Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers' developing conceptions about (a) the nature of mathematical modeling in simulations of "real life" problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike…

This study investigated the effects of applying mathematical modeling on revising students' preconception of the process of optimizing area enclosed by a string of a fixed length. A group of 28 high school pre-calculus students were immersed in modeling activity that included direct measurements, data collecting, and formulating algebraic…

A fairly traditional precalculus problem is modified to address some common concerns with the teaching of problem solving. Areas of problem solving which are illustrated include: posing the problem; modeling the problem; transforming the data; and examining the solution. (PK)

This project was designed to: (1) examine the use of the computer as a tool for simulation; (2) let students gather data, analyze hypotheses, and explore algorithms; and (3) explore the potential of high resolution graphics and large memory that will characterize the microcomputers of the 1980s. Prototypes for three different computer-based…

Presents an activity in which students collect and organize data from a real-world simulation of the scientific concept of half life. Students collect data using a marble sifter, analyze the data using a graphing calculator, and determine an appropriate mathematical model. Includes reproducible worksheets. (MDH)

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)