Considering its relationships with real life and mathematics, mathematical modeling is one of the most effective ways of learning and teaching mathematics. In this study, the effect of teaching with mathematical modeling on students' mathematics achievement was examined using the meta-analysis method. An effect size of 51 was achieved with 45…

An approach is described for teaching formulation of mathematical models to undergraduates with no modeling experience. Instruction is based on observation of successful patterns of behavior. (MP)

Describes the instructional strategies and activities used to illustrate the essential features of mathematical modeling to a group of infant and junior high school teachers. The intent was to involve the group with some number work, elementary algebra, and some simple work on arrangements by way of tree-diagrams. (JN)

Models for division are discussed: counting, repeated subtraction, inverse of multiplication, sets, number line, balance beam, arrays, and cross product of sets. Expressing the remainder using various models is then presented, followed by comments on why all the models should be taught. (MNS)

Typical difficulties involved in solving combinatorial problems are examined and seven common pitfalls are discussed. (MP)

Included are brief articles on multiplication of negative integers and testing knowledge by asking true-false questions that involve a relatively high level of abstraction. A number of specific examples are included. (MNS)

A model for directed numbers, using a sentry moving along the number line, is described. (MNS)

A model is offered which can be used for teaching addition, subtraction, multiplication, and division with directed numbers. Illustrations for all operations are given. (MNS)

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)

The National Science Education Standards (NSES) emphasize the use of models in science instruction by making it one of the five unifying concepts of science, applicable to all grade levels. The NSES recommend that models be a focus of instruction--helping students understand the use of evidence in science, make and test predictions, use logic, and…

Some single species and two species interactions in population models are presented to show how credible examples can be used to teach an underlying, common mathematical structure within apparently different concepts. The models examined consist of differential equations, and focus on real-world issues. (MP)

The activity uses an area model to analyze probabilities associated with games of chance. Three activity sheets are included, with teaching suggestions. (MNS)

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)

Shows how to model Newton's method for approximating roots on a spreadsheet. (MKR)

Illustrates the addition, subtraction, and representation of fractions using an area model and a measurement model. Also demonstrates multiplication and division of fractions by employing the area model. (ASK)