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When discussing the mathematical knowledge of elementary school teachers, the National Council of Teachers of Mathematics concludes that teachers must have a deep understanding of mathematics and be able to easily draw on that knowledge with flexibility in their teaching tasks. Mathematics teachers must understand the big ideas of mathematics and be able to represent mathematics as a coherent and connected endeavor. This inquiry and exploration-based workbook has been designed as a tool for pre-service and in-service mathematics teachers to use as a guidebook for "doing mathematics" and exploring mathematics topics in depth. The lessons chosen for this text serve as a function-based approach that connects important topics in the secondary mathematics curriculum and act as a bridge to university-level mathematics. Whether used as a course text or for individual professional development purposes, this book should be approached from the standpoint of discovery and reflection about the significance of the selected topics. It is the authors' hope that the explorations contained within serve as vehicles for classroom discussion and presentation of mathematics topics, or as starting points for further investigation. Efraim P. Armendariz is a professor of mathematics at the University of Texas at Austin. His mathematical interests include noncommutative ring theory, development of educational programs addressing accessibility issues, and development of secondary mathematics teachers. He received a Ph.D. in Mathematics from the University of Nebraska-Lincoln in 1966. Mark L. Daniels is a clinical associate professor of mathematics and UTeach Natural Sciences at the University of Texas at Austin. His research interests involve the preparation of pre-service teachers and the incorporation of instructional methodology in mathematics courses taken by students seeking certification.