Surreal Numbers


Book Description

Nearly 30 years ago, John Horton Conway introduced a new way to construct numbers. Donald E. Knuth, in appreciation of this revolutionary system, took a week off from work on The Art of Computer Programming to write an introduction to Conway's method. Never content with the ordinary, Knuth wrote this introduction as a work of fiction--a novelette. If not a steamy romance, the book nonetheless shows how a young couple turned on to pure mathematics and found total happiness. The book's primary aim, Knuth explains in a postscript, is not so much to teach Conway's theory as "to teach how one might go about developing such a theory." He continues: "Therefore, as the two characters in this book gradually explore and build up Conway's number system, I have recorded their false starts and frustrations as well as their good ideas. I wanted to give a reasonably faithful portrayal of the important principles, techniques, joys, passions, and philosophy of mathematics, so I wrote the story as I was actually doing the research myself."... It is an astonishing feat of legerdemain. An empty hat rests on a table made of a few axioms of standard set theory. Conway waves two simple rules in the air, then reaches into almost nothing and pulls out an infinitely rich tapestry of numbers that form a real and closed field. Every real number is surrounded by a host of new numbers that lie closer to it than any other "real" value does. The system is truly "surreal." quoted from Martin Gardner, Mathematical Magic Show, pp. 16--19 Surreal Numbers, now in its 13th printing, will appeal to anyone who might enjoy an engaging dialogue on abstract mathematical ideas, and who might wish to experience how new mathematics is created. 0201038129B04062001







My Very First Book of Shapes


Book Description

Can you find what is round? What is square? In this timeless new split-pageboard book, children can find the bottom half of a page that matches the top half. Find the right pairs, and you will learn to identify all kinds of shapes. From dome-shaped ladybugs to diamond- shaped kites, this clever board book makes learning fun.




A Letter from Your Teacher


Book Description

From the author and illustrator of Our Class is a Family, this touching picture book expresses a teacher's sentiments and well wishes on the last day of school. Serving as a follow up to the letter in A Letter From Your Teacher: On the First Day of School, it's a read aloud for teachers to bid a special farewell to their students at the end of the school year. Through a letter written from the teacher's point of view, the class is invited to reflect back on memories made, connections formed, and challenges met. The letter expresses how proud their teacher is of them, and how much they will be missed. Students will also leave on that last day knowing that their teacher is cheering them on for all of the exciting things to come in the future. There is a blank space on the last page for teachers to sign their own name, so that students know that the letter in the book is coming straight from them. With its sincere message and inclusive illustrations, A Letter From Your Teacher: On the Last Day of School is a valuable addition to any elementary school teacher's classroom library.













Papers and Addresses


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Number Sense Routines


Book Description

Just as athletes stretch their muscles before every game and musicians play scales to keep their technique in tune, mathematical thinkers and problem solvers can benefit from daily warm-up exercises. Jessica Shumway has developed a series of routines designed to help young students internalize and deepen their facility with numbers. The daily use of these quick five-, ten-, or fifteen-minute experiences at the beginning of math class will help build students' number sense. Students with strong number sense understand numbers, ways to represent numbers, relationships among numbers, and number systems. They make reasonable estimates, compute fluently, use reasoning strategies (e.g., relate operations, such as addition and subtraction, to each other), and use visual models based on their number sense to solve problems. Students who never develop strong number sense will struggle with nearly all mathematical strands, from measurement and geometry to data and equations. In Number Sense Routines, Jessica shows that number sense can be taught to all students. Dozens of classroom examples -- including conversations among students engaging in number sense routines -- illustrate how the routines work, how children's number sense develops, and how to implement responsive routines. Additionally, teachers will gain a deeper understanding of the underlying math -- the big ideas, skills, and strategies children learn as they develop numerical literacy.




American Medicine


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