Four algorithms for subtraction are described: borrow and pay back,'' equal additiions, shopkeepers' subtraction,'' and decomposition. (DT)

Using negative digits in writing numerals and in calculation is explained. This is the second article in the series; for the first, see Vol. 1, No. 7, Nov., 1972, pp. 8-9. (DT)

A discussion of the various algorithms used for multiplication. Repeated addition, arrays, the distributive law, Egyptian and Russian Peasant Multiplication, Gelosia, Napier's Rods and Genaille's Rods are all described, and examples of multiplying using each method are explained. (DT)

Two alternatives are given to the decomposition and equal addition subtraction algorithms. (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)

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

The author presents and elaborates on a division algorithm devised by his 9-year-old son. (MK)

The importance of place value is discussed. Examples illustrating place value in addition and subtraction are given. (MK)

Describes a research project designed to monitor the transition from work based on concrete materials to the more formalized aspect of mathematics found in secondary schools. The topic of subtraction was chosen by three teachers who were involved in the investigation. (PK)

It is suggested that the reasons for teaching the standard written algorithms for calculations are not out of date. Alternative algorithms, such as mental algorithms, calculators, and nonstandard written methods, are discussed. (MP)

Basic computational problems admit several different solution algorithms. A student's choice of method may be related to personal characteristics which also bear on his ability to learn other mathematical techniques and theories. (SD)

Describes activities in a mathematics class for six-year-olds. The article makes several points, including: working independently is very absorbing; investigative work is as important as algorithms; and children working in groups can achieve more than even the brightest child working alone. (PK)

In spite of current sentiment to the contrary, the wellsprings of mathematics are not utility and relevance, but creativity, imagination, and an appreciation of the beauty of the subject. This has implications for the teaching of mathematics. (PK)

The first aim in school might be to help children become more aware of the algorithmic processes they use; then, ensure that they can devise algorithms and define them. Many examples of how these aims can be met are given, including the use of calculators and computers. (MNS)

Algorithmic and investigative approaches to mathematics are compared and discussed. Their mutually contradictory spirit is explored. Examples of the application of each method to a mathematics problem are presented. (CW)