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 submission contains the Proceedings of the 2011 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at Memorial University of Newfoundland in St. John's, Newfoundland. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning.…

This paper reviews the present state, recent trends, and prospective lines of development concerning applied problem solving, modeling, and their respective applications. Four major trends are scrutinized with respect to curriculum inclusion: a widened spectrum of arguments, an increased universality, an increased consolidation, and an extended…

Examples of subroutines that generate both symbolic and graphic solutions to differential equations are presented for the two computer algebra systems, MAPLE and Mathematica. Included are the listings for the Mathematica procedures developed for use in this article. (JJK)

The author outlines the development, structure, and teaching and assessment problems of one introductory discipline-independent mathematical modelling course. (MN)

How computers have affected diagnosis in mathematics is discussed. A distinction is made between errors and mistakes, followed by consideration of computers as a diagnostic tool. The development of algorithms to diagnose errors and of models of student performance is described. (MNS)

This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…

Presents two mathematical methods for fitting the logistic curve to population data supplied by the U.S. Census Bureau utilizing computer algebra software to carry out the computations and plot graphs. (JKK)

This article describes a calculus lesson that illustrates the nature of cycles in simple systems of nonlinear differential equations through the use of the Lotka-Volterra predator-prey model as incorporated in the computer software package, Phaser (version 1.0). (JJK)

This review features new examples of using the computer relative to college-level mathematics to enhance pedagogy, solve problems, and model real-life situations. Included is a LOGO program that can be used to create and to stimulate subsequent investigations of spirolaterals, those figures generated by repeatedly drawing basic loops. (JJK)

Presented are student activities that involve two standard problems from geometry and calculus--the volume of a box and the bank shot on a pool table. Problem solving is emphasized as a method of inquiry and application with descriptions of the results using graphical, numerical, and physical models. (JJK)

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…

Reports on the graphing work of children, aged eight and nine years, who have access to portable computers across the curriculum. Describes two learning sequences: in one, the children collected data and then explored the computer graphing facilities; and in the other, graphing is used iteratively as an integral part of the ongoing task.…

Discussed is the place and teaching of trigonometry in a NCTM Standards-based mathematics curriculum. Presented is how these standards can be implemented in a technology-rich environment that encourages reasoning, communication, problem solving, and confidence building. Examples focus on functions, graphical sense, modeling, and identities. (KR)

The quadratic function can be modeled in real life by a suspension bridge that supports a uniform weight. This activity uses concrete models and computer generated graphs to discover the mathematical model of the shape of the main cable of a suspension bridge. (MDH)