Discusses steps involved in model building and simulation: understanding a problem, building a model, and simulation. Includes a mathematical model (focusing on a problem dealing with influenza) written in the DYNAMO computer language, developed specifically for writing simulation models. (Author/JN)

Ideas are presented regarding: (1) unique learning activities for students who have difficulty with operations with signed numbers; (2) a mathematical inspection of a unique card trick that can be expressed as an equation; and (3) sketching of graphs of composite trigonometric functions. (MP)

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)

Monte Carlo methods are used to simulate activities in baseball such as a team's "hot streak" and a hitter's "batting slump." Student participation in such simulations is viewed as a useful method of giving pupils a better understanding of the probability concepts involved. (MP)

Shows how attention to transcending functions provides a new integrative approach to mathematics that can improve the critical thinking and problem-solving skills required for addressing large-scale problems. Contains 38 references. (DDR)

Presents a typical cost-allocation problem with possible solutions, including geometric and combinatoric ones. Provides students with a real-life application of the mathematics that they know. (KHR)

Discusses the nature of tasks used to elicit the development of such systems by middle school students. Analyzes mathematical reasoning development of students across tasks and the diversity of thinking patterns identified on problem tasks. Discusses student reasoning about the relationships between and among quantities and their application in…

Presents a case study in which two 8th grade students developed knowledge for modeling a physical device called a winch. Demonstrates that students have and can use criteria for evaluating algebraic representations. Explains how students can develop modeling knowledge by coordinating criteria with knowledge for generating and using algebraic…

Describes similarities and differences between modeling cycles and stages of development. Includes examples of relevant constructs underlying children's developing ways of thinking about fractions, ratios, rates, proportions, or other mathematical ideas. Concludes that modeling cycles appear to be local or situated versions of the general stages…

The second response conditional probability model of decision-making strategies used by examinees answering multiple choice test items was revised. Increasing the number of distractors or providing distractors giving examinees (N=106) the option to follow the model improved results and gave a good fit to data for 29 of 30 items. (SLD)

Two scheduling problems, one involving setting up an examination schedule and the other describing traffic light problems, are modeled as colorings of graphs consisting of a set of vertices and edges. The chromatic number, the least number of colors necessary for coloring a graph, is employed in the solutions. (MDH)

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 difficulties that primary students experience when dealing with real-world related word problems have been discussed extensively. These difficulties are not only related to complex, non-routine problems but already occur with respect to routine problems that involve the application of a simple algorithm. Due to difficulties with the…

This paper outlines a theoretical perspective for studying student understandings of the concept of addition. The notion of operational sense is defined as a way to describe the notion of addition as a mathematical object, paving the way for an application of the theory of reification at this level. Previous frameworks relative to problem solving…