Today's engineers, designers, and technologists are often thrust into the role of problem solver, from the initial design phase of a product or process all the way to final development. Many engineers in manufacturing environments are tasked with solving problems and continuously improving processes to enhance company profitability, efficiency,…

Context is what makes mathematical modeling tasks different from more traditional textbook word problems. Math problems are sometimes stripped of context as they are worked on. For modeling problems, however, context is important for making sense of the mathematics. The task should be brought back to its real-world context as often as possible. In…

The purpose of our modeling effort is to predict future outcomes. We assume the data collected are both accurate and relatively precise. For our oscillating data, we examined several mathematical modeling forms for predictions. We also examined both ignoring the oscillations as an important feature and including the oscillations as an important…

The spread of swine flu has been a cause of great concern globally. With no vaccine developed as yet, (at time of writing in July 2009) and given the fact that modern-day humans can travel speedily across the world, there are fears that this disease may spread out of control. The worst-case scenario would be one of unfettered exponential growth.…

Electricity is regarded as one of the most challenging topics for students of all ages. Several researchers have suggested that naive misconceptions about electricity stem from a deep incommensurability (Slotta and Chi 2006; Chi 2005) or incompatibility (Chi et al. 1994) between naive and expert knowledge structures. In this paper we argue that…

This paper proposes modelling based learning as a tool for learning and teaching mathematics. The example of modelling real world problems leading to the exponential function as the solution of differential equations is described, as well as the observations about students' activities during the process. The students were acquainted with the…

This paper explores the use of spreadsheets to develop an exploratory environment where mathematics students can develop their own understanding of the parameters of commonly encountered families of functions: linear, logarithmic, exponential and power. The key to this understanding involves opening up the definition of rate of change from the…

In current curriculum materials for middle school students in the US, data and chance are considered as separate topics. They are then ideally brought together in the minds of high school or university students when they learn about statistical inference. In recent studies we have been attempting to build connections between data and chance in the…

Discusses areas in the undergraduate curriculum that are important due to recent technological changes (such as contributing effectively to group projects and the ability to take advantage of continuing education opportunities). Examines possible responses to these areas, focusing on the role of computers and on the mathematics curriculum. (JN)

Describes the use of an instructional module used to introduce college students to a combined mathematical modeling and normative analysis approach to the investigation of public policy issues. The module, which was designed to bridge several courses and combined independent work with discussions, was judged to be successful in promoting…

The paper discusses an elementary spring model representing the motion of a magnet suspended from the ceiling at one end of a vertical spring which is held directly above a second magnet fixed on the floor. There are two cases depending upon the north-south pole orientation of the two magnets. The attraction or repelling force induced by the…

Investigates problems of modeling and application based on a paradigmatic case study of a classroom situation in which students deal with functions within a computer-aided learning environment. Analysis of the case study shows that computer-supported operating with functions as objects does not automatically lead to a better understanding of the…

The true state of the system described here is characterized by a probability vector. At each stage of the system an action must be chosen from a finite set of actions. Each possible action yields an expected reward, transforms the system to a new state in accordance with a Markov transition matrix, and yields an observable outcome. The problem of…

The first of five sections in this report places intelligent computer-assisted instruction (ICAI) in its historical context through discussions of traditional computer-assisted instruction (CAI) linear and branching programs; TICCIT and PLATO IV, two CAI demonstration projects funded by the National Science Foundation; generative programs, the…

Describes the Chemistry Visualization (ChemViz) Project, a Web venture maintained by the University of Illinois National Center for Supercomputing Applications (NCSA) that enables high school students to use computational chemistry as a technique for understanding abstract concepts. Discusses the evolution of computational chemistry and provides a…