## Abstract

Originating in Eastern Europe, Math Circles spread to the USA in the 1990s. They emerged approximately at the same time on both the east and west coast, and have spread to almost each state, numbering around 200 today. While the first wave of Math Circles in the USA started with a focus on preparing mathematically talented high school age youth for advanced mathematical competitions, their focus has now broadened. Math Circles for now serve a range of ages (preschool through high school) as well as teachers. Some still focus on preparing students for local or national competitions; others provide non-competitive, mathematical enrichment experiences for all interested students. We provide an overview of the history of Math Circles in America. We begin with a discussion of their origins in Eastern Europe and spread to the USA, then turn our focus to how these few pioneering circles combined with a confluence of events and people to catalyze the growth of the Math Circle community in the USA.

### Keywords

- Math Teacher
- Inspirational Motivation
- Circle Network
- Mathematical Science Research Institute
- Mathematical Competition

*These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.*

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## Appendix: Sample Math Circle Problems

### Appendix: Sample Math Circle Problems

### 1.1 Sample Activity - Ratio and Scale Factors via Shrinky Dinks

Shrinky Dinks are large flexible plastic sheets that when heated in an oven, shrink to small hard plates without altering their shape or color. This makes them particularly suitable for exploring ratios, proportions, and scaling. Students can create their own designs on the plastic sheets or use pre-prepared designs to color as they choose. Students can explore questions such as, “what size will my shape be after it is heated in the oven?” or the converse question, “if I want my shape to be a certain size after I heat it (say for a necklace), then what must the initial size be?” This project connects well with science, setting up discussions about the impact of heat on the plastic and why certain writing utensils are or are not suitable for use (e.g., oily or waxy items such as crayons melt with the high heat). Ratio, proportions, and scaling are challenging concepts for middle school students, yet crucial ones that form the basis for understanding lines, and hence algebra. This activity helps deepen students understanding in a fun, informal setting.

### 1.2 Sample Activity - Open-Ended Exploration

An instructor writes the numbers from 1 to 100 on the board. Students select any two of the numbers, erase them, and write on the board the sum plus the product of the two numbers. For example, if you erased 2 and 5, the sum plus the product is 7 plus 10, or 17, and so you write a 17 on the board. Now there are two 17s, but that is okay. The class repeats this process of selecting two numbers and replacing them with their sum plus their product. The question is then posed to the class, “What are the possible outcomes?” The mathematical question in this exploration is intentionally open-ended; the point is not to get the “answer” but rather to question, probe, and explore the rich mathematics that arises. In addition, while working on the posed question students have plenty of time to practice their mathematical content skills, as they sum and multiply multiple numbers over the course of the lesson.

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Wiegers, B., White, D. (2016). The establishment and growth of Math Circles in America. In: Zack, M., Landry, E. (eds) Research in History and Philosophy of Mathematics. Proceedings of the Canadian Society for History and Philosophy of Mathematics/La Société Canadienne d’Histoire et de Philosophie des Mathématiques. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-46615-6_17

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