An attempt to introduce subtraction of negative integers early in the secondary school curriculum is described. The attempt was not successful, and several aspects of the experiment are discussed. (SD)

The teacher's guide for the third unit of this SMSG series covers the two chapters on number theory and on the integers. The overall purpose for each of the chapters is described, the prerequisite knowledge needed by students is specified, the mathematical development of each chapter is detailed, behavioral objectives are stated, and a time…

Examined were the effects of varying the number of practice problems in a programed unit on negative bases designed for high school students. A sample of 421 students from grades 9 through 12 was divided into three groups on the basis of amount of mathematics coursework completed. Students were given four pretests (numeration, arithmetic…

The third student text in this SMSG series of 14 covers the following topics from number theory: the division algorithm, divisibility, prime numbers, prime factorization, common divisors and common multiples, and properties of the whole number system. A second chapter discusses properties and operations with integers. For a special edition of this…

An instructional sequence in which number lines and beads are used to illustrate addition and subtraction of directed numbers is described. (SD)

Addition and subtraction of integers can be approached through the use of chips of two colors. (SD)

The author observes that checking the closure property is redundant for most number systems and therefore hard for students to understand. He defines several systems which are not closed, develops two concepts related to closure, and provides many related examples. (SD)

Hypothesizing that subtraction of (negative) integers requires formal operations, the author describes a study of children's understanding of related concepts. The study involves the use of apparatus embodying properties of the number line. (SD)