Matrices occupy an awkward spot in a typical algebra 2 textbook: sandwiched between solving linear systems and solving quadratics. Even teachers who do not base their course timeline and pacing on the class textbook may find a disconnect between how matrices are taught (procedurally) and how other topics are taught (conceptually or with real-world…

Often, students who solve fraction tasks respond in ways that indicate inadequate conceptual grounding of unit fractions. Many elementary school curricula use folding, partitioning, shading, and naming parts of various wholes to develop children's understanding of unit and then nonunit fractions (e.g., coloring three of four parts of a pizza and…

For centuries, the basic operations of school mathematics have been identified as addition, subtraction, multiplication, and division. Notably, these operations are "basic," not because they are foundational to mathematics knowledge, but because they were vital to a newly industrialized and market-driven economy several hundred years…

In this article, Lorraine Jacob and Joanne Mulligan discuss how arrays can be used to promote students' early learning in relation to multiplication and division. They provide examples of activities that can be used from Foundation to Year 5.

Arguing that mathematics is a form of communication that students need help in understanding, this article describes a set of seven simple interactive LogoWriter tools that can be used to help children explore the language of multiplication. Examples of the use of graphics in responding to children's commands are provided and several exercises are…

Discusses an approach to teaching multiplication that establishes an association between what is learned and what is already known. Notes that this technique recognizes the qualities of a set of facts has in common, applies this knowledge to the grouping of facts, presents a visual illustration of the multiplication table, and offers an…

Describes a technique from Japan, the lesson study, where teachers study ways of teaching one lesson for several hours while focussing on the concepts of multiplication and division. (ASK)

Students who can compute mathematical problems in their heads have learned a skill that is important for estimating and for understanding the number system. Practice activities that can help students master mental computation skills are described. (PP)

Describes the psychological analysis of the instruction of the concept of multiplication in the former Soviet Union. Presents a system of instructional situations in introducing multiplication and the main results of instruction for grade two. (MDH)

Investigates the arithmetic curiosity that when any integer is raised to the fifth power, the digits unit of the result is always the same as the digits unit of the original number. Explores results in number bases other than 10 via the computer. (PK)

Provides a bibliography of children's literature exploring mathematical concepts: classification; place value and numeration systems; counting, addition, and subtraction; multiplication and division; fractions; estimation; big numbers; geometry; measurement; and games and puzzles. Highlights one book for each concept, suggests class activities,…