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)

Suggests that issues surrounding the teaching of algorithms focus not on whether to teach them but rather on balancing and connecting the development of algorithmic thinking. Presents an approach to help students develop their algorithmic thinking. Contains 18 references. (ASK)

Defines psychic intelligence as an inclination all children possess to use whatever cognitive intelligence they have for learning, adaptive behavior, and pleasure; strongly suggests that algorithmic drill usually damages the mentality of children by stifling psychic intelligence; and discusses the use of pocket calculators to prevent this effect.…

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

A real world sample of actual data that students can use to see the application of the Hardy-Weinberg law to a real population is provided. The directions for using a six-step algorithmic procedure to determine Hardy-Weinberg percentages on the data given are described. (KR)

A strategy to make the transition from manipulative materials to a written algorithm for division is outlined in dialogue form. (MNS)

The following ideas are shared: (1) a low-stress subtraction algorithm that eliminates the traditional borrowing process, and (2) an approach to graphing circular functions that looks at the process of modifying simple functions as a series of shifting, sliding, and stretching adjustments, with its biggest advantage viewed as its generality. (MP)

The author feels teaching division of fractions is worthwhile because it will help students understand other algorithms. (MK)

Three short essays provide teaching suggestions for lessons on base two, order of operations, and ratios used to motivate a number of mathematical ideas. (MK)

The first section promotes use of student notebooks in mathematics instruction as incentives for pupils to do daily work. Part two looks at a geometric interpretation of the Euclidean algorithm. The final section examines an open box problem that is thought to appear in virtually every elementary calculus book. (MP)

An unusual algorithm for approximating square roots is presented and investigated using techniques common in algebra. The material is presented as a tool to interest high school students in the logic behind mathematics. (MP)

Topics covered include alternate methods for finding LCM and GCF, imaginative word problems, and a primes-breakdown method of factoring quadratics. (MP)

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)

A model of the division algorithm is described which relates step-by-step to the standard algorithm. Use of the model in instruction requires the distribution of a special worksheet. The focus of the instruction is on students sharing some amount of money equally among several friends. (MP)