Sign up now for a 2025 VMI summer course
The VMI is offering several mathematics education courses this summer in the Burlington area. Courses are open to those enrolled in the VMI Master’s program as well as those interested in taking courses for professional development/recertification purposes. Many of these courses will support relicensing and endorsement efforts in elementary, middle, and secondary mathematics as well as Vermont’s new Math Specialist endorsement.
The following courses are being offered. Click on the course name to get more information or scroll down.
Mathematics as a Second Language –Burlington - July 7-11, 2025
This course provides for a deep understanding of the basic themes of arithmetic as well as the inter-relationships among arithmetic, algebra, and geometry. As VMI’s signature course, a major theme of Mathematics as a Second Language is the understanding of arithmetic and algebra through language. Participants will explore the mathematics content related to these topics, the intimate relationship among them, and the important pedagogical strategies and skills that educational research suggests can have a strong impact on student learning.
Functions and Algebra I –Burlington- July 14-18, 2025
This course builds upon the prior course Mathematics as a Second Language and extends and reinforces the learning from that course. Participants will obtain a deep understanding of the concept of a function, appreciate the pervasiveness of the function idea in everyday life, and engage in a variety of problem solving activities that hone arithmetic and algebra skills. Topics include functions, graphs, inverse functions, linear functions, the algebra and geometry of straight lines, linear inequalities, solving linear equations, and an introduction to nonlinear functions.
The Mathematics as a Second Language course and the Functions and Algebra I courses are seamlessly related, with the latter course starting from where the former left off, building from the ideas of constant rate, ratio, proportion, and graph of the proportion. The central idea in this course is the notion of a function, which is an extremely powerful concept that provides an overarching umbrella for the study of patterns, tables, formulas, and graphs.
Prerequisite: Mathematics as a Second Language or by permission (contact Judi Laird, VMI Director)
Geometry for Teachers – Burlington- July 7-11, 2025
This course introduces teachers to the study of Geometry, a major area of mathematics in its own right, but one that is also integrally related to other areas of mathematics. This course highlights the intimate relationship among arithmetic, algebra and geometry and examines the importance of geometric imagery, the characteristics of geometric figures, and the idea that behind every measurement lies a geometric concept. This course examines decomposing, rearranging and shearing as a way to understand why a measurement formula works; symmetry as an important geometric concept; and the use of conjecture in geometric investigations.
Statistics I –Burlington - July 14-18, 2025
As discussed by Moore and Cobb (1997), “Statistics is a methodological discipline. It exists not for itself, but rather to offer to other fields of study a coherent set of ideas and tools for dealing with data. The need for such a discipline arises from the omnipresence of variability.” The Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report, endorsed by the American Statistical Association, is the authoritative report that guides curricular decisions in K-12 and college education. The GAISE report describes this focus on the omnipresence of variability as the distinguishing feature of statistics education and the idea that sets statistics apart from mathematics. As described in the report (2005), “a major objective of statistics education is to help students develop statistical thinking. Statistical thinking, in large part, must deal with this omnipresence of variability; statistics problem solving and decision making depend on understanding, explaining, and quantifying the variability in the data.” (p. 6)
This Vermont Mathematics Initiative (VMI) course begins the study of statistical thinking and introduces descriptive statistics with an emphasis on applications in education as well as connections to other areas of K-12 mathematics. Topics include graphical and numerical organization and presentation of data, summary statistics for quantitative data, including measures of center, and measures of variability, properties of the normal curve, placement of individuals within a distribution, and measures of relationship between variables.
Discrete Mathematics for Teachers – June 23-27, 2025
Discrete math topics are becoming more common in high school curricula and there is an escalating need for teachers to understand the ideas, methods and applications in this area in order to be better prepared to facilitate student discovery. In this course, teachers will look deeply at the fundamental ideas which span seemingly unrelated topics and will develop a problem solving habit of mind towards the subject. This course in discrete mathematics will draw from topics in the following areas of study: basic counting methods, the binomial theorem, recursion, modular arithmetic, graph theory, set theory, logic, Latin squares, number bases and finite differences. This course will be structured in a problem-solving format which will promote assisted discovery, communication of process & examination of alternate solution routes.
