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)

Performance assessment, a method that makes possible the assessment of multiple dimensions of students' progress, including dispositions, is described. Criteria for good performance tasks are given, and their structure is illustrated through an example. A list of 10 dispositions toward mathematics and a self-evaluation group-performance rating…

The "positive-negative charge" model is described and demonstrated with all four operations on integers. Its major advantages are that it is both concrete and complete. (MNS)

Presents a program to introduce fifth graders to everyday economic life by constructing a true-to-life simulation of an economic community. Students apply mathematics skills to managing a checking account, calculating electric bills, and managing shops using computers. (MDH)

Arrays are seen as excellent models for beginning multiplication examples, but that they are often put aside by teachers when they become unwieldly for greater factors, possibly depriving learners just when they need the help. The use of grids made on paper marked in squares is suggested. (MP)

A fifth- and sixth-grade project is described that requires each student to build a bridge to specified dimensions using only specified materials. (MK)

Discusses: (1) different types of learning (concepts, properties, facts, procedures, algorithms, skills, and problem solving); (2) types of learning behaviors; and (3) types of representational models, considering concreteness, meaningfulness, and manipulation (active manipulation, passive manipulation, and nonmanipulation). (JN)

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)

A model of the division algorithm is described which relates step-by-step to the standard algorithm. Use of the model in instruction requires the distribution of a special worksheet. The focus of the instruction is on students sharing some amount of money equally among several friends. (MP)

Money models that can be used in a group-instruction mode and a shorthand notation that allows students to demonstrate their ability to count out change by a written procedure are described and discussed. (MK)

A model that can be effectively used to develop the notion of function and provide varied practice by using "real world" examples and concrete objects is covered. The use of Popsicle-sticks is featured, with some suggestions for tasks involving functions with one operation, two operations, and inverse operations covered. (MP)

Use of prepartitioned models is proposed to help students construct a meaningful concept of fractions. Partitioning, geometric shapes as fractional models, concepts related to successful partitioning, and other benefits from partitioning experiences are discussed. Sample activities are suggested. (CW)

Discusses ways to simulate a probability problem of interest to middle school students in which students calculate the average number of packets of trading cards purchased to obtain a complete set of cards. Simulations utilize a spinner, a table of random numbers, and a computer. Includes the BASIC program utilized in the simulation. (MDH)

The design, selection, and organization of instructional materials that integrate calculators are described in relation to a model based on movement and representational level. Instructional resources and advantages of the model are described. (MNS)

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