Discussed the use of Cuisenaire rods in teaching the multiplication of fractions. Considers whole number times proper fraction, proper fraction multiplied by proper fraction, mixed number times proper fraction, and mixed fraction multiplied by mixed fractions. (JN)

This article discusses the algorithm for multiplication that is referred to as lattice multiplication. Evidence of how the author's preservice students' conceptual understanding of the algorithm grew through the semester is given. In addition, the author extends the conceptualization of the algorithm from the multiplication of whole numbers to the…

Everyone knows that teachers do not have unlimited time, a log of experience, or a deep understanding of all the mathematics they teach. To solve this problem, teachers often use textbooks, and the accompanying teacher's resource books, as sources of activities and advice about how to help students learn mathematics. The activity that prompted…

Multiplication, division and fractions are "hotspots" for students in the middle years with many students experiencing difficulty with these concepts. Arrays effectively model multiplication and help children develop multiplicative thinking and learn multiplication facts. In this article the authors show how an open-ended array problem…

Discussed is the topic of least common multiple (LCM), a rationale for its importance, and suggestions for when and how to teach it. (RH)

Discusses a number series made from the multiplication of numbers to digits. Presents a number series for diverse multiplication numbers. (YP)

Describes a teaching experiment examining the possibility of the redefinition of a multiplication problem from a problem of remembering, to a problem of figuring out why arithmetic rules make sense. (YP)

A four-day exploration of mathematics provides a learning opportunity for students to practice number sense, multiplication and division skills. The students designed the gardening theme to explore the topic of multiplication using the array model, and see the application of mathematics to their everyday life.

Reviews the author's research on students' conceptions of mathematics and suggests ways to overcome or prevent misconceptions. (MP)

Discusses arithmetic during long-multiplications and long-division. Provides examples in decimal reciprocals for the numbers 1 through 20; connection with divisibility tests; repeating patterns; and a common fallacy on repeating decimals. (YP)

Describes how five-year-old children responded to the investigation of looking for patterns in a multiplication square. Provides a 10 x 10 multiplication square for the investigation. (YP)

Describes the basic and exceptional calculation abilities of a calculating prodigy whose performances were investigated in single- and multi-digit number multiplication, numerical comparison, raising of powers, and short-term memory tasks. Shows how his highly efficient long-term memory storage and retrieval processes, knowledge of calculation…

This article explores children's responses to a task that requires them to represent square units in a grid pattern, and highlights the importance to a child's mathematical development of recognizing pattern and structure. The grid task explores children's imagery association with area measurement, and provides clear evidence of students'…

Discusses the generalization of the meaning of multiplication for whole numbers. Presents an example for multiplication of fractions. Provides several diagrams to help improve understanding. (YP)

This article presents a teaching experiment on the relationship between informal out-of-school and formal in-school mathematics, and the ways each can inform the other in the development of abstract mathematical knowledge. This study concerns the understanding of some aspects of the multiplicative structure of decimal numbers. It involved a series…