For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards…

Engaging students in worthwhile learning requires more than a knowledge of underlying principles of good teaching. It demands considerable practice as well as images of what good teaching in particular situations and for particular purposes might look like. This volume provides these images. These cases were written from authentic, unrehearsed…

This article describes the positive impact of Montessori manipulative materials on four seventh grade students who qualified for academic intervention services because of previous low state test scores in mathematics. This mathematics technique for teaching multi-digit multiplication uses a placemat-sized quilt with different color-coded squares…

"Concept study" is described in this article as a collaboration of teachers to investigate images, analogies, metaphors, exercises, and other experiences that are used to support students' understandings of concepts. The discussion is illustrated with the examples of multiplication and prime numbers. (Contains 3 figures.)

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

The strategies for learning multiplication concepts are discussed. The strategies involve introduction of the multiplication concepts through problem solutions with linkage between new concepts and prior knowledge, provision of concrete experiences and semi-concrete representations prior to purely symbolic notations, explicit teaching of the rules…

This article presents an alternative to the traditional method of multiplying polynomials, FOIL. The method can be used with any size of polynomial.

It is not often that one can introduce primary school students to a problem at the forefront of mathematics research, and have any expectation of understanding; but with magic squares, one can do exactly that. Magic squares are an ideal tool for the effective illustration of many mathematical concepts. This paper assumes little prior knowledge on…

Provides an alternative to traditional instruction in multiplication and division to develop computational fluency in students. (Author/NB)

In this article, the author presents an innovative approach to teaching multiplication facts for children in middle school or younger. After introducing the dangers of some contradictions that persist, relating a brief summary of related research and guidelines regarding math facts and their relation to strategic approaches to more complex math,…

Learning mathematics has traditionally been thought of as a sequential progression. Children learn to count to 10, then to 20, and then to 100. They learn to add without regrouping and then with regrouping. The authors teach addition before multiplication and the two-times table before the six-times table. They usually teach division as a separate…

Discusses the interpretation given to the multiplication symbol ("x") in elementary school textbooks, the meaning of multiplication, and how it should be introduced to children. Also considers several aspects of multiplication, including: (1) equal steps on a line; (2) the array; (3) equal groupings; and (4) allocation (rate). (JN)

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…

Offers practical suggestions to help children learn their multiplication tables. (Author/CCM)

In this note, using the method of undetermined coefficients, we obtain the power series for exp ( f ( x )) and ln ( f ( x )) by means of a simple recursion. As applications, we show how those power series can be used to reproduce and improve some well-known results in analysis. These results may be used as enrichment material in an advanced…