Mathematics

The object of this book is to show how visualization techniques may be employed to produce pictures that have interest for the creation, communication and teaching of mathematics. Mathematical drawings related to proofs have been produced since antiquity in China, Arabia, Greece and India but only in the last thirty years has there been a growing interest in so-called 'proofs without words.' In this book the authors show that behind most of the pictures 'proving' mathematical relations are some well-understood methods. The first part of the book consists of twenty short chapters, each one describing a method to visualize some mathematical idea (a proof, a concept, an operation,...) and several applications to concrete cases. Following this the book examines general pedagogical considerations concerning the development of visual thinking, practical approaches for making visualizations in the classroom and a discussion of the role that hands-on material plays in this process.

Student success in mathematics is dependent on focusing in class, practice, and the ability to verbally express mathematical thoughts. Write On Math is a program that engages secondary school mathematics students in on-going writing projects that will strengthen their focus, their mathematics, and their oral and written communication skills. The program teaches technical writing strategies while demonstrating seven different levels of note taking and dozens of strategies to improve the sentence structure of students' mathematical explanations. Today's curricula and extensive testing policies require students to supply written explanations as part of their answers. Write On Math will systematically teach students how to take better notes in math class. There is no better way to ensure you know something well than to have to teach it to somebody else, and the Write On Math program requires students to do exactly that--that is why it improves their mathematics as well as teaches them valuable communication and writing techniques not taught in Humanities classes. For teachers using the program, Write On Math will improve they way you, as a teacher, present material to your students in class and on your handouts For students using the program, the strategies will apply to college classes and to other disciplines in addition to mathematics.