Abstract
A teachers of mathematics, we represent mathematics in the schools. It is an honor to have the responsibility to represent the ancient discipline of mathematics. We are also learners, and it is likely that we know and understand only a small percent of the vast universe of mathematical knowledge. The same statement applies, of course, to professional mathematicians. Throughout our lives, certainly our teaching lives, we will continue to learn more mathematics. The authors of the Professional Standards for Teaching Mathematics (NCTM 1991) use the section “Standards for the Professional Development of Teachers of Mathematics” to address the depth of our understanding of mathematics and the ways in which that understanding affects our teaching. I happened to learn more about mathematics because of a question that a student asked in class. This experience taught me that school-level mathematics has the potential for being a source of exploration and discovery for a professional mathematician. I found that there are many new things to learn and that it is exciting to learn along with my students.
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