Relations among aptitude, spatial task solution strategy, and task performance were explored through mathematical models of performance latency. Different models fit different subjects on each of three task steps (encoding, synthesis, and comparison), suggesting that different subjects used different strategies for solving the same items. Aptitude…

In this study, we examined 139 prospective elementary teachers' solution processes to additive word problems for which the solution is 1 more or 1 less than the answer produced by the straightforward application of the addition or subtraction of the two given numbers. For each problem, five aspects of their solution processes were examined: (a)…

Explains that primitive living structures furnish real-world problems that are solvable using mathematics and computer-modeling techniques. (KHR)

Presents mathematical models to determine whether seven-game baseball playoff series are significantly fairer than five-game series. Compares the results obtained from the models to actual playoff results. (MDH)

Presents a motion problem that students in a college physics class are asked to solve and later asked to continue to analyze until they have stopped learning from the problem or the problem itself is finished. (MDH)

Presents an activity to investigate the dimensions of the maximum rectangular area given a fixed perimeter using mathematical modeling and manipulative materials. Students collect and compare data, find patterns, graph data, write functions, and discuss the meaning of the related mathematical model. Provides three reproducible worksheets for the…

Discusses an activity which models the building of a tunnel by ants using the definitions of derivative and indefinite integral from calculus. Includes a discussion of reasonableness and interpretation of the problem. (MKR)

An interview protocol was devised to determine whether demands on working memory are reduced by the use of drawn or telegraphic formats. Students were chosen because some aspect of their group testing on presentation formats was provocative (e.g. high spatial score, but low reading comprehension score; high drawn score and low verbal score, etc.).…

The primary task in solving a physics problem is to select ways of viewing the problem in terms of physical systems whose behavior is described by physical laws. The physical systems are, in general, only approximate models of the real-world systems. As models of real-world systems are made more accurate, the equations involved quickly become…

This volume is an exposition of a mathematical modeling technique for use in the evaluation and solution of complex educational problems at all levels. It explores in detail the application of simple algebraic techniques to such issues as program reduction, fiscal rollbacks, and computer curriculum planning. Part I ("Introduction to the…

This paper analyzes the quantitative and situational structure of algebra story problems, uses these materials to propose an interpretive framework for written problem soving protocols, and then presents an exploratory study of the episodic structure of algebra story problem solving in a sizable group of mathematically competent subjects. Analyses…

Recent research on solving addition and subtraction word problems has resulted in the construction of theoretical models of children's problem-solving processes. Some of these models have been translated into computer programs. Characteristics and predictions of the theoretical analysis developed by Riley, Greeno, and Heller (1983) are discussed…

This module is designed to apply mathematical models to nuclear deterrent problems, and to aid users in developing enlightened skepticism about the use of linear models in stability analyses and long-term predictions. An attempt is made at avoiding overwhelming complexities through concentration on land-based missile forces. It is noted that after…

Two units make up this material. They focus on applications of second-order difference equations to American politics. The goals of the first module include helping the user understand: 1) the difference between a theoretical construct and an observable; 2) the nature of choices which exist in modeling any particular empirical phenomenon; and 3)…

This study investigated a theoretical structure which attempts to explain the problem-solving strategies used by first-grade students who are successful in solving simple arithmetic story problems. The structure used describes the problem-solving procedure as consisting of a three-stage model building process: (1) comprehending the story, (2)…