The Joy of Following Students Down Unexpected Paths

Catherine Lane


As our students think and reason mathematically, sometimes we need to follow their paths, even if they are different than those we have anticipated they will take. Occasionally these unexpected paths can lead to surprising connections. In this article, the author describes new paths her class took to generalize the sum of the interior angles of convex polygons.

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Boyd, Cummins, Malloy, Carter, & Flores (2004). Geometry. New York: Glencoe Mathematics.

National Council of Teachers of Mathematics (2009). Focus in high school mathematics: Reasoning and sense making. Reston, VA: Author.

Ohio Department of Education (2010). Ohio’s new learning standards: Mathematics standards. Retrieved from

Polya, G. (2004). How to solve it: A new aspect of mathematical method. Princeton University Press.


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Copyright (c) 2017 Catherine Lane

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ISSN 2472-5986 (print)
ISSN 2472-601X (online)