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)

Examples are provided which demonstrate the use of the computer as an instructional aid for the algebra curriculum. While the basic content of an algebra course would remain intact, computer technology can enhance and expand methods of algebra instruction. (JN)

Some easy-to-state number properties are suggested as the subjects of proofs that are readily understood and interesting to pupils. (MP)

The creation of "false laws" of mathematics by many pupils as they attempt to rephrase new ideas and make them understandable and useful is discussed. The reasons for these mistakes and some ways teachers can help students adopt correct rules are reviewed. (MP)

The nature of the aptitude-treatment interaction between spatial visualization ability and instructional treatment in mathematics was investigated. No significant positive correlation was observed between the aptitude measures (spatial visualization test) and the outcome measures (algebra structures exam). (CJ)

Three teaching ideas are presented: (1) the use of "factor cards" to teach the concept of greatest common factor; (2) examples and tools used in student graphing in three dimensions; and (3) ways to use cuisenaire rods, cubes, and flats to discover binomial expansions. (MP)

The use of a "constructivist approach" in introducing the concept of equation in algebra is promoted and presented. (MP)

Special ways of using computers as a useful tool in algebra instruction are reviewed, with applications to linear equations featured. (MP)

The use of mathematical modelling as a systematic framework for solving word problems is presented. Applications for typical elementary algebra and calculus problems are featured. (MP)

Activities geared to reinforcing the skills involved in solving linear equations are given. The material is prepared on worksheets designed for duplication. Student use of calculators is suggested, and the material can aid in promoting mental computation and estimation. (MP)

Research to determine whether female and male students with comparable mathematics backgrounds will have comparable achievement patterns in algebra is presented. Sex differences discovered appear to have little to do with algebra, with further research recommended on pupil use of applied problem-solving skills. (MP)

Practical tips on the teaching of subtraction, addition and subtraction of fractions, and finding the vertex of a parabola are given. (MK)

A problem, motivated by the conversion of Fahrenheit to Celsius, is related to classical Diophantine equations. (MK)

Two problems are presented and discussed as a means of demonstrating that the calculator can play a more important role in the mathematics class than simply as a computational tool. (MP)

Three examples are given illustrating the use of the calculator in problems where determining patterns and making conjectures are stressed. (MP)