When the new programming language Pascal was developed in the 1970's, Walter Gander did not like it because because many features which he appreciated in prior programming languages were missing in Pascal. For example the block structure was gone, there were no dynamical arrays, no functions or procedures were allowed as parameters of a procedure,…

After briefly presenting possible origins for the use of the decimal system for counting and the duodecimal (base twelve) system for many measures, a notational scheme using six positive'' digits and six negative'' digits is presented. Examples and algorithms using this set of digits for operations with whole numbers, fractions, and in…

Instruction on properties of whole numbers, the meanings of operations on whole numbers, symbolic representation and algorithms for completing these operations is discussed. Many activities appropriate to each of these topics, and suitable for primary school children, are presented. (SD)

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)

PRODUCED AS PART OF A PROJECT FOR THE IMPROVEMENT OF CLASSROOM TEACHING, THIS BOOK DISCUSSES THE BASIC CONCEPTS AND OPERATIONS OF ARITHMETIC WHICH ARE TAUGHT TO ELEMENTARY SCHOOL STUDENTS. THE CONCEPT OF A SET IS USED THROUGHOUT AS A BASIS FOR EXPLANATION, AND THE DISCUSSION STRESSES WAYS BY WHICH STUDENTS CAN BE BROUGHT TO UNDERSTAND THE…

The theory of unary and binary operations are discussed and illustrated with examples from school mathematics. Presentations of selected inverse operations are made and attention is drawn to certain "typical" problems that occur during instruction and learning of these concepts. (MP)

The trick focuses on a theorem that the sum of the digits of the difference between any natural number and the sum of its digits is divisible by nine. Two conditions of using the trick are noted. The reason that the theorem works is established through a proof. (MP)

Students recognized as less successful individuals in mathematics are tested for their understanding of fractions. The data reveals that most were only able to apply remembered rules to problems without actually knowing if the rule worked for the given situation. (MP)

A teaching sequence for the division algorithm is detailed. (MP)

Forty-five children aged four-and-a-half to five-and-a-half years old were given number conservation tasks in three conditions: (1) a count condition in which children were helped to count each set after the transformation; (2) a match condition in which children were helped to connect by a string each animal with its peanut; and (3) the standard…