In this article, Jason Taff shares an approach that he presented to advanced seventh-grade prealgebra students. He begins by summarizing some of the shortcomings of equating the order of operations concept with the PEMDAS (often rendered mnemonically as "Please Excuse My Dear Aunt Sally") procedure with the hope of helping teachers at…

In this article, a mathematics teacher educator presents an activity designed to pique the interest of prospective secondary mathematics teachers who may doubt the value of learning abstract algebra for their chosen profession. Herein, he contemplates: what "is" intended by the widespread requirement that high school mathematics teachers…

Subtractive magic triangles are discussed and questions raised for exploration with mathematics classes. Answers are also included. (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 use of two different colored beans or chips to represent positive and negative charges is discussed as a method of demonstrating operations with integers. (MP)

Several subtraction algorithms are analyzed to see if they involve borrowing. The main focus is on an analysis of a procedure called the residue method. The operational arithmetic which underlies the symbolic manipulations is examined and conditions where the method does and does not use borrowing are highlighted. (MP)

Discussed is a way of playing with numbers that leads to interesting results and provides well-disguised drill. (JP)

The author examines a well known number trick, in other number bases, and finds that equivalent results arise. (CT)

An algorithm is given for the addition and subtraction of fractions based on dividing the sum of diagonal numerator and denominator products by the product of the denominators. As an explanation of the teaching method, activities used in teaching are demonstrated. (MN)

A unique magic hexagon, which can be used to help improve students' computational skills, is presented. (JT)

A subtraction algorithm that does not involve borrowing is presented and called the residue method. It has been taught in junior and senior high school classes and preservice and inservice classes for teachers. The method has helped in classes where arithmetic in other bases is presented. (MP)

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

Programing a microcomputer to solve problems in whole-number arithmetic, rather than using the built-in operations of the computer, is described. Not only useful, it also enhances important mathematical concepts and is adaptable to a range of student abilities. (MNS)

Introduces a toy, the Educated Monkey, developed to help students learn multiplication tables and associated division, factoring, and addition tables and associated subtraction. Explains why the monkey works and reviews geometric, algebraic, and arithmetic concepts. (KHR)