Synopsis
Teachers know the difficulties in motivating many students to develop the habits of mind and critical thinking skills necessary to thoroughly understand the concepts of calculus. The purpose of this book is to use Geometry Expressions software in order to facilitate and enhance the calculus syllabus by allowing students to ground calculus concepts in a geometric way. The 29 student explorations in this book cover the major topics of a standard course of calculus, and are completed with the help of the constraint-based dynamic software package, Geometry Expressions. Using Geometry Expressions in learning calculus, students have the opportunity to develop general investigation skills, make connections between geometric and algebraic representations of major calculus ideas, interpret analytic problems visually and geometric problems algebraically, and develop facility with using a computer to prove general mathematics statements. Geometry Expressions enables more extensive calculus investigation than is possible in a traditional course of calculus. Open-ended explorations and investigations reinforce students' intellectual development. Students appreciate challenges and enjoy taking ownership in the problem solving process. This book, together with Geometry Expressions enables the student to do just that.
About the Author
Irina Lyublinskaya is an associate professor of mathematics and science education at CUNY College of Staten Island, Staten Island, NY. She received her Ph.D. in Theoretical and Mathematical Physics from Leningrad State University and has published substantially in that field. She has taught at the university as well as the high school level for over 20 years. In recent years she has directed her professional endeavors to curriculum development and research in the area of integrating technology into mathematics and science education and to the professional development of mathematics and science teachers. Lyublinskaya is a recipient of the Radioshack/Tandy Prize for Teaching Excellence in Mathematics, Science, and Computer Science, the NSTA Distinguished Science Teaching Award and citation, the Education's Unsung Heroes Award for innovation in the classroom, and the NSTA Vernier Technology Award for innovative use of technology in the classroom. She has published multiple articles and 13 books about the teaching of mathematics and science. Valeriy Ryzhik is a mathematics instructor and curriculum supervisor at Lycee "Physical- Technical High School" in St. Petersburg, Russia. He received an Ed.D. in Mathematics Education from the Russian Pedagogic University, St. Petersburg. He has published 20+ books, including various mathematics textbooks for secondary schools and supplementary books for teachers. He has published over 50 articles on teaching mathematics in secondary schools and assessment. He has been awarded the title of Distinguished Master Teacher of the Russian Federation in 1998 and received the Russian Presidential Award for Teaching Mathematics in 2006. He was one of the first Russian educators to implement dynamic geometry software and computer algebra systems in teaching mathematics in Russia. Ron Armontrout is a mathematics teacher at the Hotchkiss School in Lakeville, CT. Ron has been a middle and high school mathematics teacher for over 30 years in public and private schools. Chosen as a Woodrow Wilson Fellow for the 1986 Mathematics Institute, Geometry in the Technological Age, at Princeton University, Ron has been involved in curriculum and writing projects ever since. He worked with TI to design TI Interactive! and TI Connect. He co-authored TI Interactive! Data Collection and Analysis, by Texas Instruments. Ron presented at numerous mathematics conferences, including over 30 national and regional NCTM conferences, regional and international T3 - Teachers Teaching with Technology conferences, the Exeter Academy Mathematics and Technology Conference, and the Peddie School Conference for Middle School Teachers. He also consults with public school systems to implement state standards.
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