A random sample of 214 fourth grade students randomly assigned to two treatments completed 15 programmed lessons on multiplication of whole numbers. The treatments differed in the physical referent used in the programmed lessons. One group used an array as the physical referent (Repeated-Addition). The other used a coordinate system and ordered…

Fifteen answers are given by a third-grade class to the question, How can you find the answer for 7x8? The author concludes that a wide variety of experience is necessary to nurture children's wide diversity of learning capabilities. (Author/MP)

Monsters are used as an example to illustrate that multiplication of the natural numbers is associative. (JT)

This is the third in a series of articles on using mathematical techniques from history to provide an interesting way for middle graders to practice math. (Editor)

Assessment of effects of school principal involvement on acquisition of multiplication facts by 309 intermediate grade students found that taking the timed test three times per week resulted in consistent sustained gains and that a math game with the principal contingent on improved class performance was the most effective principal-initiated…

Early calculating methods and devices are discussed. These include finger products, the abacus, ancient multiplication algorithms, Napier's bones, and monograms. (MP)

Provides an alternative to traditional instruction in multiplication and division to develop computational fluency in students. (Author/NB)

Introduces addition, subtraction, multiplication, and division of fractions using area models such as rectangles and circles, or linear models such as the number line and fraction strips. (ASK)

Most people struggle to process information auditorily but this is often the way that it is taught. Presents a highly effective method for teaching multiplication that can be accessed at students' fingertips. (ASK)

Presents an activity on visualizing fingers for arithmetic, counting, and multiplication. (ASK)

Presents problem situations that support students when discovering the multiplication principle, permutations, combinations, Pascal's triangle, and relationships among those objects in a concrete context. (ASK)

In this article, the author presents an innovative approach to teaching multiplication facts for children in middle school or younger. After introducing the dangers of some contradictions that persist, relating a brief summary of related research and guidelines regarding math facts and their relation to strategic approaches to more complex math,…