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,…

Learning mathematics has traditionally been thought of as a sequential progression. Children learn to count to 10, then to 20, and then to 100. They learn to add without regrouping and then with regrouping. The authors teach addition before multiplication and the two-times table before the six-times table. They usually teach division as a separate…

This study investigated the development of children's knowledge of many-to-one counting. Four-year-olds ("n" = 51) either participated in a training or in a control group. The training taught children how to allot "Y" physically not present items to each of "X" objects and how to count these items in the process. It…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

This article describes how the story of Alice in Wonderland helps students understand the operation of multiplying by a rational number less than 1 and related aspects of ratio and proportion. Included with this article is a "How Tall Is Alice?" Worksheet. (Contains 1 table and 6 figures.)