A mathematical model is used to represent a physical problem. The resulting polynomial is graphed and analyzed. Students are asked to plot families of related polynomial functions and observe patterns. A partial list of possible observations is included. End behavior, complete graph, and classroom use of technology are discussed. (GW)

This study describes the learning of researchers who engage in mathematics teacher education as an integral part of their practice. As teacher educators working with teachers on the subject of proportional reasoning, the authors reflected on teachers solutions to a standard problem and analyzed answers that would conventionally be considered…

These materials on geometric probability are the first unit in a course being developed by the Mathematics Department at the North Carolina School of Science and Mathematics. This course is designed to prepare high school students who have completed Algebra 2 for the variety of math courses they will encounter in college. Assuming only a knowledge…

This document looks at specific applications of calculus to engineering. It is noted that for an automobile traveling at constant speed, the mathematical relationship between the directional heading and the angular deflection of the steering wheel can be calculated with respect to time. An analysis is presented which derives the relationship from…

A general model for a quantitative description of individual growth in learning was developed. Published data in a variety of areas and data on learning sequences in a classroom were processed through the model. Findings suggest that the general growth model governs growth phenomena. (Author/RD)

Described is a learning activity that requires students to observe, read, and interpret graphs and organize and describe data. Included are the grade level, materials, objectives, prerequisites, directions, answers to questions, and copies of handouts. (KR)

Solves the problem of the reproduction of rabbit pairs utilizing the Fibonacci sequence. Examines modified versions of the problem, and presents a vignette of one modification based on the author's experience in using the approach with preservice middle school teachers. Extends the approach to other related problems. (MDH)

After a year of instruction, 70 kindergarten children were individually interviewed as they solved basic, multistep, and nonroutine word problems. Thirty-two used a valid strategy for all 9 problems, and 44 correctly answered 7 or more problems. Modeling provided a unifying framework for thinking about problem solving. (Author/MDH)

This article discusses the analysis of a decision-making process faced by contestants on the television game show "The Price is Right". The included analyses of the original and related problems concern pattern searching, inductive reasoning, quadratic functions, and graphing. Computer simulation programs in BASIC and tables of…

Described is the use of story telling as a context to introduce mathematical concepts by providing a model, offering problem-posing situations, stimulating investigation, and illustrating concepts. Examples of appropriate stories are given for the primary and low secondary levels. (MDH)

Presents activities in which students develop and analyze scatterplots on graphing calculators to model corn growth, decay, a box of maximum volume, and weather prediction. Provides reproducible worksheets. (MDH)

This article examines students' ability to use the balance model to solve for unknowns. A teaching experiment was conducted in four Year 3 classrooms. This experiment focused on exploring the application of the balance model as an analogue for representing equations and solving for unknowns. The teaching experiment promoted a shift by students…

This text provides educational administrators with a working knowledge of the problem-solving techniques of PERT (planning, evaluation, and review technique), Linear Programming, Queueing Theory, and Simulation. The text includes an introduction to decision-making and operations research, four chapters consisting of indepth explanations of each…

The rule space model permits measurement of cognitive skill acquisition, diagnosis of cognitive errors, and detection of the strengths and weaknesses of knowledge possessed by individuals. Two ways to classify an individual into his or her most plausible latent state of knowledge include: (1) hypothesis testing--Bayes' decision rules for minimum…

Proceedings of the 1980 annual forum of the Association for Institutional Research (AIR) on the topics of meeting the challenges of the eighties by redirecting resources for renewal are presented. Contents include the following addresses: "Planning: An Adaptive Process," by Barbara S. Uehling; "Catastrophe Models in…