individual learners including English language learners and those with disabilities and special health needs, group instruction techniques, the development of literacy in the mathematics classroom, roles of the teacher in the

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classroom, and planning both curriculum and individual lessons. Includes 6 hours per week for 10 weeks of preservice field experience in high schools. Pre/Corequisite: MEDU 2010, ENG 1121

Course: MEDU 3020 Title: Methods of Teaching Secondary 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 will be on the needs of individual learners including English language learners and those with disabilities and special health needs, group instruction techniques, the development of literacy in the mathematics classroom, roles of the teacher in the classroom, and planning both curriculum and individual lessons. Includes 6 hours per week for 10 weeks of preservice field experience in high schools. Prerequisite: MEDU 3010

Course: MEDU 3030 Title: Assessment Techniques in Mathematics Credit Hours: 1 cl hr, 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. Pre/Corequisite: MEDU 3010

Course: MEDU 4010 Title: Supervised Student Teaching and Seminar in Middle School Mathematics Credit Hours: 1 cl hr, 9 field hrs/week, 4 cr Catalogue Description: The course consists of a field-based, student teaching experience and a seminar component. The field-based experience involves 20 days or 120 hours of supervised student teaching in grades 7 through 9. Under the guidance and supervision of an experienced teacher and a faculty member, students will implement and refine pedagogical strategies, classroom management techniques, and assessment approaches. The seminar component provides a discussion forum for students, guided by a faculty member, to refine pedagogical strategies, and to address and resolve pedagogical issues that students face during the concurrent field placement. Prerequisite: MEDU 3010 and permission of department one semester in advance.

Course: MEDU 4020 Title: Supervised Student Teaching and Seminar in Secondary School Mathematics Credit Hours: 1 cl hr, 9 field hrs/week, 4 cr Catalogue Description: The course consists of a field-based, student teaching experience and a seminar component. The field-based experience involves 20 days or 120 hours of supervised

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student teaching in grades 10 through 12. Under the guidance and supervision of an experienced teacher and a faculty member, students will implement and refine pedagogical strategies, classroom management techniques, and assessment approaches. The seminar component provides a discussion forum for students, guided by a faculty member, to refine pedagogical strategies, and to address and resolve pedagogical issues that students face during the concurrent field placement. Prerequisite: MEDU 3020 and permission of department one semester in advance.

5. C. Mathematics Component

The mathematics component of the proposed program will provide future middle school and secondary 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.

The mathematics component consists of 37 credits of required mathematics coursework listed in the table below. In addition to these 37 credits of mathematics, MAT 1475 Calculus I, and MAT 1575 Calculus II are part of the liberal arts and science component requirements, which brings the total required credits in mathematics to 45. Additional mathematics courses may be taken within the mathematical applications component described in subsection 5. D.

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 the non- traditional courses MAT 1476L Calculus Laboratory, and MAT 2630 Applied Mathematics Technology. In the Calculus Laboratory, 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 such errors.

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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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 2070 Introduction to Proofs and Logic 3 *MAT 3020 Number Theory 3 *MAT 3050 Geometry I 3 *MAT 3075 Introduction to Real Analysis 4 *MAT 3080 Modern Algebra 3 *MAT 4050 Geometry II 3 *MAT 4030 History of Mathematics 3 Total Credits in the Math Component 37 **MAT 1475 Calculus I 4 **MAT 1575 Calculus II 4 Total Required Math Credits in the Proposed Program 45 * Indicates a new course ** Indicates a mathematics course included in the Liberal Arts and Science Core Component Requirements.

Catalogue Descriptions of Proposed Mathematics Courses

Course: MAT 2070 Title: Introduction to Proofs and Logic 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

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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

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

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5. D. Mathematical Applications Component

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, Applied Mathematics, and Physics. 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 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 Applied Mathematics Engineering Technology EET MAT 1102 Electrical Tech 2 2680 Diff Equations 3 1122 Circuit Analysis I 4 3770 Math Modeling I 3 1222 Circuit Analysis II 5 4880 Math Modeling II 3 2672 Probability and Statistics II 4 Physics PHYS 2443 Physics 3.3 4 2605 Introduction to Laser Physics 4 and Photonics 1117 Astronomy I 4 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 Component. See Appendix N.

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5. E. Liberal Arts and Science Core Component

The liberal arts and science core component 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 component course requirements are illustrated in the table below.

Liberal Arts & Science Component Requirements

Component Course Requirement Credits Area ENG ENG 1101 English Composition I 3 MATH I MAT 1475 Calculus I 4 MATH II MAT 1575 Calculus II 4 SCI I* PHYS 1441 Physics 1.3, 4-5 CHEM 1110 Chemistry I, or BIO 1101 Biology I. SCI II* PHYS 1442 Physics 2.3, 4-5 CHEM 1210 Chemistry II, or BIO 1201 Biology II. LIT ENG 2000/3400 series, AFR, PRS 2200 series 3 LIT/AES/PHIL Two additional courses from two of the three LAP categories: 6 Literature: any ENG 2000/3400 series, AFR, PRS 2200 series or Aesthetics: any ARTH, MUS, THE, AFR 1300/2300 series or Philosophy: any PHIL 2000 series or higher, AFR 2600 series. BS/SS PSY 1101 Introduction to Psychology 3 PSY 2501 Child and Adolescent Development 3 PSY 3502 Human Learning and Instruction 3 COMM ENG 1121 English Composition II 3 SPE 1330 Effective Speaking 3 Total 43-45

* The physics sequence is 10 credits. The biology and chemistry sequences are each 8 credits.

5. F. Summary of Degree Credit Requirements

Pedagogy Component 29 Credits Mathematics Component 37 Credits Liberal Arts and Science Core Component 43-45 Credits Mathematical Applications Component 9-11 Credits (to make 120 credits) Total 120 Credits

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6. Cost Assessment: Immediate Space and Equipment Needs

Currently the department has sufficient space and equipment to run the proposed program in mathematics education.

7. References

[1] Boyd, D. (2009). Recruiting Effective Math Teachers, How do math immersion teachers compare? Evidence from New York City. Teacher Policy Research.

[2] Boyd, D., Grossman, P., Lankford, H., Loeb, S., & Wyckoff, J. (2008). Who Leaves? Teacher Attrition and Student Achievement. The National Bureau of Economic Research.

[3] Boyd, D., Grossman, P., Lankford, H., Loeb, S., & Wyckoff, J. (2006). How changes in entry requirements alter the teacher workforce and affect student achievement. Education Finance and Policy 1(2): 176-216.

[4] Bureau of Labor Statistics, Occupational Outlook Handbook, 2010-11 Edition. Teachers—Secondary Teachers. Retrieved December 1, 2010 from http://www.bls.gov/oco/ocos318.htm

[5] Common Core State Standards Initiative. Key Points of the Math Standards. Retrieved March 5, 2011 from http://www.corestandards.org/assets/KeyPointsMath.pdf.

[6] Department of Mathematics, Stonybrook University. (2005). Undergraduate Mathematics Handbook. Retrieved February 11, 2011 from http://www.math.sunysb.edu/docs/ug-handbook/ug-handbook.pdf.

[7] Druva, A., & Anderson, R. (1983). Science Teacher Characteristics by Teacher Behavior and by Student Outcome: A Meta-Analysis of Research. Journal of Research in Science Training, 20(5): 467-479.

[8] Graham, K. J., Li, Y., & Buck, C. J. (2000). Characteristics of mathematics teacher preparation programs in the United States: An exploratory study. The Mathematics Educator, 5(112): 5-31.

[9] Hawkins, E., Stancavage, F., & Dossey, J. (1998). School Policies and Practices Affecting Instruction in Mathematics: Findings from the National Assessment of Educational Progress. National Center for Education Statistics. Washington D.C.

[10] Hanushek, E., Kain, J. & Rivkin, S. (2004). Why public schools lose teachers. Journal of Human Resources 39(2) 326-254.

[11] Ingersoll, R.M. (1999). The problem of underqualified teachers in American Secondary Schools. Educational Researcher 28(2): 26-37.

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[12] Milbourne, L.A. (2002). Finding Mathematics Teachers. Clearinghouse for Science, Mathematics, and Environmental Education, Columbus, OH. ERIC/CSMEE.

[13] National Council for Accreditation of Teacher Education. (2008). Professional Standards for the Accreditation of Teacher Preparation Institutions.

[14] National Council of Teachers of Mathematics. (2003). Program Standards for Initial Preparation of Mathematics Teachers.

[15] National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics.

[16] National Council of Teacher of Mathematics. (2005). A position of the NCTM: Highly qualified teachers. Retrieved February 5, 2011 from http://www.nctm.org/uploadedFiles/About_NCTM/Position_Statements/qualified.pdf

[17] National Comprehensive Center for Teacher Quality. (2006). Key Issue: Recruiting Mathematics and Science Teachers at the High School Level. Retrieved February 11, 2011 from http://www2.tqsource.org/strategies/recruit/recruithigh.pdf.

[18] National Science Foundation. (2006). Chapter 1: Elementary and secondary education. Science and engineering indicators 2006. Arlington, VA: Author. Retrieved May 15, 2006, from http://www.nsf.gov/statistics/seind06/pdf/c01.pdf

[19] New York State Education Department. (2010). Pedagogical Component Requirements for Programs Leading to Certification in Teacher Education. Retrieved February 11, 2011 from http://www.highered.nysed.gov/ocue/aipr/register.html#Teacher

[20] NYU Steinhardt School of Culture, Education, and Human Development. (2011). Mathematics Education. Retrieved February 11, 2011 from http://steinhardt.nyu.edu/teachlearn/math/.

[21] Posam, A.S., & Coppin J.R. (2005). How the nation’s largest city is managing one of its severest math teacher shortages. Mathematics Teacher, 98(9): 582-584.

[22] Yunas, A., Hamazah, R., & Ismail, H. (2008). Mathematics teacher’s preparation program: Determining the balance between content in mathematic and pedagogy. European Journal of Social Science, 6(4): 125-132.

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Appendix A. Course Syllabi for New Pedagogy Courses

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New York City College of Technology The City University of New York

DEPARTMENT: Mathematics

PREPARED BY: Professor Andrew Douglas

COURSE: MEDU 1010

TITLE: Foundations of Mathematics 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, D., & Eggen, P. (2011). Introduction to Teaching: Becoming a Professional 4th Ed. Merril.

CREDIT HOURS: 3 cl hrs, 0 lab hrs, 3 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 ASSESSMENT

For successful completion of the course, Instructional Activity, Evaluation Methods students should be able to: and Criteria Identify knowledge and skills necessary to Classroom Discussion, Essays, Group become an effective teacher. Presentation, Final Exam Identify the characteristics of effective Classroom Discussion, Essays, Group instruction. Presentation, Final Exam Provide an overview of the historical Classroom Discussion, Essays, Group development of American education. Presentation, Final Exam Describe various general philosophies and Classroom Discussion, Essays, Group philosophers of education; give their Presentation, Final Exam philosophy of education and relate it to a formal philosophy. Identify social problems affecting children Classroom Discussion, Essays, Group and youths and explain how these problems Presentation, Final Exam challenge schools and teachers. Explain how schools are financed. Classroom Discussion Identify the legal principles that affect Classroom Discussion, Essays, Group public education. Presentation, Final Exam Trace the steps in becoming a licensed Classroom Discussion teacher in New York State.

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? 1 Developing as a Professional 2 2-3 Student Diversity: Culture, Language and Gender 4 Student Diversity: Development, Ability and Exceptionalities 5 4-6 Philosophical, Historical and Sociological Foundations of 3, 6, 7 American Education 7 The Organization of American Schools 8 Governance and Finance: Regulating and Funding Schools 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 12 Management 13 Instruction in Today’s Schools 13 Assessment, Standards and Accountability 14 14 Student Presentations 15 Final Exam

Additional Resources

1. Ornstein, C., Levine, D., & Gutek, G. (2011). Foundations of Education, 11th Edition. Cengage Learning.

2. Webb, L., Metha, A., & Jordan, K. (2009). Foundations of American Education, 6th Edition. Prentice Hall.

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New York City College of Technology The City University of New York

DEPARTMENT: Mathematics

PREPARED BY: Professors Arnavaz Taraporevala, Estela Rojas, and Peter Deraney

COURSE: MEDU 1020

TITLE: Teaching and Learning Strategies for Mathematics Teachers

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. • 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.

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

INSTRUCTIONAL OBJECTIVES AND ASSESSMENT:

INSTRUCTIONAL OBJECTIVES ASSESSMENT

For successful completion of the course, Instructional Activity, Evaluation Methods students should be able to: and Criteria Explore teaching and learning strategies Discussion and student presentation used in mathematics Explore theories of teaching and learning Discussion and student presentation processes and motivation Develop strategies to address students' Discussion and student presentation learning difficulties in mathematics based on emotional intelligence, learning styles and other theories Explore active learning through the arts of Discussion and student presentation 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

WEEKLY COURSE OUTLINE:

WEEK TOPIC CHAPTERS/SECTIONS 1 NY State, NCTM, and NCATE Standards 2 Secondary School Students’ Proportional Chapter 1 Reasoning 3 Role of Problem Solving in the Secondary Chapter 2 School Mathematics Classroom 4 Learning and Teaching Algebra in Chapter 3 Secondary School Classrooms 5 Geometry and Proofs in Secondary School Chapter 4 Classrooms 6 Probability and Statistics in Secondary Chapter 5 School Classrooms

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7 The Role of Curricular Materials in Chapter 6 Secondary School Mathematics Classrooms 8 The Influence of technology on Secondary Chapter 7 School Students’ Mathematics learning 9 Secondary School Mathematics Teachers’ Chapter 8 Classroom Practices 10 Qualities of Effective Secondary School Chapter 9 Mathematics teachers 11 How Teachers’ Actions Affect What Chapter 10 Students learn in Secondary School Mathematics Classrooms 12 Formative Assessment in Secondary School Chapter 11 mathematics Classrooms 13 Language, Culture, and Equity in Secondary Chapter 12 School mathematics Classrooms 14 Project Presentation 15 Project Presentation

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New York City College of Technology The City University of New York

DEPARTMENT: Mathematics

PREPARED BY: Professor Peter Deraney and Professor Arnavaz Taraporevala

COURSE: MEDU 2010

TITLE: Pedagogy of Mathematics Applications and Technology

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: Mathematics: Modeling Our World (MMOW) Course 1, the Consortium for Mathematics and its Applications, 2nd edition.

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 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.

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4. use appropriate technology in the solution of problems involving mathematics applications.

INSTRUCTIONAL OBJECTIVES AND ASSESSMENT:

INSTRUCTIONAL ASSESSMENT OBJECTIVES Instructional Activity, Evaluation Methods and Criteria For successful completion of the course, students should be able to: Evaluate instructional models Working collaboratively in small groups, complete model appropriate to the secondary lessons from the text , Evaluate the effectiveness of these school curriculum which lessons in writing and in oral presentation. incorporate mathematics applications. Construct a model lesson As a term project, construct a new model lesson incorporating incorporating mathematics mathematical applications. 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 In the written summary of each model lesson, discuss the of technology in the instructional appropriate use of technology in clarifying and facilitating the models reviewed in class and solution of the problem. developed for the term project.

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% • 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.

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WEEKLY COURSE OUTLINE:

Week Topics Assignments 1 Introduction to Course; Purchase Textbook and Supplies Application: Basic Mathematics Text: Chapter 0: Lessons 1 and 2 Chapter O: Pick a Winner: Decision Making in a Democracy 2 Application: Algebra and Text: Chapter 1: Lessons 1 – 3 Functional Notation Chapter 1: Secret Codes and the Power of Algebra (Part 1) 3 Application: Algebra and Text: Chapter 1: Lessons 4 – 6 Functional Notation Chapter 1: Secret Codes and the Power of Algebra (Part 2) 4 Application: Geometry Text: Chapter 2: Lessons 1 – 4 Chapter 2: Scene from Above 5 Application: Graphing and Text: Chapter 3: Lessons 1 – 4 Statistics Chapter 3: Prediction 6 Application: Graphical Text: Chapter 4: Lessons 1 – 5 Representation of Functions Chapter 4: Animation/Special Effects 7 Review of weeks 1 – 6 Midterm Exam Review Exercises Midterm Exam 8 Application: Functions; Text: Chapter 5: Lessons 1 – 2 Parametric Equations Chapter 5: Wildlife (Part 1) 9 Application: Exponential Growth Text: Chapter 5: Lessons 3 – 5 and Decay Submit topic and outline for term project Chapter 5: Wildlife (Part 2) 10 Application: Probability Text: Chapter 6: Lessons 1 – 4 Chapter 6: Imperfect Testing 11 Application: Probability; Curve Text: Chapter 7: Lessons 1 –3 Fitting Submit draft of term project Chapter 7: Testing 1, 2, 3 (Part 1) 12 Application: Quadratic Functions Text: Chapter 7: Lessons 4 – 5 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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Additional Resources

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

2. Teaching Mathematics and Its Applications, Oxford Journals.

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New York City College of Technology The City University of New York

DEPARTMENT: Mathematics

PREPARED BY: Professor 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 will be on the needs of individual learners including English language learners and those with disabilities and special health needs, group instruction techniques, the development of literacy in the mathematics classroom, roles of the teacher in the classroom, and planning both curriculum and individual lessons. Includes 6 hours per week for 10 weeks of preservice field experience in high 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 2010, 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 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.

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INSTRUCTIONAL OBJECTIVES AND ASSESSMENT:

INSTRUCTIONAL OBJECTIVES ASSESSMENT

For successful completion of the course, Instructional Activity, Evaluation Methods students should be able to: and Criteria Plan for teaching middle school Develop and implement course, unit and mathematics. lesson outlines both in the classroom and in the field. Implement effective instructional strategies Develop and carry out lesson plans at the middle school level. incorporating instructional strategies and reflect on their effectiveness. Implement instructional strategies to Develop and carry out lesson plans support students with disabilities and incorporating instructional strategies and special needs. reflect on their effectiveness. Incorporate manipulatives, technology and Create lesson plans incorporating various other materials. 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.

WEEKLY COURSE OUTLINE:

WEEK TOPIC CHAPTERS/SECTIONS 1 Introduction Introduction Teaching in Middle School: An Overview 2 Problem Solving Chp 1.1-1.3 3-5 Teaching and Learning Techniques Unit One introduction Manipulatives and other Materials Chp 1.4-1.7 Use of Technology

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Literacy in the Mathematics Classroom Math Topics: Number Sense and Operations 6-8 Theories of Learning Chp 2.1-2.5 Students with Disabilities and Special Needs Math Topics: Rational Numbers & Proportions 9-10 Lesson Planning Chp 3.1-3.6 Math Topics: Geometry and Measurement 11-13 Assessment Techniques Chp 4.1-4.5 Math Topics: Probability and Statistics 14-15 Curriculum Development Chp 5.1-5.3 State and National Standards Professional Development

Additional Resources

", Brumbaugh, et al. (2006). Teaching Middle School Mathematics, 3rd Edition. Lawrence Erlbaum Publishers.

#, Montague, et al. (2006). Teaching Mathematics to Middle School Students with Learning Difficulties, 1st Edition. The Guilford Press.

$, Schoen, H., & Charles, R. (2003). Teaching Mathematics through Problem Solving: Grades 6-12. NCTM.

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New York City College of Technology The City University of New York

DEPARTMENT: Mathematics

PREPARED BY: Professor Jonas Reitz

COURSE: MEDU 3020

TITLE: Methods of Teaching Secondary 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 will be on the needs of individual learners including English language learners and those with disabilities and special health needs, group instruction techniques, the development of literacy in the mathematics classroom, roles of the teacher in the classroom, and planning both curriculum and individual lessons. Includes 6 hours per week for 10 weeks of preservice field experience in high schools.

TEXT: Brumbaugh, et al. (2006). Teaching Secondary School Mathematics, 3rd Edition. Lawrence Erlbaum Publishers.

CREDIT HOURS: 3 cl hrs, 6 field hours/week, 3 cr

PREREQUISITES: MEDU 3010

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. 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.

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

INSTRUCTIONAL OBJECTIVES AND ASSESSMENT:

INSTRUCTIONAL OBJECTIVES ASSESSMENT

For successful completion of the course, Instructional Activity, Evaluation Methods students should be able to: and Criteria 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 Develop and carry out lesson plans for a variety of students, including students incorporating instructional strategies and with disabilities and special needs. reflect on their effectiveness. Implement instructional strategies to Develop and carry out lesson plans support language acquisition and literacy incorporating instructional strategies and development. reflect on their effectiveness. Incorporate problem solving and Create lesson plans incorporating problem technology. solving and technology. Assess student progress. Design and implement assessment tools in the classroom and in the field.

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.

WEEKLY COURSE OUTLINE:

WEEK TOPIC CHAPTERS/SECTIONS 1 - 2 Teaching in a High School: An Overview Chp 1 Professional Responsibilities Ethical Behavior Leadership Structures Professional Development Opportunities 3 - 5 Learning Theories and Curriculum Chp 2 A review of competing theories of learning as

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applied to mathematics Students with disabilities and special needs Overall views of curriculum The establishment of mathematics curriculum 6 Knowledge of Mathematics Chp 9 The need of the Teacher to have a solid background in Mathematics Competency testing 7 Assessment Issues Chp 2 8-10 Lesson Planning Chp 3 Long Range Planning – (whole course) Chp 10-15 (selections) Unit Planning – (a couple of weeks) Detailed Daily Lesson Plans - (daily) 11-13 Instructional Models Chp 4, 5, 7 Questioning Skills Language acquisition and literacy development Inductive and deductive models Presenting mathematics lessons Appropriate uses of technology in teaching lessons 14 Problem solving issues Chp 6 15 Proofs Chp 8

Additional Resources

1. Beckmann, et al. (2009). Teaching and Learning High School Mathematics. Wiley.

2. Posam, et al. (2009). Teaching Secondary Mathematics: Techniques and Enrichment Units, 8th Edition. Allyn and Bacon.

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New York City College of Technology The City University of New York

DEPARTMENT: Mathematics

PREPARED BY: Professor Andrew Douglas, Professor Estela Rojas

COURSE: MEDU 3030

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.

TEXT: Popham, W.J. (2010). Classroom Assessment: What Teachers Need to Know. Pearson.

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

PRE/COREQUISITE: MEDU 3010

LEARNING OUTCOMES:

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

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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.

INSTRUCTIONAL OBJECTIVES AND ASSESSMENT:

INSTRUCTIONAL OBJECTIVES ASSESSMENT

For successful completion of the course, Instructional Activity, Evaluation Methods and students should be able to: Criteria Discuss reliability and validity and their Guided discussion, learning logs, homework importance to mathematics classroom assignments, student portfolio, final exam. assessment. Construct mathematics tests including question Guided discussion, learning logs, homework items that measure concept understanding, assignments, student portfolio, classroom high-level cognition and problem solving. 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 Guided discussion, learning logs, homework assessment in the mathematics classroom assignments, student portfolio, classroom including performance assessment, learning group work/activities, final exam. logs and student portfolios. Discuss the effects of state-level, national and Guided discussion, learning logs, homework international mathematics assessment on assignments, student portfolio, classroom classroom teaching. 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% 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

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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? 1 Assessment vs. Evaluation 2-3 Reliability of Assessment 2 Validity of Assessment 3 4 Absence of Bias 4 Deciding what to Assess and How, rubrics 5,8 5-6 Math Test Construction Instructor Provided Document, Samples of Quizzes, Tests, Exams 7-10 Alternative Assessment in Mathematics, Learning Logs, 8,9,10,12 Student Portfolios, Performance Assessment, Affective Assessment, Formative Assessment, assessment issues in a Technology rich environment. 11-12 State-Level Assessments in Mathematics (APDA) 13 National Assessments in Mathematics (NAEP) NAEP Documents International Assessment in Mathematics (TIMSS, PISA) TIMSS Documents APDA Documents 13 Student Presentations 14 Student Presentations 15 Final Exam

Additional Resources

1. Bush, W., Greer, A., & Compton, H. (1999). Mathematics Assessment: A Practical Handbook: For Grades 9-12 (Classroom Assessment for School Mathematics Seires). National Council of Teachers of Mathematics.

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2. Kulm, G. (1994). Mathematics Assessment: What Works in the Classroom, 1st Edition. Josey-Bass.

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New York City College of Technology The City University of New York

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 course consists of a field-based, student teaching experience and a seminar component. The field-based experience involves 20 days or 120 hours of supervised student teaching in grades 7 through 9. Under the guidance and supervision of an experienced teacher and a faculty member, students will implement and refine pedagogical strategies, classroom management techniques, and assessment approaches. The seminar component provides a discussion forum for students, guided by a faculty member, to refine pedagogical strategies, and to address and resolve pedagogical issues that students face during the concurrent field placement.

REFERNCE: Rubenstein, R. N., Beckman, C. E., & Thompson, D. R. (2004). Teaching and learning middle grades mathematics. Emeryville, CA: Key Curriculum Press

CREDITS HOURS: 1class hours, 9 field hours/week, 4 credits

PREREQUISITE: MEDU 3010 and permission of department one semester in advance.

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 AND ASSESSMENT:

INSTRUCTIONAL OBJECTIVES ASSESSMENT

For the successful completion of this course, Instructional Activity, Evaluation Methods and Criteria students should be able to: Plan and implement curriculum and Supervisor’s Evaluation for Student Teachers instruction 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 Cooperating Teacher’s Evaluation for Student Teachers teaching methodologies Apply teaching and learning theories in Cooperating Teacher’s Evaluation for Student Teachers practical situations Discussion in seminar Portfolio Evaluate assessment strategies Cooperating Teacher’s Evaluation for Student Teachers Discussion in seminar Develop student activities to foster literacy Field logs and communication skills. Discussion Forum - Blackboard Discussion in seminar Identify strengths, and individualize Field logs instruction for students with disabilities and Discussion Forum - Blackboard 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% 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 teaching 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 pedagogical experiences and issues faced in the concurrent field placement. The class, under the supervision of the instructor, will address these issues and experiences.

In addition to the class discussions initiated from student teaching, the topics outlined in the table below will be examined.

Seminar Topic Assignments Session 1 Overview of Supervised Student -Sign Student Teaching Contract with cooperating Teaching teacher. -Design an activity to collect student information. -Design an introduction letter to students’ parents/guardians. 2 Identify strengths, and -Discuss the variety of disabilities and special individualize instruction for needs that teacher are likely to encounter. students with disabilities and -Prepare lesson plans and activities consistent special needs. 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 -Discuss ways to develop literacy and skills Development. 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. Alternative assessment: learning -Group Activity: Create a learning log to be used 11,12,13,14 logs, portfolio assessment, in a high school mathematics class. performance assessment - Group Activity: Design a lesson plan with a performance assessment.

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-Create (or update) a student teaching portfolio under the guidance of the instructor. 15 Final Class -Submit student teaching portfolio and field logs.

Additional Resources

1. Artzt, A., & Thomas. (2007). Becoming a reflective mathematics teacher, 2nd edition. Routledge.

2. Chappell, M., & Pateracki, T. (2004). Empowering the Beginning Teacher of Mathematics in Middle School. National Council of Teachers of Mathematics.

3. Erickson, T., & Craig, R. (2005). Get it Together: Math Problems for Groups Grades 4-12, 11th Edition. EQUALS/ Lawrence Hall of science.

4. Malloy, C., & Ellis, M. (2008). Mathematics for Every Student: Responding to Diversity in Grades 6-8. National Council of Teacher of Mathematics.

%"! ! !

New York City College of Technology The City University of New York

DEPARTMENT: Mathematics

PREPARED BY: Professor Andrew Douglas, Professor Janet Liou-Mark

COURSE: MEDU 4020

TITLE: Supervised Student Teaching and Seminar in Secondary School Mathematics

DESCRIPTION: The course consists of a field-based, student teaching experience and a seminar component. The field-based experience involves 20 days or 120 hours of supervised student teaching in grades 10 through 12. Under the guidance and supervision of an experienced teacher and a faculty member, students will implement and refine pedagogical strategies, classroom management techniques, and assessment approaches. The seminar component provides a discussion forum for students, guided by a faculty member, to refine pedagogical strategies, and to address and resolve pedagogical issues that students face during the concurrent field placement.

REFERENCE: Brumbaugh, et al. (2006). Teaching Secondary School Mathematics, 3rd Edition. Lawrence Erlbaum Publishers.

CREDITS HOURS: 1class hours, 9 field hours/week, 4 credits

PREREQUISITE: MEDU 3020, and permission of department one semester in advance.

LEARNING OUTCOMES:

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

1. Demonstrate mastery of the 10 through 12 grades secondary 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 secondary school mathematics classroom. 4. Effectively implement formal and informal assessment strategies in a secondary school mathematics classroom.

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INSTRUCTIONAL OBJECTIVES AND ASSESSMENT:

INSTRUCTIONAL OBJECTIVES ASSESSMENT

For the successful completion of this course, Instructional Activity, Evaluation Methods and Criteria students should be able to: Plan and implement curriculum and Supervisor’s Evaluation for Student Teachers instruction 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 Cooperating Teacher’s Evaluation for Student Teachers teaching methodologies Apply teaching and learning theories in Cooperating Teacher’s Evaluation for Student Teachers practical situations Discussion in seminar Portfolio Evaluate assessment strategies Cooperating Teacher’s Evaluation for Student Teachers Discussion in seminar Develop student activities to foster literacy Cooperating Teacher’s Evaluation for Student Teachers and communication skills. Discussion in seminar Portfolio Identify strengths, and individualize Cooperating Teacher’s Evaluation for Student Teachers instruction for students with disabilities and Discussion in seminar special needs. Portfolio

GRADING PROCEDURE:

* 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:

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WEEKLY SEMINAR OUTLINE:

In addition to the class discussions initiated from student teaching, the topics outlined in the table below will be examined.

Seminar Topic Assignments Session 1 Overview of Supervised -Sign Student Teaching Contract with cooperating Student Teaching teacher. -Design an activity to collect student information. -Design an introduction letter to students’ parents/guardians. 2 Identify strengths, and -Discuss the variety of disabilities and special needs individualize instruction for that teacher are likely to encounter. students with disabilities and -Prepare lesson plans and activities consistent with special needs. 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 -Discuss ways to develop literacy and skills Development. 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. Alternative assessment: -Group Activity: Create a learning log to be used in 11,12,13,14 learning logs, portfolio a high school mathematics class.

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assessment, performance - Group Activity: Design a lesson plan with a assessment performance assessment. -Create (or update) a teaching portfolio under the guidance of the instructor. 15 Final Class -Submit student teaching portfolio and field logs.

Additional Resources

1. Artzt, A., & Sultan, A. (2010). The mathematics that every high school teacher should know. New York: Routledge.

2. Chappell, M., Choppin, J. & Salls, J. (2004). Empowering the Beginning Teacher of Mathematics in High School. National Council of Teachers of Mathematics.

3. Malloy, C. (2009). Mathematics for Every Student: Responding to Diversity in Grades 9-12. National Council of Teachers of Mathematics.

4. Posam, et al. (2009). Teaching Secondary Mathematics: Techniques and Enrichment Units, 8th Edition. Allyn and Bacon.

5. Uskin et al. (2002). Mathematics for High School Teachers-An Advanced Prospective. Prentice Hall.

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Appendix B. Course Syllabi for New Math Courses

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New York City College of Technology The City University of New York

DEPARTMENT: Mathematics

PREPARED BY: Professor Victoria Gitman, Professor Yalin Celikler

COURSE: MAT 2070

TITLE: Introduction to Proofs and Logic

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. Schumacher, C. (2000). Chapter zero: fundamental notions of abstract mathematics, 2nd edition. Addison Wesley. 2. Morris, D.W., & Morris, J. 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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INSTRUCTIONAL OBJECTIVES ASSESSMENT

For successful completion of the course, Instructional Activity, Evaluation Methods students should be able to: and Criteria Evaluate truth of statements in Lecture, group work, homework propositional and first-order logic assignments, examinations Reason in accordance with laws of Lecture, group work, homework propositional and first-order logic assignments, examinations Use the axiomatic method in establishing Lecture, group work, homework the truth of mathematical statements assignments, examinations Analyze and prove elementary statements Lecture, group work, homework about group theory, number theory, set assignments, examinations theory, and graph theory View mathematics from the perspective of Lecture, group work, homework its constituent blocks – sets assignments, examinations Construct real numbers and derive their Lecture, group work, homework properties starting from the natural assignments, examinations 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

WEEKLY COURSE OUTLINE:

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 4 Proofs, games, and puzzles methods of proof, examples and counterexamples,

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proving theorems and solving puzzles, existence theorems and uniqueness theorems 5 Proofs, games, and puzzles proofs using induction and continued 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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New York City College of Technology The City University of New York

DEPARTMENT: Mathematics

PREPARED BY: Professor 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: Burton, D.M. (2011). Elementary Number Theory, 7th Ed. McGraw-Hill.

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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INSTRUCTIONAL OBJECTIVES AND ASSESSMENT:

INSTRUCTIONAL OBJECTIVES ASSESSMENT

For successful completion of the course, Instructional Activity, Evaluation students should be able to: Methods and Criteria State the hypothesis and apply basic class discussion, written assignments, class theorems such as the Division algorithm, presentations and in class examinations the Euclidean algorithm, the fundamental theorem of arithmetic, Fermat’s little theorem and Wilson’s theorem. Offer a simple proof of the infinitude of class discussion, written assignments, class primes. presentations and in class examinations Understand the properties of congruences, class discussion, written assignments, class be able to prove simple properties and apply presentations and in class examinations them to solve problems Be able to test conjectures and provide class discussion, written assignments, class proofs in simple cases. presentations and in class examinations

GRADING PROCEDURE:

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

TEACHING/LEARNING METHODS:

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

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WEEKLY COURSE OUTLINE:

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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New York City College of Technology The City University of New York

DEPARTMENT: Mathematics

PREPARED BY: Professors H. Carley, F. Celikler, N. Katz, and 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: Martin, G.E. (1975). The Foundations of Geometry and the Non-Euclidean Plane. Springer, 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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INSTRUCTIONAL OBJECTIVES AND ASSESSMENT:

INSTRUCTIONAL OBJECTIVES ASSESSMENT

For successful completion of the course, Instructional Activity, Evaluation students should be able to: Methods and Criteria state a consistent set of axioms for class discussion, written assignments, class Euclidean geometry and apply them in presentations and in class examinations proofs state the hypotheses and conclusions of class discussion, written assignments, class basic theorems in synthetic Euclidean presentations and in class examinations geometry and apply them in proofs apply the group of rigid transformations of class discussion, written assignments, class the Euclidean plane in proofs presentations and in class examinations use ruler and protractor constructions to class discussion, written assignments, class produce examples in synthetic Euclidean presentations and in class examinations geometry

GRADING PROCEDURE:

• 3 Term Test 45% • Homework, presentations, written assignments 20% and class participation • Final Examination 35%

TEACHING/LEARNING METHODS:

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

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WEEKLY COURSE OUTLINE:

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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New York City College of Technology The City University of New York

DEPARTMENT: Mathematics

PREPARED BY: Professors H. Carley, F. Celikler, N. Katz, 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: Spivak, M. (2008). Calculus 4th Ed. Publish or Perish Press, Houston Texas.

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. 1. 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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INSTRUCTIONAL OBJECTIVES AND ASSESSMENT:

INSTRUCTIONAL OBJECTIVES ASSESSMENT

For successful completion of the course, Instructional Activity, Evaluation students should be able to: Methods and Criteria list limit and order properties of real class discussion, written assignments, class numbers and use those properties to prove presentations and in class examinations 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 class discussion, written assignments, class function presentations and in class examinations formulate the construction of the Reimann class discussion, written assignments, class integral and prove basic facts about its presentations and in class examinations properties. find approximation of functions using class discussion, written assignments, class Taylor polynomials including estimation of presentations and in class examinations error check a sequence of functions for point- class discussion, written assignments, class wise and uniform convergence presentations and in class examinations

GRADING PROCEDURE:

• 3 Term Tests 45% • Homework, presentations, written assignments 20% and class participation • Final Exam 35%

TEACHING/LEARNING METHODS:

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

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WEEKLY COURSE OUTLINE:

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, 10, 11 l'Hôpital's rule 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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New York City College of Technology The City University of New York

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: Gallian, J.A. (2010). Contemporary Abstract Algebra, 7th Ed. Brooks/Cole Cengage Learning.

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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INSTRUCTIONAL OBJECTIVES ASSESSMENT

For successful completion of the course, Instructional Activity, Evaluation Methods and students should be able to: Criteria Define the terms group, ring and field and be Class and Blackboard discussion, Tests, Final able to give examples of each of these kinds of Exam. algebraic structures. Define the concept of a subgroup and Graded Homework, Group Work, Tests, Final determine (prove or disprove), in specific Exam. examples, whether a given subset of a group is a subgroup of the group. Solve problems and prove simple propositions Graded Homework, Group Work, Tests, Exam. involving concepts, terms and theorems of group theory. Compare rings, fields and integral domains. Class and Blackboard Discussion, Graded Homework. Solve problems and prove simple propositions Graded Homework, Group Work, Tests, Exam. involving concepts, terms and theorems of ring theory. Apply the reducibility and the irreducibility Graded Homework, Group Work, Tests, Exam. tests for polynomials. Describe applications and relationships of Graded Homework, Class and Blackboard group theory to geometry discussion, Tests, Exam.

GRADING PROCEDURE:

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

TEACHING/LEARNING METHODS:

• 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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WEEKLY COURSE OUTLINE:

WEEK TOPIC CHAPTERS 1 Preliminaries: Properties of Integers, Modular Arithmetic, 0 Mathematical Induction, Equivalence Relations. 2 Motivation and Introduction: Symmetries of a Square, the Dihedral 1 Group, applications of the Dihedral group (e.g., Designing a Zip code reader) 3 Groups: Definition, Examples, Elementary Properties of Groups. 2 Subgroups: Terminology and Notation, Subgroup Test, Examples. 3 4 Cyclic Groups and Permutation Groups: Definitions and Basic 4,5 Properties. 5 Normal Subgroups: Definitions, examples, applications. 9 Homomorphism: Definitions, examples, properties. 10 6-8 Cosets and Lagrange’s Theorem: Properties of Cosets, Lagrange’s 7 Theorem, the Rotation Group of a Cube. Symmetry Groups: Isometries, Finite Plane Symmetry Groups, Finite 29 Groups of Rotation in R3, the groups of rotation of the platonic solids, the Euclidean Group in R2 and R3 . 9 Introduction to Rings: Definitions and Motivation, Examples of Rings, 12 Properties of Rings, Subrings. 10 Integral Domains: Definition and Examples, Fields. 13 11-13 Polynomial Rings: Notation and Terminology, The Division Algorithm 16 and Consequences. Factorization of Polynomials: Reducibility Tests, Irreducibility Tests, 17 Factorization in Z[x]. 14 Vector Spaces: Definitions and examples of vector spaces, subspaces, 19 linear independence. 15 Final Exam

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New York City College of Technology The City University of New York

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. Katz, V. (2008). History of Mathematics, 3rd edition. Addison Wesley. 2. Dunham, W. (1990). Journey through Genius. Penguin Books.

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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INSTRUCTIONAL OBJECTIVES ASSESSMENT

For successful completion of the course, Instructional Activity, Evaluation students should be able to: Methods and Criteria Trace the development of mathematical Lecture, reading assignments, homework disciplines through history assignments, examinations, term paper Analyze where key mathematical concepts Lecture, reading assignments, homework came from and how they fit together assignments, examinations, term paper Prove key mathematical theorems Lecture, group work, homework assignments, examinations Improve their oral and written Reading assignments, homework communications skills in the context of assignments, examinations, term paper, mathematics. oral presentation Understand how culture and mathematics Lecture, reading assignments, homework influence each other assignments, examinations, term paper Learn about the contributions of female Lecture, reading assignments, homework and non-western mathematicians assignments, examinations, term paper

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

TEACHING/LEARNING METHODS: • Lecture and guided discussion • Student presentations • Use of online resources • Writing intensive assignments

WEEKLY COURSE OUTLINE:

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 decimal arithmetic, al- Midterm Khwarizmi’s algebra, algebra of polynomials (negative exponents), induction 7 Medieval Europe and Fibonacci numbers, Renaissance 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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New York City College of Technology The City University of New York

DEPARTMENT: Mathematics

PREPARED BY: Professors Holly Carley, Firat Celikler, 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. Hahn, L.S. (1994). Complex numbers and geometry. The Mathematical Association of America. 2. Martin, G.E. (1975). The Foundations of Geometry and the Non-Euclidean Plane. Springer, 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 M!bius transformations to the complex plane. 3. Students will be familiar with basic properties of hyperbolic geometry and the Poincaré disc.

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INSTRUCTIONAL OBJECTIVES AND ASSESSMENT:

INSTRUCTIONAL OBJECTIVES ASSESSMENT

For successful completion of the course, Instructional Activity, Evaluation students should be able to: Methods and Criteria state the hypotheses and conclusions of the class discussion, written assignments, class Ptlolemy-Euler, Clifford, Simson's, Cantor, presentations and in class examinations Feuerbach, and Morley theorems and apply them in proofs make geometric proofs using analytic class discussion, written assignments, class techniques presentations and in class examinations apply stereographic projection and M!bius class discussion, written assignments, class transformations to figures in the plane presentations and in class examinations compare and contrast non-Euclidean class discussion, written assignments, class geometry with the Euclidean plane presentations and in class examinations

GRADING PROCEDURE:

• 3 Term Test 45% • Homework, presentations, written assignments 20% and class participation • Final Examination 35%

TEACHING/LEARNING METHODS:

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

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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 1.6—1.8 of the complex plane 3 roots of unity and complex exponentiation, triangles in the 1.9—1.10, complex plane 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 M!bius transformations 3.1, 3.2 9 cross ratios and symmetry under M!bius transformations 3.3, 3.4 10 circles under M!bius transformations 3.5, 3.6 11 classification of M!bius 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 Program Scheduling

• Indicate academic calendar type: _X_Semester __Quarter __Trimester __Other (describe) • Label each term in sequence, consistent with the institution’s academic calendar (e.g., Fall 1, Spring 1, Fall 2) • Use the table to show how a typical student may progress through the program; copy/expand the table as needed. Term: Fall 1 Check course classification(s) Term: Spring 1 Check course classification(s) LA Course Number & Title Cr S Maj New Prerequisite(s) Course Number & Title Cr LAS Maj New Prerequisite(s) MAT 1475 Calculus I MAT 1375, or a MAT 1575 Calculus II 4 X X MAT 1475 score of at least 65 on the Algebra part, 50 on the 4 X X College Algebra part, and 36 on the Trigonometry part of the CUNY Math Placement Test SPE 1330 Effective Speaking CUNY ENG 1121 English Composition II 3 X X ENG 1101 3 X X proficiency reading/writing ENG 1101 English Composition I CUNY PSY 2501 Child and Adolescent 3 X X PSY 1101 3 X X proficiency Development reading/writing PSY 1101 Intro. to Psychology CUNY Mathematical Applications Elective 3 3 X X proficiency reading/writing MAT 1476L Calculus Laboratory MEDU 2901 Peer Leader Training in 1 X MAT 1275 or Coreq: Mathematics higher, ENG 1 X X MAT1475 or 1101, and MAT 1575 department permission MAT 2580 Intro. to Linear Algebra 3 X X Term credit total: 14 14 15 Term credit total: 17 13 13 Term: Fall 2 Check course classification(s) Term: Spring 2 Check course classification(s) LA Course Number & Title Cr S Maj New Prerequisite(s) Course Number & Title Cr LAS Maj New Prerequisite(s) MAT 2675 Calculus III 4 X X MAT 1575 MAT 2630 Applied Mathematics 3 X X MAT 1575, Technology MAT 2580 MAT 2070 Intro. to Proofs and Logic 3 X X X MAT 1575 MAT 3075 Intro. to Real Analysis 4 X X X MAT 1575, MAT 2070

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MEDU 1010 Foundations of Mathematics 3 X X CUNY MEDU 1020 Teaching and Learning 2 X X MAT 1375, Education proficiency Strategies for Math. Teachers CUNY proficiency Science Elective 4-5 X Science Elective 4-5 X

Term credit total: 14- 11- 10 Term credit total: 13- 11- 9 15 12 14 12 Term: Fall 3 Check course classification(s) Term: Spring 3 Check course classification(s) Course Number & Title LA Course Number & Title Cr S Maj New Prerequisite(s) Cr LAS Maj New Prerequisite(s) MAT 2572 Probability and Mathematical MAT 3080 Modern Algebra 3 X X X MAT 2580, 4 X X MAT 1575 Statistics I MAT 3075 MAT 3020 Number Theory MAT 3050 Geometry I 3 X X X MAT 2070, 3 X X X MAT 2070 MAT 3080 (coreq) MEDU 3010 Methods of Teaching Middle MEDU 2010, MEDU 3020 Methods of Teaching 3 X X MEDU 3010 3 X X School Mathematics ENG 1121 Secondary School Mathematics MEDU 2010 Pedagogy of Mathematic MEDU 1020, EDU 2455 Methods and Materials for 3 X None 2 X X Applications and Technology MAT 1475 Special Needs Students Literature Elective MEDU 3030 Assessment Techniques in 2 X X MEDU 3010 3 X Mathematics

Term credit total: 15 10 12 Term credit total: 14 6 14 Term: Fall 4 Check course classification(s) Term: Spring 4 Check course classification(s) LA Course Number & Title Cr S Maj New Prerequisite(s) Course Number & Title Cr LAS Maj New Prerequisite(s) MAT 4050 Geometry II 3 X X X MAT 3050, MAT 4030 History of Mathematics 3 X X X MAT 2070, MAT 3080 MAT 3020 MEDU 4010 Supervised Student Teaching 4 X X MEDU 3010 and MEDU 4020 Supervised Student 4 X X MEDU 3020 and Seminar in Middle School Mathematics permission of Teaching and Seminar in Secondary and permission dept. School Mathematics of dept. EDU 4600 Professional Development 2 X MEDU 3010, PSY 3502 Human Learning and 3 X X ENG 1101, Seminar MEDU 4010 Instruction PSY 1101 (coreq) Mathematical Applications Elective 3 Literature /Aesthetics/Philosophy 3 X Elective Literature/Aesthetics/Philosophy Elective 3 X Mathematical Applications Elective 3-5 (Choose 3-5 credits to make overall total 120)

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Term credit total: 15 6 9 Term credit total: 16- 9 10 18

Program Totals: Credits: 120 Liberal Arts & Sciences: 80-82 Major: 92 Elective & Other: 9-11

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Appendix D Full-Time Faculty Teaching Assignments

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Faculty teaching at the graduate level must have an earned doctorate/terminal degree or demonstrate special competence in the field. Provide information on faculty members who are full-time at the institution and who will be teaching each course in the major field or graduate program. The application addendum for professional licensure, teacher certification, or educational leadership certification programs may provide additional directions for those types of proposals.

Faculty Member Name Percent Highest and Other Applicable Earned Additional Qualifications: list related certifications/ licenses; and Title (include and Program Courses to be Taught Time to Degrees & Disciplines (include occupational experience; scholarly contributions, etc. identify Program Director) Program College/University)

Professor Andrew Douglas MAT 3080 Modern Algebra Ph.D., Mathematics, University of Toronto Licensed to teach in the province of Ontario, Canada MAT 3020 Number Theory (Ontario Certified Teacher, Registration #426674). MAT 3050 Geometry I M.Ed., Education, Lakehead University B.Ed., Education, Lahehead University Published numerous articles in top journals in the fields of MAT 4050 Geometry II M.A., Mathematics, York University mathematical physics, and mathematics. MEDU 1010 Foundations of Mathematics B.Sc., Mathematics, University of Toronto Education Co-Director of the Center for Logic, Algebra and Computation. MEDU 3010 Methods of Teaching Middle School Mathematics 40% Has given numerous talks at the regional, national and international MEDU 3030 Methods of Teaching level in mathematics, and mathematics education. Secondary School Mathematics MEDU 4010 Supervised Student Teaching His master’s thesis in education focused on the relationship among and Seminar in Middle School Mathematics math anxiety, math self-confidence and mathematics performance in a study including over 300 high school students in Northwestern Ontario. MEDU 4020 Supervised Student Teaching

and Seminar in Secondary School Co-developed mathematics curriculum for the New Community Mathematics College, CUNY. Professor Janet Liou-Mark MEDU 2901 Peer Leader Training in Ph.D., Education, New York University Director of the Honors Scholars Program at New York City College of Mathematics Technology (2004-present) MEDU 1010 Foundations of Mathematics B.A., New York University Education National Society of Collegiate Scholars (NSCS) Charter and Faculty MEDU 3010 Methods of Teaching Middle Advisor (2002-present) School Mathematics Peer-Led Team Learning (PLTL) Workshop Coordinator for MEDU 3030 Methods of Teaching Mathematics and Science (2006-present) Secondary School Mathematics 30% MEDU 4010 Supervised Student Teaching Teaching Portfolio Workshop Coordinator and Facilitator and Seminar in Middle School Mathematics (2002-present) MEDU 4020 Supervised Student Teaching and Seminar in Secondary School City Tech Women and Science, Technology, Engineering, and Mathematics Mathematics Faculty Advisor (2007-present)

City Tech’s Black Male Initiative Task Force Member (2006-present)

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Professor Johanna Ellner MEDU 3030 Assessment Techniques in Ed.D., Education, Nova University Mathematics MEDU 3010 Methods of Teaching M.A., B.A., Brooklyn College 10% Middle School Mathematics MEDU 3030 Methods of Teaching Secondary School Mathematics Professor Holly Carley MAT 3075 Introduction to Real Ph.D., Mathematics, University of Virginia Analysis MAT 3050 Geometry I 10% M.S., B.S., University of Central Florida MAT 4050 Geometry II Professor Victoria Gitman MAT 2070 Introduction to Proofs and Ph.D., Mathematics, CUNY Graduate Numerous publications in the fields of logic and set theory. Logic Center 10% MAT 4030 History of Mathematics B.S., Brooklyn College Professor Delaram Kahrobaei MAT 3080 Modern Algebra Ph.D., Mathematics, CUNY Graduate Numerous publications in the areas of pure mathematics, applied Center mathematics, and computer science. MAT 2070 Introduction to Proofs and Logic M.S., City College Co-founder of New York Women in Mathematics. MAT 3020 Number Theory 10% M.S., Claremont University MAT 4030 History of Mathematics B.Sc., Sharif University Director of the Center for Logic, Algebra and Computation.

Has given numerous talks at the regional, national and international level. Satyanand Singh, Lecturer MAT 3020 Number Theory M.A., B.S., City College Co-authored the text: Visualizing Calculus by way of Maple, 10% which is published by McGraw Hill publishers and will be available in May 2011. Professor Estela Rojas MEDU 3030 Assessment Techniques in Ed.D., M.A., Education, Teachers College Director of the Learning Communities Program at NYCCT. Mathematics Columbia University MEDU 1010 Foundations of Past PI of a large NSF educational grant supporting Learning Mathematics Education B.A., State Technical University of Chile Communities at NYCCT. MEDU 3010 Methods of Teaching Middle School Mathematics Runs annual, one-week long pedagogical training workshops for faculty at City Tech. MEDU 3030 Methods of Teaching 30% Secondary School Mathematics Has given a plethora of mathematics education talks at the regional, MEDU 4010 Supervised Student national and international levels. Teaching and Seminar in Middle School Mathematics MEDU 4020 Supervised Student Teaching and Seminar in Secondary School Mathematics

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Professor Jonas Reitz MEDU 3010 Methods of Teaching Ph.D., Mathematics, CUNY Graduate Several publications in the fields of logic and set theory. Middle School Mathematics Center 10% MEDU 3030 Methods of Teaching Co-developed mathematics curriculum for the New Community Secondary School Mathematics B.A., University of California at Santa Cruz College, CUNY. Professor Neil Katz MAT 3050 Geometry I Ph.D., Mathematics, SUNY Stony Brook Has prestigious mathematical publications. MAT 3050 Geometry II 10% MAT 3075 Introduction to Real B.Sc., University of Toronto Analysis Professor Peter Deraney MEDU 1020 Teaching and Learning M.A., Mathematics, University of Michigan Co-director of the remedial mathematics program at NYCCT. Strategies for Mathematics Teachers MEDU 2010 Pedagogy of Mathematics Has well over 30 years of teaching experience. Applications and Technology Taught high school in Connecticut for one year. MEDU 4010 Supervised Student 10% Teaching and Seminar in Middle School Has taken graduate courses in mathematic and mathematics Mathematics education at New York University. MEDU 4020 Supervised Student Teaching and Seminar in Secondary School Mathematics Professor Arnavaz MEDU 1020 Teaching and Learning Ph.D., Mathematics, Michigan State Has several mathematics education publications, including co- Taraporavala Strategies for Mathematics Teachers University authoring the text: Visualizing Calculus by way of Maple, which MEDU 2010 Pedagogy of Mathematics is published by McGraw Hill publishers and will be available in Applications and Technology 10% M.Stat., Indian Statistical Institute New May 2011. Delhi B.S. Delhi University Has given numerous mathematics and mathematics education talks. Professor Arthur Kramer MEDU 1010 Foundations of Ph.D., Math Education, New York Authored four applied math textbooks including “Math for Mathematics Education University Electricity and Electronics,” published by Delmar Cengage Learning, 2005. M.A., Columbia University 10% B.M.E., Cooper Union Has well over 30 years of teaching experience.

Designed and taught courses at the New School in Historical and Cultural Mathematics and Techniques of Problem Solving.

"#! ! !

Appendix E Faculty to be Hired

If faculty must be hired, specify the number and title of new positions to be established and minimum qualifications. Title/Rank of No. of New Minimum Qualifications (including degree F/T or Percent Time Expected Course Expected Position Positions and discipline area) P/T to Program Assignments Hiring Date Assistant 2 Either a doctorate in mathematics education F/T 80% Any course with an MEDU 2014, 2016 Professor with a master’s in mathematics; or a doctorate designation, and MAT in mathematics with a master’s in education or courses at least up to and other significant formal pedagogical training. including MAT 2580. Experience teaching at the middle school or high school level is desired.

"#! ! ! Appendix F New Resources

Expenditures Year 1 Year 2 Year 3 Year 4 Year 5 Full Time Faculty 0 0 76,629.28 79,278.64 158,960.27 Part Time Faculty 3,639.74 15,143.04 0 0 0

Full Time Staff 0 0 0 0 Part Time Staff 0 0 0 0 0 Library (Includes 1800 0 0 0 0 Staffing) Equipment 0 0 0 0 0 Laboratories 0 0 0 0 0 Supplies and 2000 2000 1000 1000 1000 Expenses (Other than Personal Services) Capital 0 0 0 0 0 Expenditures Other 0 0 0 0 0 Total all 7,439.74 17,143.04 77,629.28 80,278.64 159,960.27

[1] Specify the inflation rate used for projections. [2] Specify the academic year [3] Include fridge benefits

""! ! !

Appendix G Projected Revenue

1st Year 2nd Year 3rd Year 4th Year 5th Year Revenues1 Academic Academic Academic Academic Academic Year2 Year2 Year2 Year2 Year2

Tuition Revenue3 $0 $65,392 $159,899 $276,800 $387,857 01. From Existing Sources4 02. From New Sources5 $108,900 $197,523 $289,647 $385,378 $432,540 03. Total $108,900 $262,915 $449,546 $662,178 $820,397 State Revenue6 $0 $0 $0 $0 $0 04. From Existing Sources4 $0 $0 $0 $0 $0 05. From New Sources5 $0 $0 $0 $0 $0 06. Total Other Revenue7 $0 $0 $0 $0 $0 07. From Existing Sources4 $0 $0 $0 $0 $0 08. From New Sources5 $0 $0 $0 $0 $0 09. Total Grand Total8 $0 $73,455 $178,174 $310,817 $446,796 10. From Existing Sources4 $108,900 $197,523 $289,647 $385,378 $432,540 11. From New Sources5 $108,900 $262,915 $449,546 $662,178 $820,397 TOTAL

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 1 Specify the inflation rate used for projections. 2 Specify the academic year. 3 Please explain how tuition revenue was calculated. 4 Existing sources means revenue that would have been received by the institution even if the proposed program were not approved. 5 New sources means revenue engendered by the proposed program. The revenue from new sources from the previous year should be carried over to the following year as revenues from new sources with adjustments for inflation, if a continuing source of revenue. 6 Public institutions should include here regular State appropriations applied to the program. Independent institutions should estimate Bundy aid generated by degrees awarded in the program. 7 Specify what is included in "other" category. 8 Enter total of Tuition, State and Other Revenue, from Existing or New Sources.

"#! ! !

Appendix H Supporting Material for Projected Revenue

"$! ! !

The Five-Year Revenue Projections for Program SENIOR COLLEGE WORKSHEET

Year Year Year Year Year One Two Three Four Five Tuition & Fees: Existing Students are students currently enrolled in another program at your college, or students who would have enrolled in another program at your college, had the new program not been established. Number of Majors (Enter # of EXISTING FULL TIME In State Students) 0 12 28 47 64 Tuition Income (Specify Rate per credit) calculates 2% increase per year $4,830 $4,927 $5,025 $5,126 $5,228 Total Tuition $0 $59,119 $140,704 $240,905 $334,601 Student Fees (enter ANNUAL program fees other than standard CUNY fees) Total Fees 0 0 0 0 0 Total Instate Tuition & Fees $0 $59,119 $140,704 $240,905 $334,601

Tuition & Fees: Number of Majors (Enter # of EXISTING FULL TIME Out of State Students) 0 0 0 0 0 Tuition Income (Specify Rate per credit) calculates 2% increase per year $13,050 $13,311 $13,577 $13,849 $14,126 Total Tuition $0 $0 $0 $0 $0 Student Fees (enter ANNUAL program fees other than standard CUNY fees) Total Fees 0 0 0 0 0 Total Out of State Tuition & Fees $0 $0 $0 $0 $0

TOTAL EXISTING FULL TIME TUITION REVENUE $0 $59,119 $140,704 $240,905 $334,601

#%! ! !

Year One Year Two Year Three Year Four Year Five Tuition & Fees: Number of Majors (Enter # of EXISTING PART-TIME In State Students) 0 2 6 11 16 Total Enrolled Credits (Enter Avg # credits per student per year-Fall+ Spring+Summer) i.e. 6 Fall, 6 Spring, 3 Summer=15 15 15 15 15 15 Tuition Income (Specify Rate per credit) calculates 2% increase per year $205 $209 $213 $218 $222 Total Tuition $0 $6,273 $19,195 $35,895 $53,256 Student Fees (enter ANNUAL program fees other than standard CUNY fees) Total Fees 0 Total Instate Tuition & Fees $0 $6,273 $19,195 $35,895 $53,256

Tuition & Fees: Number of Majors (Enter # of EXISTING PART-TIME Out of State Students) 0 0 0 0 0 Total Enrolled Credits (Enter Avg # credits per student per year-Fall+ Spring+Summer) i.e. 6 Fall, 6 Spring, 3 Summer=15 Tuition Income (Specify Rate per credit) calculates 2% increase per year $435 $444 $453 $462 $471 Total Tuition $0 $0 $0 $0 $0 Student Fees (enter ANNUAL program fees other than standard CUNY fees) Total Fees 0 Total Out of State Tuition & Fees $0 $0 $0 $0 $0

TOTAL EXISTING PART TIME REVENUE $0 $6,273 $19,195 $35,895 $53,256

TOTAL EXISTING REVENUE (LINKS TO REVENUE SPREADSHEET ROW 5) $0 $65,392 $159,899 $276,800 $387,857

#&! ! !

Year One Year Two Year Three Year Four Year Five Tuition & Fees: New Students are students who would NOT have enrolled in another program at your college, had the new program not been established. Number of Majors (Enter # of NEW FULL TIME In State Students) 20 35 50 65 70 Tuition Income (Specify Rate per credit) calculates 2% increase per year $4,830 $4,927 $5,025 $5,126 $5,228 Total Tuition $96,600 $172,431 $251,257 $333,166 $365,970 Student Fees (enter ANNUAL program fees other than standard CUNY fees) Total Fees 0 0 0 0 0 Total Instate Tuition & Fees $96,600 $172,431 $251,257 $333,166 $365,970

Tuition & Fees: Number of Majors (Enter # of NEW FULL TIME Out of State Students) 0 0 0 0 0 Tuition Income (Specify Rate per credit) calculates 2% increase per year $13,050 $13,311 $13,577 $13,849 $14,126 Total Tuition $0 $0 $0 $0 $0 Student Fees (enter ANNUAL program fees other than standard CUNY fees) Total Fees 0 0 0 0 0 Total Out of State Tuition & Fees $0 $0 $0 $0 $0

TOTAL NEW FULL TIME TUITION REVENUE $96,600 $172,431 $251,257 $333,166 $365,970

#'! ! !

Year One Year Two Year Three Year Four Year Five Tuition & Fees: Number of Majors (Enter # of NEW PART-TIME In State Students) 4 8 12 16 20 Total Enrolled Credits (Enter Avg # credits per student per year-Fall+ Spring+Summer) i.e. 6 Fall, 6 Spring, 3 Summer=15 15 15 15 15 15 Tuition Income (Specify Rate per credit) calculates 2% increase per year $205 $209 $213 $218 $222 Total Tuition $12,300 $25,092 $38,391 $52,211 $66,570 Student Fees (enter ANNUAL program fees other than standard CUNY fees) Total Fees 0 Total Instate Tuition & Fees $12,300 $25,092 $38,391 $52,211 $66,570

Tuition & Fees: Number of Majors (Enter # of NEW PART-TIME Out of State Students) 0 0 0 0 0 Total Enrolled Credits (Enter Avg # credits per student per year-Fall+ Spring+Summer) i.e. 6 Fall, 6 Spring, 3 Summer=15 Tuition Income (Specify Rate per credit) calculates 2% increase per year $435 $444 $453 $462 $471 Total Tuition $0 $0 $0 $0 $0 Student Fees (enter ANNUAL program fees other than standard CUNY fees) Total Fees 0 0 0 0 0 Total Out of State Tuition & Fees $0 $0 $0 $0 $0

TOTAL NEW PART TIME REVENUE $12,300 $25,092 $38,391 $52,211 $66,570

TOTAL NEW REVENUE (LINKS TO REVENUE SPREADSHEET ROW 7) $108,900 $197,523 $289,647 $385,378 $432,540

#(! ! !

Year Year Year Year Year One Two Three Four Five State Revenue from EXISTING sources- identify sources 0 0 0 0 0

STATE BUDGET APPROPRIATIONS FROM EXISTING SOURCES -LINKS TO REVENUE SPREADSHEET ROW 9 $0 $0 $0 $0 $0

State Revenue from NEW sources-identify sources 0 0 0 0 0

STATE BUDGET APPROPRIATIONS FROM NEW SOURCES -LINKS TO REVENUE SPREADSHEET ROW 11 $0 $0 $0 $0 $0

FOR YEARS 2-5 INCLUDE CONTINUING RESOURCES FROM PREVIOUS YEARS

Year Year Year Year Year One Two Three Four Five Other Revenue From Existing Sources (specify and explain)-LINKS TO REVENUE SPREADSHEET ROW 13) 0 0 0 0 Other Revenue New (specify and explain) (LINKS TO REVENUE SPREADSHEET ROW 15) 0 0 0 0

#)! ! !

Appendix I Five-Year Financial Projections

Year 1 Year 2 Year 3 Year 4 Year 5 Current Full Time Faculty Replacement Costs (list separately) Current Full time Faculty Overload (include Summer) New Full Time Faculty Base Salary (list separately) 0 0 $57,616 $59,608 1 @ $61,903 1 @ $57,616 New Full Time Faculty Overload (include Summer) New Faulty Re-assigned Time (list separately) Full Time Employee Fringe Benefits (33%) 0 0 $19,013.28 $19,670.64 $39,441.27 Total (Links to Full-Time Faculty on Program Exp 0 0 $76,629.28 $79,278.64 $158,960.27 Worksheet)

Part Time Faculty Actual Salaries $3,308.85 $13,766.4 0 0 0 (3 credits) (12 credits) Part Time Faculty Actual Fringe Benefits (10%) $330.89 $1,376.64 Total (Links to Part-Time Faculty Program Exp Worksheet) $3,639.74 $15,143.04 0 0 0

Full Time Staff Base Salary (list separately) Full Time Staff Fringe Benefits (33%) Total (Links to Full Time Staff on Program Exp Worksheet) 0 0 0 0 0

Part Time Staff Base Salary (list separately) Graduate Assistants Student Hourly Part Time Employee Fringe Benefits (10%) Total (Links to Part Time Staff on Program Exp Worksheet) 0 0 0 0 0

LIBRARY Library Resources 1800 0 0 0 0 Library Staff Full Time (list separately) Full Time Staff Fringe Benefits (33%) Library Staff Part Time (List Separately) Part Time Employee Fringe Benefits (10%) Total (Links to Library on Program Exp Worksheet) 1800 0 0 0 0

EQUIPEMENT Computer Hardwar Office Furniture Other (Specify) Total (Links to Equipment on Program Exp Worksheet) 0 0 0 0 0

LABORATORIES Laboratory Equipment Other (list separately) Total (Links to Laboratories on Program Exp Worksheet) 0 0 0 0 0

#*! ! !

SUPPLIES AND EXPENSES (OTPS) Consultants and Honoraria Office Supplies 500 500 500 500 500 Instructional Supplies 1500 1500 500 500 500 Faculty Development Travel and Conferences Membership Fees Advertising and Promotion Accreditation Computer Software Computer License Fees Computer Repair and Maintenance Equipment Repair and Maintenance New Total Supplies and OTPS Expenses (Link to Supplies on 2000 2000 1000 1000 1000 Program Exp Worksheet)

CAPITAL EXPENDITURES Facility Renovations Classroom Equipment Other (list separately) TOTAL (Links to Capital Expenditures on Program Exp 0 0 0 0 0 Worksheet)

Other (list separately) TOTAL (Links to Other on Program Exp Worksheet) 0 0 0 0 0

#+! ! !

Appendix J. Articulation Agreements: Bronx Community College, Borough of Manhattan Community College

#"! ! !

ARTICULATION AGREEMENT FORM

College of Agreement Initiation: New York City College of Technology

SENDING AND RECEIVING INSTITUTIONS

Sending College: Bronx Community College Department: Mathematics and Computer Science Program: Mathematics Degree: Associate in Science

Receiving College: New York City College of Technology Department: Mathematics Program: Mathematics Education Degree: Bachelor of Science

______

PROGRAM DESCRIPTION FOR THE BACHELOR OF SCIENCE IN MATHEMATICS EDUCATION

The Bachelor of Science in Mathematics Education at New York City College of Technology will prepare students to teach middle school and secondary school mathematics (grades 7 to 12) in New York State. The program includes an intensive course of study in mathematics and mathematics pedagogy. The program also includes a mathematical application component. In this component, students take electives from among the following areas: Architecture, Electrical Engineering Technology, Computer Systems, Applied Mathematics and Physics. These electives provide teacher candidates with a deeper understanding of the application and importance of mathematics.

ADMISSION REQUIREMENTS FOR SENIOR COLLEGE PROGRAM

• 2.5 overall GPA • Interview by Faculty of Mathematics Department of NYCCT • Essay submission

Total transfer credits granted toward the baccalaureate degree: 60

Total additional credits required at the senior college to complete baccalaureate degree: 60

##! ! !

COURSE-TO-COURSE EQUIVALENCIES AND TRANSFER CREDIT AWARDED

New York City College of Technology Equivalent Credit Bronx Community College (Or Other Evaluation) Granted Course & Title Cr. Course & Title Cr. Core Requirements ENG 11 Composition and Rhetoric I OR 3 ENG 1101 English Composition I 3 3 ENG 10 Fundamentals of Composition and Rhetoric CMS 11 Fundamentals of Interpersonal 3 Communications 3 3 Communications HIS 10 History of the Modern World, or HIS 11 3 Literature 3 3 Introduction to the Modern World MTH 31 Calculus and Analytic Geometry I 4 MAT 1475 Calculus I 4 4 Choose one of the following sequences: 8 8- 8 10 PHY 31 Physics I PHYS 1441 Physics 1.3 (5 Cr.) PHY 32 Physics II, OR PHYS 1443 Physics 2.3 (5 Cr.), OR

CHM 11 General College Chemistry I CHEM 1110 Chemistry I (4 Cr.) CHM 12 General College Chemistry II, OR CHEM 1210 Chemistry II (4 Cr.), OR

BIO 11 General Biology I BIO 1101 Biology I (4 Cr.) BIO 12 General Biology II BIO 1201 Biology II (4 Cr.) SUBTOTAL 21 Required Areas of Study ENG 12 Composition and Rhetoric II 3 ENG 1121 English Composition II 3 3 ART 11 Introduction to Art OR 3 Literature/Aesthetics/Philosophy 3 3 MUS 11 Introduction to Music PSY 11 Psychology 3 PSY 1101 Introduction to Psychology 3 3 SUBTOTAL 9 Specialization Requirements MTH 32 Analytic Geometry and Calculus II 5 MAT 1575 Calculus II+MAT 1476L 5 5 MTH 33 Analytic Geometry and Calculus III 5 MAT 2675 Calculus III+1 Cr math applications elective 5 5 MTH 42 Linear Algebra (4 Cr), 12 MAT 2580 Linear Algebra (3 Cr), MTH 46 Abstract Algebra (4 Cr), and MAT 2070 Introduction to Proof and Logic MTH 34 Differential Equation and Selected (3 Cr), 12 Topics in Advanced Calculus (4 Cr) MAT 2680 Differential Equations (3 Cr), and MAT 3080 Modern Algebra (3 Cr) 12 SUBTOTAL 22 Free Electives MTH 48 Advanced Calculus 4 MAT 3075 Introduction to Analysis 4 4 PHY 33 Physics III OR 4 PHY 2443 Physics 3.3 OR 4 4 AST 11 Stellar Astronomy PHY 1117 Astronomy I SUBTOTAL 8 TOTAL 60

#$! ! !

SENIOR COLLEGE COURSES REMAINING FOR BACCALAUREATE DEGREE

The courses are arranged into four components: The Mathematics Component, Pedagogy Component, Liberal Arts and Science Core Component, and the Mathematical Applications Component.

Mathematics Component

Course and Title Credits MAT 2630 Applied Mathematics Technology 3 MAT 3020 Number Theory 3 MAT 2572 Probability and Statistics I 4 MAT 3050 Geometry I 3 MAT 4050 Geometry II 3 MAT 4030 History of Mathematics 3 Component Subtotal 19

Pedagogy Component

Course and Title Credits MEDU 2901 Peer Leader Training in Mathematics 1 MEDU 1010 Foundations of Mathematics Education 3 MEDU 1020 Teaching and Learning Strategies for Mathematics Teachers 2 MEDU 2010 Pedagogy of Mathematics Applications and Technology 2 MEDU 3010 Methods of Teaching Middle School Mathematics 3 MEDU 3020 Methods of Teaching Secondary School Mathematics 3 MEDU 3030 Assessment Techniques in Mathematics 2 MEDU 4010 Supervised Student Teaching and Seminar in Middle School 4 Mathematics MEDU 4020 Supervised Student Teaching and Seminar in Middle School 4 Mathematics EDU 2455 Methods and Materials for Special Needs Students 3 EDU 4600 Professional Development Seminar 2 Component Subtotal 29

Mathematical Applications Component

Course and Title Credits CST 1101 Intro Programming 3 Component Subtotal 3

$%! ! !

Liberal Arts and Science Core Component

Course and Title Credits PSY 2501 Child and Adolescent Development 3 PSY 3502 Human Learning and Instruction 3 One additional course from: 3 Literature: any ENG 2000/3400 series, AFR, PRS 2200 series or Philosophy: any PHIL 2000 series or higher, AFR 2600 series. Component Subtotal 9

Summary of Remaining Courses

Component Credits Mathematics 19 Pedagogy 29 Liberal Arts and Science Core 9 Mathematical Applications 3 Total 60

Procedures for reviewing, up-dating, modifying or terminating agreement

Both colleges will confer every three years to review the agreement. Any changes or modifications to program requirements will be reported to the other college subsequent to the date of the change or modification. The agreement will then be updated accordingly. Given notification, both colleges have the right to terminate the agreement at any time.

Procedures for evaluating agreement, e.g., tracking the number of students who transfer under the articulation agreement and their success:

Verification of data from sources such as: Admissions office, Assessment & Institutional Research, Transfer Office and/or Enrollment Management will be used to follow students’ progress.

Sending and receiving college procedure for publicizing agreement, e.g., college catalogs, transfer advisers, Websites, etc.:

Notice of articulation will be placed in the respective catalogs, recruiting brochures, websites, and on CUNY’s TIPPS website. Respective transfer advisors will be informed and provided with copies of the agreement.

$&! ! !

Effective Date: Spring 2012

______Dr. Bonne August Dr. George L. Sanchez Provost Vice President for Academic Affairs New York City College of Technology Bronx Community College

______Dr. Henry Africk Dr. Andrew McInerney Chair, Department of Mathematics Chair, Department of Mathematics and New York City College of Technology Computer Science Bronx Community College

$'! ! !

ARTICULATION AGREEMENT FORM

College of Agreement Initiation: New York City College of Technology

SENDING AND RECEIVING INSTITUTIONS

Sending College: Borough of Manhattan Community College Department: Mathematics Program: Mathematics Degree: Associate in Science

Receiving College: New York City College of Technology Department: Mathematics Program: Mathematics Education Degree: Bachelor of Science ______

ADMISSION REQUIREMENTS FOR SENIOR COLLEGE PROGRAM

• 2.5 overall GPA • Interview by Faculty of Mathematics Department of NYCCT • Essay submission

Total transfer credits granted toward the baccalaureate degree: 60

Total additional credits required at the senior college to complete baccalaureate degree: 60

$(! ! !

COURSES TRANSFERRED FROM BOROUGH OF MANHATTAN COMMUNITY COLLEGE

Students transferring from BMCC with an Associate’s Degree in Mathematics shall enter the Bachelor of Science in Mathematics Education program at NYCCT as juniors. They will have the following courses transferred to NYCCT. COURSE-TO-COURSE EQUIVALENCIES AND TRANSFER CREDIT AWARDED

Borough of Manhattan Community College New York City College of Technology Course and Title Credits Credits Granted ENG 101 English Composition I 3 ENG 1101 English Composition I 3 ENG 201 English Composition II 3 ENG 1121 English CompositionII 3 SPE 100 Fundamentals of Speech 3 SPE 1330 Effective Speaking 3 Choose one of the three sequences 8 General Education Science, SCI 8 (all courses are 4 Cr.): 1A and 2A

PHY 215 University Physics I, and PHY 225 University Physics II OR CHE 201 Chemistry I CHE 202 Chemistry II OR BIO 210 Biology I BIO 220 Biology II PSY 100 General Psychology 3 PSY 1101 General Psychology 3 PSY 240 Developmental Psychology 3 PSY 2501 Child and Adolescent 3 Psychology HED 100 Health Education (2 Cr.), 10-12 General Education Core Courses 10-12 Modern Foreign Language (6-8 Cr.), and Music/Art (2 Cr.) MAT 320 Abstract Algebra (3) 3 MAT 3080 Modern Algebra (3) 3 MAT 301 Analytic Geometry and 4 MAT 1475 Calculus I 4 Calculus I MAT 302 Analytic Geometry and 4 MAT 1575 Calculus II 4 Calculus II MAT 303 Analytic Geometry and 4 MAT 2675 Calculus III 4 Calculus III MAT 315 Linear Algebra 3 MAT 2580 Linear Algebra 3 MAT 505 History of Mathematics 3 MAT 4030 History of 3 Mathematics MAT 200 Introduction to Discrete 6-8 MAT 1476L (1) + Mathematical 6-8 Mathematics (4) OR Applications Electives (5-7) MAT 501 Ordinary Differential Equations (3) OR MAT 470 Mathematical Foundations of Computer Networking (4) TOTAL 60

Students that transfer to NYCCT after earning the AS in Mathematics at BMCC by completing the 60 credits shown, will be required to satisfactorily complete the following 60 credits at NYCCT in order to earn the BS in Mathematics Education.

$)! ! !

SENIOR COLLEGE COURSES REMAINING FOR BACCALAUREATE DEGREE

Course and Title Credits MAT 2070 Introduction to Proofs and Logic 3 MAT 2630 Applied Mathematics Technology 3 MAT 3020 Number Theory 3 MAT 2572 Probability and Statistics I 4 MAT 3050 Geometry I 3 MAT 3075 Introduction to Real Analysis 4 MAT 4050 Geometry II 3

MEDU 2901 Peer Leader Training in Mathematics 1 MEDU 1010 Foundations of Mathematics Education 3 MEDU 1020 Teaching and Learning Strategies for Mathematics Teachers 2 MEDU 2010 Pedagogy of Mathematics Applications and Technology 2 MEDU 3010 Methods of Teaching Middle School Mathematics 3 MEDU 3020 Methods of Teaching Secondary School Mathematics 3 MEDU 3030 Assessment Techniques in Mathematics 2 MEDU 4010 Supervised Student Teaching and Seminar in Middle School 4 Mathematics MEDU 4020 Supervised Student Teaching and Seminar in Middle School 4 Mathematics EDU 2455 Methods and Materials for Special Needs Students 3 EDU 4600 Professional Development Seminar 2

Mathematical Applications Electives 5

PSY 3502 Human Learning and Instruction 3 TOTAL 60

$*! ! !

Procedures for reviewing, up-dating, modifying or terminating agreement

Procedures for evaluating agreement, e.g., tracking the number of students who transfer under the articulation agreement and their success:

Verification of data from sources such as: Admissions office, Assessment & Institutional Research, Transfer Office and/or Enrollment Management will be used to follow students’ progress.

Sending and receiving college procedure for publicizing agreement, e.g., college catalogs, transfer advisers, Websites, etc.:

Effective Date: Spring 2012

______Dr. Bonne August, Dr. Sadie Bragg Provost Provost New York City College of Technology Borough of Manhattan Community College

______Dr. Henry Africk Dr. Annie Han Chair, Department of Mathematics Chair, Department of Mathematics New York City College of Technology Borough of Manhattan Community College

$+! ! !

Appendix K. State Requirements for Teacher Preparation Programs

Below we list the state pedagogical requirements outlined by the New York State Education Department for accreditation of Adolescence Teacher Preparation Programs (grades 7-12) (NYSED, 2010). These standards are divided into two groups: General Pedagogical Component Requirements, and Program-Specific Requirements. Following each list, we present a table indicating required courses that meet each of these standards.

I. General Pedagogical Component 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 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.

$#! ! !

General Pedagogical Required Courses that Address Each GPCR Component Requirements (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, EDU 2455 (iv) Required Communication Skills Electives including ENG 1101, SPE 1330, MEDU 3010, MEDU 3020, MEDU 4010, MEDU 4020 (v) MEDU 1010, MEDU 1020, MEDU 1020, MEDU 2010, MEDU 3010, MEDU 3020, MEDU 4010, MEDU 4020, EDU 2455 (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. (iv) Student teaching shall include both adolescence education settings, grades 7 through 9 and grades 10 through 12.

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(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 L. NCATE and NCTM Accreditation Standards

There are 14 standards under which mathematics programs are evaluated by NCATE. These standards are grouped into “process standards”, “pedagogy standards,” “content standards,” and “field-based experience standards.” The standards have been created in coordination with the National Council of Teachers of Mathematics. Evidence that these standards have been met must be submitted to NCATE and will be examined by NCTM-trained reviewers.

Below we list the 14 standards. Each standard is clarified with a number of “indicators.” We do not list the indicators below. They may be found at http://www.nctm.org/uploadedFiles/Math_Standards/NCTMSECONStandards.pdf. It should be noted that for accreditation, 80 percent of indicators must be met, with at least one indicator in each standard met.

Following the list of standards is a chart listing the courses in the proposed program that address each of these standards. The proposed program exceeds the NCATE standards.

Process Standards

Standard 1: Knowledge of Mathematical Problem Solving Candidates know, understand, and apply the process of mathematical problem solving.

Standard 2: Knowledge of Reasoning and Proof Candidates reason, construct, and evaluate mathematical arguments and develop an appreciation for mathematical rigor and inquiry.

Standard 3: Knowledge of Mathematical Communication Candidates communicate their mathematical thinking orally and in writing to peers, faculty, and others.

Standard 4: Knowledge of Mathematical Connections Candidates recognize, use, and make connections between and among mathematical ideas and in contexts outside mathematics to build mathematical understanding.

Standard 5: Knowledge of Mathematical Representation Candidates use varied representations of mathematical ideas to support and deepen students’ mathematical understanding.

Standard 6: Knowledge of Technology Candidates embrace technology as an essential tool for teaching and learning mathematics.

Standard 7: Dispositions Candidates support a positive disposition toward mathematical processes and mathematical learning. Pedagogy Standards

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Standard 8: Knowledge of Mathematics Pedagogy Candidates possess a deep understanding of how students learn mathematics and of the pedagogical knowledge specific to mathematics teaching and learning.

Content Standards

Standard 9: Knowledge of Number and Operation Candidates demonstrate computational proficiency, including a conceptual understanding of numbers, ways of representing number, relationships among number and number systems, and meanings of operations.

Standard 10: Knowledge of Different Perspectives on Algebra Candidates emphasize relationships among quantities including functions, ways of representing mathematical relationships, and the analysis of change.

Standard 11: Knowledge of Geometries Candidates use spatial visualization and geometric modeling to explore and analyze geometric shapes, structures, and their properties.

Standard 12: Knowledge of Calculus Candidates demonstrate a conceptual understanding of limit, continuity, differentiation, and integration and a thorough background in the techniques and application of the calculus.

Standard 13: Knowledge of Discrete Mathematics Candidates apply the fundamental ideas of discrete mathematics in the formulation and solution of problems.

Standard 14: Knowledge of Data Analysis, Statistics, and Probability Candidates demonstrate an understanding of concepts and practices related to data analysis, statistics, and probability.

Standard 15: Knowledge of Measurement Candidates apply and use measurement concepts and tools.

Field-Based Experiences Standards

Standard 16: Field-Based Experiences Candidates complete field-based experiences in mathematics classrooms.

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Standard Courses in Proposed Program Addressing Standard 1 All MAT courses, MEDU 2010, MEDU 3010, MEDU 3020, MEDU 4010, MEDU 4020. 2 MAT 2580, MAT 2070, MAT 3075, MAT 3080, MAT 3050, MAT 4050. 3 All MAT and MEDU courses. SPE 1300, ENG 1101, ENG 1121 4 MEDU 2010, mathematical applications component. 5 All MAT and MEDU courses. 6 All MAT and MEDU courses. In particular MAT 1476L, MAT 2630, MEDU 2010. 7 All MEDU courses. In particular MEDU 3030. 8 EDU 2455, all MEDU courses. 9 All MAT courses. 10 MAT 2580, MAT 3080, MAT 4030 11 MAT 3050, MAT 4030, MAT 4050 12 MAT 1475, MAT 1575, MAT 2675, MAT 3075, MAT 4030, MEDU 2010 13 MAT 2070, MAT 3020, MAT 3080, MAT 4030, MEDU 2010 14 MAT 2572, MAT 4030 15 MAT 1475, MAT 1575, MAT 2675, MAT 2580, MAT 4030 16 MEDU 3010, MEDU 3020, MEDU 4010, MEDU 4020

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Appendix M. 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.

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Appendix N.

Dear Andrew,

Yes, the math-oriented topics will remain. The primary difficulty will be that the new 1111 (3 credits) will have a required "Visual Studies" co-requisite (2 credits), making this a 5-credit block. Other options are the new 1st and 2nd semester Building Technology courses (3 credits each). These will be combination lecture and construction drawing/detailing courses. ARCH 1250 will be the subject of more minor revisions.

I am sorry that this is a moving target . . . but I am sure the Math Ed proposal is not the only proposal pending with this problem!

Please let me know if you have further questions. Shelley - Hide quoted text -

On 1/30/2011 6:48 PM, AD wrote: Dear Professor Smith,

I'm currently meeting with the subcommittee of the Curriculum Committee that is examining the math education proposal. As you may recall, we plan to offer students the option of taking courses in your department. The subcommittee wanted to know if the planned changes to ARCH 1111, 1211, and 1250 would affect the goals of the math education program. In particular, they wanted to know if math oriented topics currently present in these courses would remain in the modified courses?

Thank you for your time.

Best regards,

Andrew Douglas

-- Shelley E Smith PhD AIA Assistant Professor and Chair Department of Architectural Technology New York City College of Technology The City University of New York 300 Jay Street, Voorhees 818 Brooklyn NY 11201 718.260.5262

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Appendix O. Student Survey Form

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 ______

Comments:

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Appendix P. Consultation with affected Departments

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

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]

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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,

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]

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Electrical & Telecommunication Engineering Technology

NEW YORK CITY COLLEGE OF TECHNOLOGY The City University of New York 300 Jay Street • Brooklyn, NY 11201-2983

Department of Electrical and Telecommunications Engineering Technology TEL (718) 260-5300 - FAX: (718) 254-8643

Dear Prof. Africk,

Your Proposal for the new Bachelor of Science in Mathematics Education is a well written and comprehensive one. The exposure of the students in this program to several application areas strengthens this program and provides them with tangible understanding of where their acquired knowledge is applied in various disciplines. I wish the department all the success in this endeavor and will do our best to provide the students with the knowledge and skills needed in our Electrical and Telecommunications Engineering Technology courses,

Best Regards,

Prof. Mohammad Razani, Chair, ETET Department October 2010

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Appendix Q. 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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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 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

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• 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.

• 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.

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• 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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Appendix R. Letter from Dean Pamela 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 component 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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Appendix S. External Letter of Support

Alfred S. Posamentier, Ph.D. 555 Broadway Dean Dobbs Ferry, NY 10552 School of Education

Gen. off. 914-674-7350 Pvt. 914-674-7447 [email protected]

February 10, 2011

Re: New York City College of Technology proposal for B.S. in mathematic education

To whom it may concern:

I am writing in support of the proposed curriculum proposal for a new Bachelor of Mathematics Education at City Tech. I served as a consultant in the spring of 2010 for the creation of the proposal, and I met with Professor Andrew Douglas in January, 2011 to further enhance the proposal.

The proposal is very strong. The mathematics component of the proposed program will provide future middle school and high school mathematics teachers with a solid foundation needed to teach mathematics with rigor and self-confidence.

The pedagogy component provides an extensive sequence of courses focused on teaching and learning and the examination of effective instructional methods. The 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.

An innovative component of the program is the mathematics applications component. This component will expose students to a wide range of applications including architecture and electrical engineering.

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The proposed program is both mathematically and pedagogy strong. I am confident that it meets the state standards for accreditation of a teacher education program.

Respectfully,

Alfred S. Posamentier Dean Professor of Mathematics Education

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Appendix T. 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 Department/Program Bachelor of Science in Mathematics Mathematics Education Department Chairperson/Coordinator Expected date course will be offered Henry Africk # of students Spring 2012 Each new course is projected to have 20 students the first time it is offered.

Proposed by Date Andrew Douglas February 12, 2011 [email protected] 718.260.4964

#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 component (29 credits), a mathematics component (37 credits), a required liberal arts component (43-45 credits), and a mathematical applications component (9-11 credits). Courses within the mathematical applications component 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.

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#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. (2010). Classroom Assessment: What Teachers Need to Know, Pearson,. $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. (2006). Teaching Secondary School Mathematics, 3rd Edition. Lawrence Erlbaum Publishers. $51.36.

• Schumacher, C. (2000). Chapter zero: fundamental notions of abstract mathematics, 2nd edition, Addison Wesley. $66.89.

• Burton, D.M. (2011). Elementary Number Theory, 7th Ed. McGraw-Hill. $130.70.

• Martin, G.E. (1975). The Foundations of Geometry and the Non-Euclidean Plane. Springer, New York. $52.47.

• Gallian, J.A. (2010). Contemporary Abstract Algebra, 7th Ed. Brooks/Cole Cengage Learning. $140.71.

• Katz, V. (2008). History of Mathematics, 3rd edition. Addison Wesley. $92.52.

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• Hahn, L.S. (1994). Complex numbers and geometry, The Mathematical Association of America. $39.95

• Kauchak, D., & Eggen, P. (2008). Introduction to Teaching: Becoming a Professional 3rd Ed. Merril-Prentice Hall. $90

• 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

• Ornstein, C., Levine, D., & Gutek, G. (2011). Foundations of Education, 11th Edition. Cengage Learning. $120

• Webb, L., Metha, A., & Jordan, K. (2009). Foundations of American Education, 6th Edition. Prentice Hall. $84

• Kulm, G. (1994). Mathematics Assessment: What Works in the Classroom, 1st Edition. Josey-Bass. $32

• Bush, W., Greer, A., & Compton, H. (1999) Mathematics Assessment: A Practical Handbook: For Grades 9-12 (Classroom Assessment for School Mathematics Seires). National Council of Teachers of Mathematics. $34

• Brumbaugh, et al. (2006). Teaching Middle School Mathematics, 3rd Edition. Lawrence Erlbaum Publishers. $55

• Montague, et al. (2006). Teaching Mathematics to Middle School Students with Learning Difficulties, 1st Edition. The Guilford Press. $27

• Posam, et al. (2009). Teaching Secondary Mathematics: Techniques and Enrichment Units, 8th Edition. Allyn and Bacon. $97

• Beckmann, et al. (2009). Teaching and Learning High School Mathematics. Wiley. $80

• Chappell, M., & Pateracki, T. (2004). Empowering the Beginning Teacher of Mathematics in Middle School. National Council of Teachers of Mathematics. $30

• Malloy, C., & Ellis, M. (2008). Mathematics for Every Student: Responding to Diversity in Grades 6-8. National Council of Teacher of Mathematics. $23

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• Erickson, T., & Craig, R. (2005). Get it Together: Math Problems for Groups Grades 4-12, 11th Edition. EQUALS/ Lawrence Hall of science. $20

• Artzt, A., & Sultan, A. (2010). The mathematics that every high school teacher should know. New York, Routledge. $81

• Uskin et al. (2002). Mathematics for High School Teachers-An Advanced Prospective. Prentice Hall. $70

• Artzt, A., and Thomas. (2007). Becoming a reflective mathematics teacher, 2nd edition. Routledge. $43

• Schoen, H., & Charles, R. (2003). Teaching Mathematics through Problem Solving: Grades 6-12. NCTM. $39

#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 component, mathematics component, and mathematical applications component courses.

The library will need to acquire the recommended books listed under #4 and additional material for the proposed pedagogy component courses and career education.

City Tech library in recent years has expanded its electronic collections. Students and

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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.

Date February 14, 2011

Library Department October 4, 2006

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Appendix U. Chancellor’s Report

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Chancellor’s Report Information

MEDU 1010 Foundations of Mathematics Education

From: To: Description 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. Class Hours Class Hours 3 Lab Hours Lab Hours 0 Credits Credits 3 Prerequisite: Prerequisite: CUNY proficiency in reading and writing Pre-or Pre-or corequisite: corequisite: Corequisite: Corequesite:

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Chancellor’s Report Information

MEDU 1020 Teaching and Learning Strategies for Mathematics Teachers

From: To: Description 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. Class Hours Class Hours 1 Lab Hours Lab Hours 2 Credits Credits 2 Prerequisite: Prerequisite: MAT 1375, CUNY proficiency in reading and writing Pre-or Pre-or corequisite: corequisite: Corequisite: Corequesite:

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Chancellor’s Report Information

MEDU 2010 Pedagogy of Mathematics Applications and Technology

From: To: Description 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. Class Hours Class Hours 1 Lab Hours Lab Hours 2 Credits Credits 2 Prerequisite: Prerequisite: MAT 1475, MEDU 1020 Pre-or Pre-or corequisite: corequisite: Corequisite: Corequesite:

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Chancellor’s Report Information

MEDU 3010 Methods of Teaching Middle School Mathematics

From: To: Description 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 will be on the needs of individual learners including English language learners and those with disabilities and special health needs, group instruction techniques, the development of literacy in the mathematics classroom, roles of the teacher in the classroom, and planning both curriculum and individual lessons. Includes 6 hours per week for 10 weeks of preservice field experience in high schools. Class Hours Class Hours 3 (6 field hours/week) Lab Hours Lab Hours 0 Credits Credits 3 Prerequisite: Prerequisite: Pre-or Pre-or ENG 1121, MEDU 2010 corequisite: corequisite: Corequisite: Corequesite:

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Chancellor’s Report Information

MEDU 3020 Methods of Teaching Secondary School Mathematics

From: To: Description 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 will be on the needs of individual learners including English language learners and those with disabilities and special health needs, group instruction techniques, the development of literacy in the mathematics classroom, roles of the teacher in the classroom, and planning both curriculum and individual lessons. Includes 6 hours per week for 10 weeks of preservice field experience in high schools. Class Hours Class Hours 3 (6 field hours/week) Lab Hours Lab Hours 0 Credits Credits 3 Prerequisite: Prerequisite: MEDU 3010 Pre-or Pre-or corequisite: corequisite: Corequisite: Corequesite:

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Chancellor’s Report Information

MEDU 3030 Assessment Techniques in Mathematics

From: To: Description 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. Class Hours Class Hours 3 Lab Hours Lab Hours 0 Credits Credits 3 Prerequisite: Prerequisite: Pre-or Pre-or MEDU 3010 corequisite: corequisite: Corequisite: Corequesite:

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Chancellor’s Report Information

MEDU 4010 Supervised Student Teaching and Seminar in Middle School Mathematics

From: To: Description Description The course consists of a field-based, student teaching experience and a seminar component. The field-based experience involves 20 days or 120 hours of supervised student teaching in grades 7 through 9. Under the guidance and supervision of an experienced teacher and a faculty member, students will implement and refine pedagogical strategies, classroom management techniques, and assessment approaches. The seminar component provides a discussion forum for students, guided by a faculty member, to refine pedagogical strategies, and to address and resolve pedagogical issues that students face during the concurrent field placement. Class Hours Class Hours 1 (9 field hours/week) Lab Hours Lab Hours 0 Credits Credits 4 Prerequisite: Prerequisite: MEDU 3010, and permission of department one semester in advance. Pre-or Pre-or corequisite: corequisite: Corequisite: Corequesite:

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Chancellor’s Report Information

MEDU 4020 Supervised Student Teaching and Seminar in Secondary School Mathematics

From: To: Description Description The course consists of a field-based, student teaching experience and a seminar component. The field-based experience involves 20 days or 120 hours of supervised student teaching in grades 10 through 12. Under the guidance and supervision of an experienced teacher and a faculty member, students will implement and refine pedagogical strategies, classroom management techniques, and assessment approaches. The seminar component provides a discussion forum for students, guided by a faculty member, to refine pedagogical strategies, and to address and resolve pedagogical issues that students face during the concurrent field placement. Class Hours Class Hours 1 (9 field hours/week) Lab Hours Lab Hours 0 Credits Credits 4 Prerequisite: Prerequisite: MEDU 3020, and permission of department one semester in advance. Pre-or Pre-or corequisite: corequisite: Corequisite: Corequesite:

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Chancellor’s Report Information

MAT 2070 Introduction to Proofs and Logic

From: To: Description 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. Class Hours Class Hours 3 Lab Hours Lab Hours 0 Credits Credits 3 Prerequisite: Prerequisite: Pre-or Pre-or MAT 1575 corequisite: corequisite: Corequisite: Corequesite:

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Chancellor’s Report Information

MAT 3020 Number Theory

From: To: Description 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. Class Hours Class Hours 3 Lab Hours Lab Hours 0 Credits Credits 3 Prerequisite: Prerequisite: MAT 2070 Pre-or Pre-or corequisite: corequisite: Corequisite: Corequesite:

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Chancellor’s Report Information

MAT 3050 Geometry I

From: To: Description 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. Class Hours Class Hours 3 Lab Hours Lab Hours 0 Credits Credits 3 Prerequisite: Prerequisite: MAT 2070 Pre-or Pre-or MAT 3080 corequisite: corequisite: Corequisite: Corequesite:

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Chancellor’s Report Information

MAT 3075 Introduction to Real Analysis

From: To: Description 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. Class Hours Class Hours 4 Lab Hours Lab Hours 0 Credits Credits 4 Prerequisite: Prerequisite: MAT 1875, MAT 2070 Pre-or Pre-or corequisite: corequisite: Corequisite: Corequesite:

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Chancellor’s Report Information

MAT 3080 Modern Algebra

From: To: Description 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. Class Hours Class Hours 3 Lab Hours Lab Hours 0 Credits Credits 3 Prerequisite: Prerequisite: MAT 2580, MAT 3075 Pre-or Pre-or corequisite: corequisite: Corequisite: Corequesite:

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Chancellor’s Report Information

MAT 4030 History of Mathematics

From: To: Description 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. Class Hours Class Hours 3 Lab Hours Lab Hours 0 Credits Credits 3 Prerequisite: Prerequisite: MAT 2070, MAT 3020 Pre-or Pre-or corequisite: corequisite: Corequisite: Corequesite:

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Chancellor’s Report Information

MAT 4050 Geometry II

From: To: Description 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. Class Hours Class Hours 3 Lab Hours Lab Hours 0 Credits Credits 3 Prerequisite: Prerequisite: MAT 3050, MAT 3080 Pre-or Pre-or corequisite: corequisite: Corequisite: Corequesite:

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