The VMI is offering several mathematics education courses this summer. Classes will be held in person on the VTSU campus in Williston, VT; 8:30-4:00. Lunch will be provided. Hotel rooms are available free of charge for people driving more than 45 minutes to class. 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 Math Specialist endorsement.
The following courses are available:
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- Discrete Mathematics – June 22-26, 2026
- Mathematics as a Second Language – July 6-10, 2026
- Discrete Mathematics – June 22-26, 2026
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- Geometry for Teachers – July 6-10, 2026
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- Functions and Algebra I – July 13-17, 2026
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- Statistics I – July 13-17, 2026
- Beyond Procedure: Coherence Across Number Systems Using Additive Thinking and Mathematical Properties – July 13-20
- Beyond Procedure: Coherence Across Number Systems Using Multiplicative and Proportional Reasoning – July 20-24
- Statistics I – July 13-17, 2026
Additional information about each course can be found below and on the one-pagers linked below.
To register click here or contact Kathryn Delay ([email protected])
June 22 - 26
Discrete Mathematics
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 virtual course will be structured in a problem solving format which will promote assisted discovery, communication of process & examination of alternate solution route
July 6 - 10
Mathematics as a Second Language (MSL)
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.
Geometry for Teachers
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.
July 13 - 17
Beyond Procedure: Coherence Across Number Systems Using Additive Thinking and Mathematical Properties (NEW!)
This course is designed for all educators, especially those providing tier 2 or 3 small group targeted instruction on K-8 standards at all levels. This could include math interventionists/specialists, special educators/learning specialists, multilingual learner educators, instructional assistants/para-educators, and classroom teachers.
This course explores math content to deepen the connection among numbers and operations, including whole numbers, fractions, decimals, and integers, using additive reasoning and mathematical properties. We will explore conceptual understanding and relationships to deepen understanding around the developmental trajectory of additive reasoning, and consider how this can be developed for learners through setting goals and planning for intervention. This will be done through evidence-based practices and learning about productive beliefs to develop equitable opportunities and understanding for learners. Each day of class will incorporate:
- Content – engage with an aspect(s) of content standards, synthesize and connect concepts from different domains, and number types
- Instruction – engage with evidence-based teaching practices (NCTM) and instructional routines/strategies, and reflect on how these practices can apply to instructional deesign
- Models and Strategies – use models flexibly to support understanding of the concept and use of multiple strategies, justify and explain models, analyze given models, and connect to conceptual understanding and strategies
- Intervention structures – discuss ideals for implementation, explore and discuss research on effective practices, and apply evidence to prepare differentiated instruction
Functions and Algebra I
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 Kathryn Delay, VMI Director)
Statistics I
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.
July 20 - 24
Beyond Procedure: Coherence Across Number Systems Using Multiplicative and Proportional Reasoning (NEW!)
This course is designed for all educators, especially those providing tier 2 or 3 small group targeted instruction on K-8 standards at all levels. This could include math interventionists/specialists, special educators/learning specialists, multilingual learner educators, instructional assistants/para-educators, and classroom teachers.
This course explores math content to deepen the connection among numbers and operations, including whole numbers, fractions, decimals, and integers, using multiplicative and proportional thinking. We will explore conceptual understanding and relationships to deepen understanding around the developmental trajectory of multiplicative and proportional reasoning, and consider how this can be developed for learners through setting goals and planning for intervention. This will be done through evidence-based practices and learning about productive beliefs to develop equitable opportunities and understanding for learners. Each day of class will incorporate:
- Content – engage with an aspect(s) of content standards, synthesize and connect concepts from different domains, and number types
- Instruction – engage with evidence-based teaching practices (NCTM) and instructional routines/strategies, and reflect on how these practices can apply to instructional deesign
- Models and Strategies – use models flexibly to support understanding of the concept and use of multiple strategies, justify and explain models, analyze given models, and connect to conceptual understanding and strategies
- Intervention structures – discuss ideals for implementation, explore and discuss research on effective practices, and apply evidence to prepare differentiated instruction
