A test for divisibility by any prime number is discussed and its proof is given. (MP)

Using various aspects of mathematical structure as unifying concepts is stressed. Specific examples are given based on the concept of equivalent fractions and on the addition property of equality. (LS)

The article presents a general test for divisibility that includes composite numbers and shows that such a test can be used to determine divisibility by several numbers simultaneously. (MK)

Suggestions for teaching the concept of division by zero are given. (MK)

The major portion of the article establishes the basis for the stated rule - to divide by a fraction, turn it upside down and multiply. With this background, three justifications for the rule are given. Several possible errors in students' use of the rule are noted. (LS)

Computational algorithms appearing in early American arithmetic text are discussed. (SD)

In this first of two articles, computational algorithms for multiplication and division which encourage use of one operation at a time are proposed. (DT)

Some techniques for developing the ability to multiply and divide by powers of ten with ease and understanding are presented. (Author/MK)

To introduce a third-grade class to division, a teacher prepared cards showing rectangular arrays from which some dots were missing; students used the remaining information to remake the cards. Related cards were used later in other activities to develop the repeated subtraction algorithm for division. (SD)

Five reports from a 2-year study are presented. Frequencies and descriptions of systematic errors in the four algorithms in arithmetic were studied in upper-middle income, regular, and special education classrooms involving 744 children. Children were screened for adequate knowledge of basic facts and for receiving prior instruction on the…