|About the Book: Learning to Think Mathematically with the Rekenrek
This 50-page book provides teachers with the theoretical basis and practical knowledge to use a powerful mathematical model called the Rekenrek (also known as the Arithmetic Rack). The book helps teachers build on the remarkable intuitions and informal reasoning of students as they learn to see numbers within other numbers, to recognize powerful combinations of five and ten, to develop a rich sense of numbers between 0-20, to build a powerful set of intuitive strategies for addition and subtraction, and to memorize addition and subtraction facts with meaning.
The book begins with a thorough explanation of the background and rationale for using the Rekenrek. Teachers learn what makes the Rekenrek unique among other mathematical models and manipulatives, and how they make use of its innovative structure to foster student understanding and confidence with number operations.
There are 18 distinct lesson plans and activities in the book, ranging in both topic and grade level appropriateness. Students begin the book by engaging in activities that will help them develop cardinality -- the recognition of the one-to-one correspondence between the number of objects in a set, and the numeral we use to denote that grouping of objects. The book concludes with a series of four lessons that elaborate the connections between the Rekenrek and Cognitively Guided Instruction (CGI), perhaps the most important framework for developing meaning and proficiency in addition and subtraction known to mathematics educators. In between, students learn how to partition numbers, use groups of five and ten strategically, recognize doubles, and develop numerous simple, yet effective, strategies to help them complete addition and subtraction problems both accurately, and with meaning.
Each lesson contains specific objectives, background information necessary for each activity, and a detailed progression of steps that can be followed closely, or used as a springboard for teachers to expand the explorations.