VMI Professional Development Courses

Summer Week 1

• Mathematics as a Second Language – The fundamentals of mathematics begins with a solid understanding of arithmetic, and its relationship to all strands of mathematics. As the VMI’s signature course, the 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 real numbers.
• Geometry for Teachers – This course highlights the intimate relationship among arithmetic, algebra, and geometry, examining the importance of geometric imagery and the idea that behind every measurement lies a geometric concept. Participants investigate decomposing, rearranging, and shearing to understand why measurement formulas work, symmetry as a geometric concept, and the use of conjecture in geometric investigations. 

Summer Week 2

• Functions & Algebra I – Building on Mathematics as a Second Language, this course provides a deep understanding of the function as a powerful concept that provides an overarching umbrella for the study of patterns, tables, formulas, and graphs. Participants engage in problem-solving activities that hone arithmetic and algebra skills, covering topics from linear functions and inequalities to an introduction to nonlinear functions.
• Functions & Algebra II (Prerequisite: Functions & Algebra I) – Building on Mathematics as a Second Language and Functions & Algebra I, this course broadens knowledge from linear to nonlinear functions, including quadratic, exponential, and logarithmic models. Participants explore parabolas, exponents, and the number $e$ with applications to interest and related problem-solving. The study extends to logarithmic functions, covering concepts like exponential growth and decay as applied to financial, biological, physical, and ecological systems.
• Statistics I – This course provides an introduction to descriptive statistics with an emphasis on applications in education and connections to K-8 mathematics. Topics include graphical and numerical organization of data, summary statistics for quantitative data (including measures of center and variability), properties of the normal curve, and measures of relationship between variables. This course forms the foundation for later work in inferential statistics, educational assessment, and school-based research.

• Teaching, Learning and Leading: Effective Mathematics Instruction for all Students – Focused on shifting from computational teaching to instruction that builds deep understanding. It introduces research-based instructional techniques that engage students in rigorous task-based learning.
• Essential Mathematics of the Primary Grades – This course builds teacher knowledge about the ways in which students construct essential mathematical understanding of numbers and additive reasoning. Teachers focus on the development of early numeracy and its essential components, the structure of our base-ten system, and the importance of using mathematical models. Participants review effective instructional and assessment approaches that address the Common Core State Standards for Mathematics (CCSS-M) for students in grades K-2.
• Calculus for Teachers (previous math content coursework required) – This course introduces teachers to calculus in a way that relates to the K-8 classroom. Topics include limits, instantaneous change, the derivative, calculation of area, the definite integral, and the Fundamental Theorem of Calculus. The goal is to empower teachers with a deep understanding of how K-8 arithmetic and algebra are foundational for success in higher-level mathematics.

• Number Theory – This course introduces the properties of positive integers with respect to multiplication and division. Teachers explore prime and composite numbers, the fundamental theorem of arithmetic, and methods for computing greatest common factors and least common multiples. Topics also include modular arithmetic, the Euclidean Algorithm, and computing in different bases to deepen understanding of the base-ten system and enrich K-12 problem-solving.
• Essential Mathematics of the Elementary Grades – This course focuses on building teacher knowledge about how students construct mathematical understanding of multiplicative and fractional reasoning. Participants in grades 3–5 explore learning progressions, models, and strategies to develop deep conceptual understanding, while reviewing research-based practices for high-quality instruction and assessment aligned with the Common Core. This course provides essential content knowledge for all PreK-8 educators, including specialists and administrators.