This article first describes some of the basic skills and knowledge that a solid elementary school mathematics foundation requires. It then elaborates on several points germane to these practices. These are then followed with a discussion and conclude with final comments and suggestions for future research. The article sets out the five…

In 1225 Fibonacci visited the court of the Holy Roman Emperor, Frederick II. Because Frederick was an important patron of learning, this visit was important to Fibonacci. During the audience, Frederick's court mathematician posed three problems to test Fibonacci. The third was to find the real solution to the equation: x[superscript 3] +…

A generalization of a well-known result for the arctangent function poses a number of interesting questions concerning the existence of integer solutions of related problems.

Flexible knowledge, knowing multiple approaches for solving problems, is a hallmark of expertise in mathematics. Frequently, the author writes, students memorize only one method of solving a certain kind of problem, without understanding what they are doing, why a given strategy works, and whether there are alternative solution methods. Comparison…

In this article, the author argues that coordinate geometry and all its trappings should be banned from key stage 2 in English schools. To explain why he makes such a strong statement, he discusses geometry problems tackled by the Ancient Greeks, showing how meaningful problem solving can occur without the use of coordinates and the corresponding…

This is a reprint of an address given at the Christmas National Council of Teachers of Mathematics (NCTM) meeting in 1958. It provides a critique of elementary instruction and discusses the changes necessary. It calls for fundamental change in the concept of mathematics teaching. (PDD)

An attempt is made to detail the nature of mathematics as perceived by mathematicians. Mathematics is viewed here as both abstract and an experimental science. The typical working mathematician is described as proceeding through problems with an attitude of discovery and examples of such an approach are given. (MP)

This discussion concerns itself with difficulties encountered by students in multiplication and concludes that when children understand a problem they can usually solve it. (MP)

Changes in the elementary and junior high school mathematics curriculum that have occurred in the last 20 years and that may occur in the future are discussed. (MK)

Quantitative literacy for students with deafness is addressed, noting work by the National Council of Teachers of Mathematics to establish curriculum standards for grades K-12. The standards stress problem solving, communication, reasoning, making mathematical connections, and the need for educators of the deaf to pursue mathematics literacy with…

This article argues that the reason the mathematics performance of students with mild disabilities is so limited is the mathematics. Using illustrations from subtraction, the article proposes number sense be a primary goal and that within the realm of number sense, big ideas be included among the dependent variables. (Contains references.)…

Many elementary and junior high school students do not become proficient with common and decimal fractions because they have established few connections between the form they learn in the classroom and understandings they already have. (Author/GC)

Suggests that the mathematics curriculum for young children can grow from children's literature. Examples given encourage children to use a variety of thinking skills including classifying, forming hypotheses, selecting strategies, and creating problems. (PK)

Describes Vygotsky's zones of proximal development, the importance of social interaction in learning through problem solving, and the benefits of modeling. Presents three implications for teaching and learning mathematics based on a teaching experiment focusing on these constructs. (MDH)

Illustrates and discusses one class of strategies to solve word problems referred to as "number-consideration strategies." Contrasts actions and goals of students who focus mainly on number considerations with those of students who focus mainly on problem understanding. (MDH)