A model for division of fractions using money as manipulative material is presented. Eight levels are described, ranging from the development of language and concept introduction through types of problems to rule discovery and application. (MNS)

Ways are presented to help students develop precomputational fraction concepts and skills using a circular-region or "pie" model. (MK)

A study documented 10 college students' understanding of the limit concept and the factors affecting changes in that understanding. Encouragement by the researchers for the students to change their common informal models of limit to more formal conceptions were met with extreme resistance. (Author/JJK)

Reviews the history of the concept of function, looks at its relationship with other sciences, and discusses its use in the study of real world situations. Discusses the process of constructing mathematical models of function and emphasizes the importance of the roles of the numerical, graphical, and algebraic representational forms. (MDH)

Presents an approach to the concept of absolute value that alleviates students' problems with the traditional definition and the use of logical connectives in solving related problems. Uses a model that maps numbers from a horizontal number line to a vertical ray originating from the origin. Provides examples solving absolute value equations and…

Applies the Lesh Translation Model to develop conceptual understanding by showing relationships between five modes of representation proposed by Lesh to learn multiplication of fractions. Presents five teaching activities based on the translation model. (MDH)

Probability theory can be developed from a theoretical or experimental probability approach. The problem, "The Gambler's Ruin," is used to study whether students are naturally sensitive to learning probability from an experimental probability approach through simulations. Results indicated that use of simulations can contribute to…

Presents a sequence of hands-on activities to help students understand the concept of arithmetic mean and gain experience in using mathematical models. Students create models in the process of solving problems and communicate to the class the meaning attached to the models. (MDH)

Presents activities to visually explore the algebraic concepts of variable, constant, the distributive property, and combining like terms. Presents four transparencies that use visual models to understand exercises in students perform the same mental calculations on a number of their choice and obtain the same result. (MDH)

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)

Described is a game that is used to introduce the concept of multiplying integers. Serving as a physical model for the concept, "Froggie Frolic" races frogs along a number line by moves that indicate direction, magnitude, and number of jumps, thus modeling integer multiplication. A teacher's guide and worksheets are provided. (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)

Presents activities that use visual-geometric models to help students develop their understanding of exponents and division of powers with the same base. Presents opportunities for students to discover patterns for themselves and communicate these findings to others. (MDH)

"Seeing Fractions" is an instructional unit for teachers in California that was trial tested in about 30 classrooms, grades 4 through 6 with diverse student populations, and designed to help students become aware of the variety of ways in which fractions are commonly used. The Introduction includes an overview of fractions and what…