In this workshop, we will continue to reflect on a models and modeling perspective to understand how students and teachers learn and reason about real life situations encountered in a mathematics and science classroom. We will discuss the idea of a model as a conceptual system that is expressed by using external representational media, and that is…

Describes some continuous models for growth of the seaweed Macrocystis pyrifera. Uses observed growth rates over several months to derive first-order differential equations as models for growth rates of individual fronds. The nature of the solutions is analyzed and comparison between these theoretical results and documented characteristics of…

Provides an example of the modeling power of Mathematics, demonstrated in a piece of A-Level student coursework which was undertaken as part of the MEI Structured Mathematics scheme. A system of two masses and two springs oscillating in one dimension is found to be accurately modeled by a system of linear differential equations. (Author/ASK)

Presents activities designed to engage students in an experiential and theoretical application of problems in precalculus and to study geometry, coordinate systems, rates, linear applications, and the concept of function. Illustrates problem situations and includes student worksheets and a teacher's guide. (KHR)

An approach to using the method of least squares, a scheme for computing the best-fitting line directly from a set of points, is detailed. The material first looks at fitting a numerical value to a set of numbers. This provides tools for solving the line-fitting problem. (MP)

A brief overview is presented of the use of soap bubbles to solve minimal problems. A new class of problems that can be solved with soap film models is presented. (MP)

Presents an integrated exposition of aspects of secondary school mathematics and a medical science specialty. Reviews clinical medical practice and theoretical and empirical literature in mathematics education and radiology to develop and pilot model integrative classroom topics and activities. Suggests mathematical applications in numeration and…

This paper investigates the role of teacher interaction in the development of mathematical understanding of five students who worked together on a math-modeling task. The dialogue between the teacher/researcher and students is analyzed. Preliminary findings suggest that where the mathematical thinking of the students was understood, interventions…

A programing language called DYNAMO, developed especially for writing simulation models, is promoted. Details of six, self-teaching curriculum packages recently developed for simulation-oriented instruction are provided. (MP)

Cellular partitioning of space is discussed. Directions are given for making geometric models of cells. (DT)

Looks at the solution to the mathematical-modeling problem asking students to find the smallest percent of the popular vote needed to elect a President. Provides assumptions from which to work the problem. (MDH)

A mathematical model giving weight which can be lifted as a function of bodyweight is formulated and compared with the actual data for the flyweight through the heavyweight classes. (MN)

The author argues the case for having students learn mathematics while developing mathematical models for real situations. Examples of mathematical models and modelling possibilities are given for various fields of interest. (MN)