Author Pam Harris argues that teaching real math--math that is free of distortions--will reach more students more effectively and result in deeper understanding and longer retention. This book is about teaching undistorted math using the kinds of mental reasoning that mathematicians do. Memorization tricks and algorithms meant to make math…

In this note we demonstrate two instances where matrix multiplication can be easily verified. In the first setting, the matrix product appears as matrix element concatenation, and in the second, the product coincides with matrix addition. General proofs for some results are provided with a more complete description for 2×2 matrices. Suggested for…

The authors have found that having students learn accessible standard algorithms by explaining them using mathematics drawings increases students' sense of place--value numbers and enables students to articulate their understanding of what is actually happening with the numbers and why. In this article, they will discuss three standard algorithms…

Describes strategies for teaching elementary students to solve a multiplication problem using the lattice method. (JOW)

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

Discusses an algorithm from Vedic mathematics that has similarities to FOIL and the standard algorithm for multiplication. (Author/NB)

Difficulty levels of 168 randomly generated multiplication problems were obtained by testing 238 fifth-graders. Variables concerning the number of operations, digits carried, and magnitude of the digits were defined, and a least-squares procedure was used to construct structural models accounting for 60-70 per cent of observed problem difficulty…

The author advocates the classroom consideration of new algorithms as a means of leading students to make original hypotheses. He discusses a multiplication algorithm based on the differences between squares. (SD)

A discussion of the various algorithms used for multiplication. Repeated addition, arrays, the distributive law, Egyptian and Russian Peasant Multiplication, Gelosia, Napier's Rods and Genaille's Rods are all described, and examples of multiplying using each method are explained. (DT)

An algorithm for multiplying natural numbers is described. The algorithm provides a chance for some unusual drill and might serve as an enrichment topic. (MK)

This study investigated two methods used to teach multidigit multiplication to fourth-grade students: the lattice method and the distributive method. Classes from four schools were randomly assigned so that the two treatment groups contained two each or urban, rural and inner city classrooms. A series of 15 lessons was prepared for each treatment…