Certificate of Advanced Graduate Study
Curriculum and Instruction in Mathematics

This program is designed for experienced educators with Master's degrees who wish to extend their knowledge of specific aspects of instructional methodology, mathematics, and/or curriculum development. Coursework is selected in areas of study in which students wish to gain more in-depth knowledge, as well as in areas of research and evaluation and social and educational policy. The program consists of significant required coursework in adult learning and development, research methods, curriculum, and social and educational policy; offers opportunities for directed study, internships, or other field experience; and is geared to serve the needs of master teachers who wish to continue in the same role or to enter new roles as consultants, supervisors or administrators.

Prerequisite: Master's Degree

COURSE DESCRIPTIONS

EEDUC 8001 Advanced Professional Seminar
This interdisciplinary seminar will focus on professional identity development and issues of professional practice. Students will be introduced to reflective practice, systems analysis, and action research. Students from diverse disciplines will learn about collaborative problem solving for the systems in which they have to function. Emphasis will be placed on understanding the cultural, social, and community contexts for professional practice from a critical perspective.

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EEDUC 7121 Assessment Issues in Mathematics: Summative and Formative
This course is designed to engage participants in the examination of both summative and formative assessments and their implications for teaching and learning. Various types of classroom assessments and how they can be used to make instructional decisions based upon student responses will be developed. Participants will also examine how to make sense of the scores reported via standardized tests, what they mean, and what the implications are at the district, school, classroom, and individual student levels.

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EAGSR 7004 Adult Learning and Development
This course will review the theories, research, and models on adult learning and development. It explores the social context in which adults learn and develop, and the influences of race, class, gender, and culture. Students will be required to apply the material to a practice setting. This is a seminar designed for advanced graduate students.

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CMATH 6103 Data Analysis
In a world dominated by quantitative information, it is imperative that all citizens be informed of the methods and conclusions of statistics. This course will focus on data analysis through the study of inferential statistics. After a brief review of descriptive statistics and probability, the course will focus on sampling distributions, estimation, and hypothesis testing. Topics include significance tests involving means and proportions, linear and multiple regressions, and analysis of variance.

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EAGSR 7103 Qualitative Research Methods I
The purpose of this class is to learn to conduct qualitative social science research. Participants will read a variety of perspectives on the philosophical bases as well as tools of the practice of qualitative data gathering and analysis. Each participant will engage in a small qualitative study that is consistent with her or his graduate study goals. They will choose a topic and research setting, negotiate research relationships, collect and analyze data, and present findings. Readings, analytic memos, interview transcriptions, and field notes will provide material for the class to work with as co-consultants.

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CMATH 6101 Number Theory
This course explores the tools and modes of thinking that are specific to classical number theory. Topics include: prime numbers and divisibility, congruencies, Diophantine equations, Euclid's algorithm, arithmetic progressions and applications of these topics. Students will be expected to experiment and formulate conjectures. There will also be an emphasis on writing clear and coherent explanations of mathematical reasoning. Participants will extend their understanding of key ideas through individual and group inquiry, case study analysis, and guided research.

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CMATH 5100 Functions and Algebra: The Study of Patterns
This course focuses on algebra and algebraic thinking through a thorough investigation of functions of various kinds. Students will also develop their capacity for mathematical thinking through a collaborative inquiry approach that will involve generating mathematical data, identifying and describing patterns, representing those patterns in a variety of ways, developing mathematical explanations, and using patterns to make predictions.

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CMATH 5101 Dynamic Geometry: Intuition, Construction, and Proof
Through interactive activities, students will explore properties of geometric figures and solids and their relationships. They will use geometric language and reasoning to express ideas, justify reasoning, and generate, critique, and support conjectures. They will also study and create geometric proofs. Students will engage with central geometric topic ideas such as symmetry, similarity, trigonometry, and transformational geometry. The course progresses from the visual and intuitive to the formal and includes many real-world context problems. Restrictions for registration: Successful completion of an algebra course or higher-level math course at the undergraduate level.

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CMATH 6111 Geometry and Measurement I: From Polygons to Pythagoras
This first course integrates the study of geometry and measurement and includes lines, angles, investigations of triangles including sorting, similarity, trigonometry, and Pythagoras' Theorem. We will also investigate quadrilaterals, polygons, area and perimeter.  Participants will examine the nature of geometric definitions, and follow a path that explores mathematical explanation, argument, and justification and how these processes connect to geometric proof.

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CMATH 6104 Measurement and Probability
This course introduces teachers to the theory of measurement (length, area, volume), develops geometric modeling in algebra, and introduces teachers to experimental and theoretical probability, and multiple methods for solving probability problems. All topics are presented in the context of problem solving; emphasis is placed on development of these mathematical ideas, and the course design makes connections with arithmetic and reinforces understanding of functions, functions notation, and topics from algebra.

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CMATH 6113 Probability: The Mathematics of Uncertainty
Participants will develop a solid conceptual understanding of the language and operations of arithmetic, as well as the interrelationships among arithmetic, algebra and geometry.  Topics include place value and the history of counting, inverse processes, the geometry of multiplication, the many faces of division, and conceptual models of integers and rational numbers.

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CMATH 6105 Trigonometry, Algebra, and Analytic Geometry
The first part of the course develops the subject of trigonometry. The course is conducted in an inquiry-based mode, and includes a review of similar triangles, the trigonometric functions and their graphs, the equation of the circle, the number pi, measuring angles in radians, and applications to measurement, wave motion, and problem solving.  The second part of the course, building on past work with linear algebra, includes quadratic functions, parabolas, higher degree polynomial functions, transformational geometry, the Pythagorean theorem (revisited), symmetry, and related problem solving.

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CMATH 6100 Calculus: The Mathematics of Change
Change is a fundamental fact of our physical universe. In this course, students will explore the underlying structure of change by studying calculus. This course examines the calculus in its conceptual and historical context and introduces its essential topics: functions, limit, continuity, the derivative, infinite series, and the definite integral. Connections among algebra, geometry, and calculus are emphasized as well as real-world applications.

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CMATH 6116 Conceptual Calculus II for Elementary and Middle School
This course continues the study of calculus and its relationship to the K-8 classroom. Topics include infinite series, calculation of area, the definite integral, and the Fundamental Theorem of Calculus -- all viewed from the perspective of the K-8 classroom teacher.

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EEDUC 7500 Curriculum and Assessment Thesis Project
This C.A.G.S. thesis project course is designed to assist students in developing and implementing a project that will contribute to the field of education. The project also helps to demonstrate that at the end of the C.A.G.S. program, students have learned how to conduct research, plan a major initiative, synthesize information, and present the work to an appropriate and critical audience.

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Lesley University reserves the right to unilaterally add, withdraw, or revise any course offering in the above-mentioned program of study, including policies, provisions, requirements, and fees.

Lesley University is an Affirmative Action/Equal Opportunity institution and does not discriminate on the basis of age, race, religion, color, creed, national or ethnic origin, sex, sexual orientation, handicap, or disability in its education programs, employment, or in admissions to, access to, or treatment in its programs or activities.