The mathematics associated with division is discussed, working from a theorem for the real division algorithm. Real-world, geometric, and algebraic approaches are discussed, as are related topics. (MNS)

Two difficulties that students have in computing with fractions are idenfitied. Then a procedure is described, stressing the identity element, that resolves these difficulties and increases students' understanding and retention. (MNS)

Computational algorithms from American textbooks copyrighted prior to 1900 are presented--some that convey the concept, some just for special cases, and some just for fun. Algorithms for each operation with whole numbers are presented and analyzed. (MNS)

Discusses the use of manipulative materials to model operations and algorithms. Indicates that they clarify the several interpretations of each operation, establish a basis for correct mathematical language, and show why algorithms work. (JN)

Outlines various subtraction methods, such as the decomposition method, equal-addends method, and low-stress algorithm. Describes a subtraction method by addition of complements. Discusses the advantages and disadvantages of the method. (YP)

Renaming fractions with the dot method is described with illustrations. It can be used to introduce renaming at the manipulative level in a meaningful way prior to moving to a more abstract level where prime factorization will be involved. (MNS)

Two worksheets are given, outlining algorithms to help students determine the day of the week an event will occur and to find the date for Easter. The activity provides computational practice. A computer program for determining Easter is also included. (MNS)

A modern adaptation of the historic lattice algorithm which can be used for multiplication and division is discussed. How it works is clearly illustrated. (MNS)

The author argues that children not only can but should create their own computational algorithms and that the teacher's role is "merely" to help. How children in grades K-3 add and subtract is the focus of this article. Grouping, directionality, and exchange are highlighted. (MNS)

A "neat and general" divisibility algorithm for prime numbers is presented. Five illustrative examples are included. (MNS)

Presents an easy method for constructing magic squares from three-by-three to general squares. Provides a computer program generating odd-order magic squares. Six references are listed. (YP)

Prior studies indicate that, given time to develop their own algorithms, primary students will process multidigit addition or subtraction problems from left to right. Gives evidence to support that idea, describes methods of getting students to invent their own algorithms, and discusses advantages of child-invented procedures. (21 references) (MDH)

Compares the development of two students' understanding of addition and subtraction. One student's understanding is based on memorized rules and the other's on understanding the concept of place value. Discusses the effects of different goals for instruction and the importance of understanding place value. (MDH)