The author considers the selection of a baseball bat from a mathematical perspective. The effectiveness of a bat-slider system is specifically analyzed. Results are presented graphically to show the effects of the mass of the slider on the swing time and on the batted ball velocity. (PK)

In its empirical part this paper establishes a general weak understanding of the process of applying a mathematical model. This is also evident in the way teachers regard the application of alternative sharing in their own problem solving and in relating to children's answers. The theoretical part analyses problems that are considered as…

This paper briefly reviews research grounded in cultural and socio-constructivist theories carried out to investigate the phenomenon of suspension of sense-making when doing school arithmetic word problems. It begins with ascertaining studies documenting and marking out the phenomenon, then provides an explanation of the observed effects that are…

This paper describes a models and modeling framework that has been applied to various areas in teaching, learning and problem solving. It examines the implications of that framework on metacognition and higher order thinking during everyday problem-solving situations that required teams of students to produce complex solutions in approximately 1-2…

Several models of grading variability are presented. It is shown that study of the models brings out some of the implications of various grading systems. (MK)

Presents a model of what it means to understand mathematics followed by examples of exercises designed to develop understanding in specific ways. Presumes that understanding is more likely to develop if it is the direct focus of exercises. (AIM)

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)

Develops covariational reasoning and proposes a framework for describing mental actions when interpreting and representing dynamic function events. Investigates calculus students' ability to reason about covarying quantities in dynamic situations. Suggests that curriculum and instruction should emphasize moving students to a coordinated image of…

Describes a classroom project involving the construction of a holiday mobile. Necessary supplies include a lightweight hanger, construction paper, string, scissors, protractors, compasses, and rulers. Concepts involved in the construction of the project include illustrating a chord, radius, diameter, shapes, metric measuring, circumference, area,…

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 the meaning of mathematics by looking at its uses in the real world. Offers mathematical modeling as a way to represent mathematical applications in real or potential situations. Presents levels of applicability, modus operandi, relationship to "pure mathematics," and consequences for education for mathematical modeling. (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)

Objectives of teaching mathematics to engineering and science students are defined, and the role of the computer, especially the interactive terminal, in achieving these objectives is discussed. (SD)