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…

By the time they reach middle school, all students have been taught to add fractions. However, not all have "learned" to add fractions. The common mistake in adding fractions is to report that a/b + c/d is equal to (a + c)/(b + d). It is certainly necessary to correct this mistake when a student makes it. However, this occasion also…

An investigation is given of exceptions to the rule for adding fractions. The use of such exceptions in instruction is discussed. (MP)

A problem about minimum distance travelled on a route through ten cities is used as a means for giving students practice in addition and with problem-solving skills. (DT)

Computational algorithms appearing in early American arithmetic text are discussed. (SD)

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)

An activity that offers computational practice, pattern recognition, and the formulation of generalizations is described. (JT)

Presents activities involving the addition of antinumbers (which uses novel numerical characters); a puzzle which combines practice in working with polynomials and solving simple equations with intriguing facts about turkets; and searching for the number of different right triangles in a given square grid (which helps develop spatial…

A card game is described which gives students practice with adding integers and which also develops the concept of "opposite." (DT)