|
Vermont Mathematics Initiative |
|
Building Capacity across Vermont for High-Quality Mathematics Instruction |
|
Course 2: Functions and Algebra for Teachers This course builds upon the prior course Mathematics as a Second Language. Participants will obtain a deep understanding of the concept of a function, utilize functions in problem solving, appreciate the pervasiveness of the function idea in the K-8 mathematics curriculum as well as everyday life, and engage in a variety of problem solving activities. Topics include functions, graphs, inverse functions, linear functions, the algebra and geometry of straight lines, and solving linear equations.
This course builds upon the arithmetic, algebra and geometry developed in prior courses. The first part of the course develops the subject of trigonometry from the perspective of the K-8 mathematics classroom. Topics include similar triangles, the trigonometric functions and their graphs, the equation of the circle, the number pi, and applications to measurement, wave motion, and problem solving. The second part of the course continues the study of algebra from the perspective of K-8 mathematics. Topics include quadratic functions, parabolas, and related problem solving.
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, as well as multiple methods for solving probability problems. Topics are presented in the context of problem solving, the course design makes connections with arithmetic, and there is an emphasis on reinforcing one’s understanding of functions, function notation, and topics from algebra.
This course introduces teachers to the branch of mathematics known as number theory, in which one studies properties of integers with respect to the operations of multiplication and division. Topics include the division algorithm, the sieve of Eratosthenes, the infinitude of primes, the fundamental theorem of arithmetic, properties of the greatest common factor and least common multiples, the Euclidean algorithm, use of base ten and expanded notation, writing numbers in different bases, and arithmetic progressions.
Course 6: Statistics, Action Research, and Inquiry into Effective Practice, I This course provides an introduction to statistics with an emphasis on research in education. Topics include graphical and numerical organization and presentation of data, summary statistics for quantitative data, measures of relationship between variables, and inference from sample data to populations. This course forms the foundation for later work in statistics and school-based research, and is followed by a series of classroom observations and feedback sessions during the upcoming school year. Course 7: Statistics, Action Research, and Inquiry into Effective Practice, II This course is designed to build upon previously completed work in statistics. The emphasis is on understanding, interpreting, and communicating results of local and national school assessment. Each participant will prepare a presentation to school leaders based on her/his own school’s data. Topics in statistics include the use of error bars in graphs, margins of error in surveys, and confidence intervals, especially in the context of school data. Course 8: Algebra and Geometry for Teachers, III This course continues the study of functions, algebra, and geometry from prior courses. Here, the focus is on exponential processes and inverse processes, with an emphasis on problem solving related to the mathematics of finance and growth and decay of biological, physical, and ecological systems. Course 9: Statistics, Action Research, and Inquiry into Effective Practice, III This course builds on prior courses in statistics and school-based research, and extends earlier concepts in descriptive and inferential statistics. New topics in statistics include regression, chi-square analysis, and design of research studies. Teachers will do critical reading of research on instructional practices in elementary and middle school mathematics and will complete the design of their own research investigations. Course 10: Calculus for Teachers, I This course builds upon prior courses in arithmetic, algebra, and geometry. It is designed to introduce teachers to the branch of mathematics known as calculus in a way that relates calculus to the mathematics taught in the K-8 classroom. Topics include the idea of a limit, the role limits play in K-8 mathematics, and the concept of instantaneous change. 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. Course 11: Calculus for Teachers 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 K-8 classroom teacher. Course 12: Capstone VMI experience This course concludes the school-based research component of the Vermont Mathematics Initiative and provides opportunities for teachers to synthesize their VMI coursework and field experiences. Teachers will revisit key mathematical concepts from basic arithmetic through calculus, study advanced topics in mathematics education and leadership, and re-examine curriculum and instruction based on their VMI learning. |
|
The VMI Master’s Degree Curriculum These 12 courses comprise the 36-hour VMI Masters Degree curriculum. Course 1: Mathematics as a Second Language This course lays the groundwork for all the Vermont Mathematics Initiative courses that follow. The theme 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. |
