Delving Deeper – Cyclical Products: The Last Shall Be First

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“Delving Deeper” offers a forum for classroom teachers to share the mathematics from their own work with the journal's readership; it appears in every issue of Mathematics Teacher. Manuscripts for the department should be submitted via For more background information on the department and guidelines for submitting a manuscript, visit

Contributor Notes

Mark A. Hugen,, is an associate professor of mathematics at Cerritos College in Norwalk, California. He serves as a mentor to future secondary school mathematics teachers in the Cerritos College Teacher TRAC program.

Gerald E. Gannnon,, is a professor of mathematics at California State University at Fullerton, where he directed the department's innovative master's program for teachers for more than thirty years. A former high school teacher and coach, he has been involved with many institutes for K–12 teachers of mathematics.

Harris S. Shultz,, is a professor of mathematics emeritus at California State University at Fullerton. He is the author of numerous published papers and has been a speaker at many conferences and colloquia.

(Corresponding author is Hugen author is Gannnon author is Shultz
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