Connecting History to Secondary School Mathematics

David J. Carrejo is an Associate Professor of Mathematics Education at the University of Texas at El Paso (UTEP). An award-winning educator, he received the prestigious University of Texas System Regents' Outstanding Teaching Award in 2015. He previously served as the Associate Dean of Undergraduate Studies and Educator Preparation in the UTEP College of Education. Dr. Carrejo's extensive teaching experience spans from high school algebra and pre-calculus to a wide range of undergraduate, graduate, and doctoral courses in mathematics education. His teaching includes pre-service elementary and middle-school math and science methods, as well as the history and philosophy of mathematics and science. In addition to his academic work, he has conducted professional development for practicing teachers, focusing on integrating math and science in elementary and middle school curricula, instructional design, and aligning curricula with state and national standards. His research explores teaching and learning analytic geometry, the history and philosophy of mathematics in mathematics education, and student learning progressions. David Dennis, holds a Ph.D. in Mathematics Education from Cornell University; he studied mathematics education with Jere Confrey, logic and the history of mathematics with Anil Nerode, and social history with David Sabean. His specialty is the history of mathematics, focusing on the early modern period, 1600-1750, and the uses of history in mathematics education. Dr. Dennis formulated a widely accepted theory concerning the uses of history in curriculum development, which is the basis for this book. This theory is was originally published as a chapter in the Handbook of Research Design in Mathematics and Science Education. Dr. Dennis’s publications have appeared in both mathematics and education journals, and as chapters in edited books. He created courses in both mathematics and the history of mathematics, especially designed for prospective teachers as part of the Partnership for Excellence in Teacher Education at the University of Texas at El Paso, part of the NSF program Model Institutions of Excellence. Susan L. Addington, Ph.D., is Professor Emerita of Mathematics at California State University San Bernardino, USA. After graduate work at Stony Brook University in arithmetic algebraic geometry, she focused on mathematics education, specifically teacher preparation, curriculum writing, and ethnomathematics. She has designed mathematics courses for prospective primary and secondary teachers, and taught mathematics courses at the undergraduate and graduate levels. Currently she is working on 21st century curriculum for first year college math courses for non-STEM students. Dr. Addington is co-author of the middle school curriculum IM 6-8 and, with David Dennis, Measuring the World: Math for Elementary and Middle School Teachers.

• 1. How Did We Get Here (and Where Should We Go)?.- 2. What Did Mathematicians in the 1600s Know?.- 3. Measuring the Immeasurable – Galileo and the Invention of Scientific Discovery.- 4. Flattening Apollonius.- 5. Euclid Fades Away – The Geometry of René Descartes.- 6. Algebra That Makes You Think -- The Code of John Wallis.- 7. On the Shoulders of a Giant -- The Rigorous Intellect of Isaac Newton.- 8. Gottfried W. Leibniz and the Future of Science.- 9. Coming Full Circle--The Science of Trigonometry and the Complex Numbers.- 10. Euler's Enduring Legacy -- From Practicality to Pedagogical Imperative.- 11. Reclaiming Mathematical Intentions -- Bridging History and the Modern Curriculum.