The knowledge and mental processes called on in mathematics can be used to improve composition. Three desirable requirements of an analogy to be used in teaching writing are that it should bridge the art of writing and science, should be readily accessible to the mind of the average student, and should allow the student to employ an architectural…

How children can be guided to see and feel the power of thinking with and about mathematical symbols is discussed. A strategy to help them bridge the gap between manipulative models and symbols is detailed. (MNS)

Helping children to bridge the gap between physical materials and symbolic representations is the focus of this article. Examples are drawn from numerical topics, with several hierarchies illustrated. (MNS)

A variety of tips about problem solving are included, with the focus on helping students recall an image. Manipulative materials and models using grids are included in most of the activities. (MNS)

The need to provide understandable problems and ways to help children understand problems are explored. An interview with a sixth grader depicts his incorrect strategies and leads to suggestions for teaching problem solving using a range of mathematical models for each operation. (MNS)

The concept of multiplication is described and illustrated using several different representational systems. A conceptual approach to teaching mathematics is compared with the procedural approach commonly found in the school curriculum. Four different methods of representing the multiplication process with numbers larger than ten are presented:…

Concrete experience should be a first step in the development of new abstract concepts and their symbolization. Presents concrete activities based on Hyde and Nelson's work with egg cartons and Steiner's work with money to develop students' understanding of partitive division when using fractions. (MDH)

Discusses area models that can be used in grades three through nine, showing how the model generalizes from discrete situations involving the arithmetic of whole numbers to continuous situations involving decimals, fractions, percents, probability, algebra, and more advanced mathematics. (14 references) (MDH)

Described is the use of story telling as a context to introduce mathematical concepts by providing a model, offering problem-posing situations, stimulating investigation, and illustrating concepts. Examples of appropriate stories are given for the primary and low secondary levels. (MDH)

Discusses the potential that school mathematics has for being a source of exploration and discovery for students and teachers. Provides a process-oriented definition of understanding mathematics. Presents activities in which students construct computer and actual models of polyhedra and make conjectures regarding a medical research application of…