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…

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)

The multiplication and division algorithms that are taught in German schools are presented. It is suggested that these algorithms may be better than standard algorithms in terms of development of useful concepts and processes. (MK)

Some techniques for developing the ability to multiply and divide by powers of ten with ease and understanding are presented. (Author/MK)

The time at which component skills are taught is studied to see whether it is a significant instructional variable. This research involved the instruction of a multiplication algorithm to 15 below-average first graders. (MP)

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)

An education major enrolled in a mathematics education course ponders confusing definitions of "multiplication" functions in dictionaries and in a handout on Euclid. This student teacher wants to teach elementary students what multiplication really is, not just impart an algorithmic skill. (MLH)

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)

An unusual way of using the long multiplication algorithm to solve problems is presented. It is conceptually harder, since it involves negative numbers but is easier to perform once mastered, since the size of the multiplication table required is smaller than the standard one. (MP)

Discusses mathematics education research on multiplication and division which implies that instruction should emphasize development of a sound conceptual basis for multiplication and division rather than memorization of tables and rules. Presents action research ideas. (10 references) (MKR)

Describes an informal research activity in which third grade students invent their own algorithms for multidigit multiplication and division. Discusses teaching implications and action research ideas. (ASK)

Programing a microcomputer to solve problems in whole-number arithmetic, rather than using the built-in operations of the computer, is described. Not only useful, it also enhances important mathematical concepts and is adaptable to a range of student abilities. (MNS)