Discusses the use of technology in solving compound interest-rate problems that can be modeled by linear relationships. Uses a graphing calculator to solve the specific problem of determining the amount of money that can be borrowed to buy a car for a given monthly payment and interest rate. (MDH)

Discusses the potential that school mathematics has for being a source of exploration and discovery for students and teachers. Provides a process-oriented definition of understanding mathematics. Presents activities in which students construct computer and actual models of polyhedra and make conjectures regarding a medical research application of…

The focus of this report is children's construction and analogical transfer of mathematical knowledge during novel problem solving, as reflected in their strategies for dealing with isomorphic combinatorial problems presented in "hands-on" and written form. Case studies of 9-year-olds, one low and one high achieving in school…

Presents an introductory lesson on remote sensing and image processing to be used in cooperative groups. Students are asked to solve a problem by gathering information, making inferences, transforming data into other forms, and making and testing hypotheses. Includes four expansions of the lesson and a reproducible student worksheet. (MKR)

This paper reports on five related studies on upper elementary school students' beliefs about the role of real-world knowledge in solving mathematical word problems, and on possibilities of overcoming their unrealistic mathematical modeling. Findings from the first study of 75 Belgian fifth-grade students showed that as a consequence of current…

The study examines the rule space model, a probabilistic model capable of measuring cognitive skill acquisition and of diagnosing erroneous rules of operation in a procedural domain. The model involves two important components: (1) determination of a set of bug distributions (bug density functions representing clusters around the rules); and (2)…

This university level course in economic geography emphasizes the need for control of the spatial allocation of our resources, and strives for heightened student awareness of the world as a complex. It may thus be considered an introduction to geocybernetics, the study of man/machine relationships in the control of spatial organization. A systems…

Presents a program to introduce fifth graders to everyday economic life by constructing a true-to-life simulation of an economic community. Students apply mathematics skills to managing a checking account, calculating electric bills, and managing shops using computers. (MDH)

A longitudinal study followed Brian from grade five through grade seven to examine his representation and development of mathematical knowledge. Some observations over the four years were that Brian liked to figure things out, responded poorly to suggestions not fitting the representation he constructed, and changed attitudes from purposeful and…

An exploratory study assessed the degree to which 13- and 14-year olds (n=100) adjusted assumptions of direct proportionality suggested by surface structure of word problems. Virtually no errors were made on "straightforward" items, but many students showed no adjustment for realistic constraints on complex items. (Contains 21…

As presented in this report the basic purpose of CAIR (Computer-Aided International Relations Teaching) is to introduce university students and policy analysts in government agencies to substantive data analysis in the field of international studies. The student will be exposed to quantitative political science, learn the role and limitations of…

This document contains four papers on aeronautics education, research, and partnerships that partly supported through the Aeronautics Education, Research, and Industry Alliance (AERIAL). The paper "2002 AERIAL Monograph" (Brent D. Bowen, Jocelyn S. Nickerson, Mary M. Fink, et al.) presents an overview of research and development in the…

We have designed model-development sequences using a common context to provide authentic problem-solving experiences for first-year students. The model-development sequence takes a model-eliciting activity a step further by engaging students in the exploration and adaptation of a mathematical model (e.g., procedure, algorithm, method) for solving…

Described is an alternative first year algebra program developed to bridge the gap between the NCTM's Curriculum and Evaluation Standards and institutional demands of schools. Increased attention is given to graphing as a context for algebra, calculator use, solving "memorable problems," and incorporating geometry concepts, while…

Describes a study which measured how ninth-grade students integrated information about mathematical concepts when working with Triple Representation Model software. Tables, graphs, and algebraic functions were linked, allowing students to manipulate several representations of the same concept. Examples of mathematical problems and student case…