MATHEMATICS Programs
COURSE DESCRIPTIONS

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.

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 topics 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.

CMATH 5102  Exploring Number
This course deepens students' prior work with the tools and modes of thinking that are specific to the nature of number.  Topics include an historical examination of number systems and counting to rational, irrational, and beyond, the mathematical basis of arithmetic operations, and an examination of the role of number sense. Throughout, the course will focus on the understanding and uses of mathematics, and a variety of ways to apply the ideas under study.  

CMATH 5103  Mathematics as a Second Language
A major theme of Mathematics as a Second Language is understanding algebra and arithmetic through language. The objective is to provide a solid conceptual understanding of the operations of arithmetic, as well as the interrelationships among arithmetic, algebra, and geometry. Topics include: arithmetic vs. algebra; solving equations; place value and the history of counting; inverse processes; the geometry of multiplication; the many faces of division; rational vs. irrational numbers and the one-dimensional geometry of numbers.                       

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.

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 regression, and analysis of variance.

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.

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.

CMATH 6106  Try Math (Online)
This introductory course contains five modules each of which will use an engaging mathematical investigation to introduce a content area of mathematics that will be focused on in depth later on in the program. In addition this course will introduce a series of mathematical themes about learning and doing mathematics such as finding patterns, making generalizations, and carrying out mathematical investigations.

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.  

CMATH 6111 Geometry & Measurement
This course develops the subject of polygonal geometry through explorations using the geoboard, dynamic geometry software with applications to problem solving. Since it is difficult to separate geometry from measurement, the theory of measurement (length, area, volume), with application to problem solving will be woven throughout the course.  The use of the apothem as a means of finding the area of a polygon will be included in the exploration of area.  Application of the Pythagorean Theorem will be integral to some of the problem solving since participants first saw it in Mathematics as a Second Language.  Participants will be engaged in completing geometric proofs which will include use of logic statements, Euclidean Proofs, and mathematical arguments.  The course will investigate properties of circles including inscribed angles, tangents, chords, area.   Right triangle trigonometry will be introduced in this course and further developed in Trigonometry and Algebra II.

CMATH 6113 Probability and Statistics
This course introduces teachers to experimental and theoretical probability; dependent and independent events; conditional probability; binomial probability distribution; and introduces some concepts of game theory. Attention is given to collecting and organizing experimental probability data with emphasis on probability trees, Venn diagrams, and contingency tables.  In the second part of the course participants will examine types of data and develop appropriate data collection instruments, data organization systems as well as visual and numerical data representation. Throughout the course the participants will engage in a variety of problem solving activities and examine how to relate the material to the K-8 mathematics classroom. 

CMATH 6116 Calculus II
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 middle school classroom teacher. Course goals include reinforcing and extending arithmetic, algebra, and geometry knowledge and skills through problem solving involving calculus, and empowering teachers with a deep understanding of how capability in K-8 arithmetic and algebra is foundational for success in higher level mathematics.

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.

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. Formerly: Qualitative Research Methods.

EEDUC 6126 Classroom and School Inquiry
Classroom and School Inquiry focuses on the understanding and critical analysis of educational research and methods for accurately communicating this information to the public. As teachers participate in redefining their educational roles, decision-making and action-oriented classroom practice will be critical in promoting student learning. Both require problem-solving, which is enhanced by the forming and testing of hypotheses, gathering data that is then analyzed, synthesized, and evaluated, and generating solutions. This course will engage students in this process by acquainting them with the knowledge and techniques necessary for them to become lifelong teacher researchers, and to present the results of their research effectively and professionally to a variety of audiences.  Note: This course is a prerequisite to EEDUC 6127.

EEDUC 6127 Action Research and Seminar
Students demonstrate their expanding understandings and competencies as teachers. They also collaborate with several classmates to design a research project that can have a direct impact on their school community, through which students may extend the research plan developed in an earlier course, EEDUC 6126. The six-credit option is designed to give students who completed a required induction experience or advanced education license an opportunity to demonstrate continued learning by applying that experience to their Lesley program and using their study to reflect on what they learned from their induction or licensure program. Prerequisite: Successful completion of EEDUC 6126 or an equivalent research course.

EEDUC 6154 Meeting Diverse Needs in the Mathematics Classroom
This course considers the theory, research, and practical applications of ensuring that all children succeed mathematically. Gender, socioeconomics, culture, language, learning differences, assessment, and differentiated instruction are considered. Offered as part of an off-campus sequence in 2006-2007.

EEDUC 6155 Developing Mathematical Understanding
This course is designed for teachers who want to learn more about how children develop mathematical ideas, how to assess children’s mathematical thinking, and how to foster the development of mathematical power. Through debate, video, case studies, reflection, and field-based applications, teachers will connect research on the learning of mathematics to their own elementary classrooms and strengthen their abilities to support children’s learning. Formerly: EEDUC 7119: Advanced Study in Mathematics Pedagogy K–6.

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. 

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. Schedule to be announced.

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. Schedule to be announced.