There are but few serious questions today about the theoretical value of meaning theory in teaching arithmetic. A previous article in THE ARITHMETIC TEACHER1 clearly states the case for meaning in arithmetic. However, previously reported research deals primarily with transfer of learning, retroactive inhibition, and drill. Relatively few leads have been provided for teachers interested in specifics such as, “What methods do I use in presenting division?” or “Just how does one use manipulative materials?”
Division of whole numbers is a relatively complicated computational process. It is complicated because it involves each of the other processes: addition, multiplication, and subtraction, and also includes principles unique to division alone. Thorough understanding of division is dependent upon knowledge and understanding of the interrelationships between the four processes—addition, subtraction, multiplication, and division. Following are the understandings commonly made explicit.
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