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)

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…

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

The role of division of whole numbers in problem solving and the implications for teaching division computation are examined. Deleting the teaching of division facts, and obtaining solutions by using multiplication facts, is advocated. (DT)

A study to determine if "random" or "careless" errors in multiplication made by individual students take on discernible patterns is described. Implications for teaching are discussed. (MK)

A case is given against teaching division of fractional numbers. Types of problems usually solved by division are solved by methods involving only multiplication. (JP)

Instructional sequences are presented for teaching two-digit multiplication and division with one- and two-digit divisors using a base-oriented approach. (MN)

Ways to combine the strengths of teacher and computer are suggested. Multiplication concepts and an algorithm for multiplication are taught in the same lessons. The computer is used as an electronic chalkboard to teach at a semiconcrete level. The computer program is included. (MNS)

A modern adaptation of the historic lattice algorithm which can be used for multiplication and division is discussed. How it works is clearly illustrated. (MNS)

An example of a lesson involving calculators that focused on calculator use is given. An examination of the traditional algorithm by the students led to student-directed investigations. (MP)