The Mathematical Association of America

Abstract

s and Biographies of Speakers The Mysterious Arithmetic of Lexicographic Codes John H. Conway, Princeton University The Mathematical Association of America Integral lexicographic codes are very simply defined (by a “greedy algorithm”), but have strange arithmetical properties that are hidden in a theorem I call “The Lexicode Theorem.” I'll tell you what the theorem says, and together we'll puzzle out what (if anything) it means. New Jersey Section Spring Meeting Rutgers University New Brunswick, NJ Saturday, March 27, 2004 2 John H. Conway is John von Neumann Distinguished Professor of Mathematics at Princeton University, NJ. Born in Liverpool, England, he received his education at the University of Cambridge and then taught at Cambridge for many years before joining the Princeton faculty in 1986. Conway is the author or co-author of at least ten books, and of many expository articles which have had substantial impact not just on research mathematicians but on mathematical amateurs as well. Conway has a rare gift for naming mathematical objects, and for inventing useful mathematical notations. He is widely known for his discovery of surreal numbers, the Conway group, and for inventing the Game of Life. Conway is a Fellow of the Royal Society, a Member of the American Association for the Advancement of Science, and recipient of the Berwick Prize of the London Mathematical Society (1971), Polya Prize of the London Mathematical Society (1987), Frederic Esser Nemmers Prize (1999), Leroy P. Steele Prize of the American Mathematical Society (2000), and Joseph Priestley Award (2001). He received an honorary doctorate from the University of Liverpool on July 4, 2001. Designing the Pre-service Teacher Curriculum to Better Meet the Needs of Our Future Teachers Mercedes McGowen, William Rainey Harper College David Ausubel claimed that “the single most important factor influencing learning is what the learner already knows. Ascertain this and teach him accordingly.” How do we determine what a student already knows and then use the evidence of learning that we collect to improve our teaching and student learning? What classroom experiences foster the development of mathematical thinking—pattern recognition, generalization, abstraction, problem solving, careful analysis, rigorous argument and flexible thinking? Designing a curriculum that builds on students’ prior knowledge to develop these skills effectively and at appropriate levels for all students is one of the biggest and most important challenges we face. To address these questions, we will analyze some mathematical tasks that illustrate how mathematical