Ancient Paradoxes Can Extend Mathematical Thinking

Have you ever thought about teaching mathematics through making connections to logic and philosophy? This article presents the Snail problem, a relatively simple challenge about motion that offers engaging extensions involving the notion of infinity. It encourages students in grades 5–9 to connect mathematics learning to logic, history, and philosophy through analyzing the problem, making sense of quantitative relationships, and modeling with mathematics (NGAC 2010). It also gives students of all ages a glimpse into the development of mathematics by introducing a reason to think about infinite convergent series.

Footnotes

Edited by Natasha Murray, Dr.NMurray@gmail.com, math educator and math teacher educator from New York. Readers are encouraged to submit manuscripts through http://mtms.msubmit.net

Contributor Notes

Jennifer A. Czocher, czocher.1@txstate.edu, is an assistant professor of mathematics education at Texas State University in San Marcos. She studies the impact of mathematical modeling tasks on students' mathematical thinking.

Diana L. Moss, mossdl@appstate.edu, is an assistant professor of mathematics education at Appalachian State University in Boone, North Carolina. She is interested in students' mathematical thinking and enjoys collaborating with teachers.

(Corresponding author is Czocher czocher.1@txstate.edu)(Corresponding author is Moss mossdl@appstate.edu)
Mathematics Teaching in the Middle School

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