Describes an activity that addresses some fundamental principles of scaling, a technique that provides a mathematical basis for explaining many biological differences between small and large organisms. (WRM)

A Mathematica[TM] package is described that uses simulations and animations to illustrate key concepts in harmonic oscillation and electric circuits for students not majoring in physics or mathematics. Students are not required to know the Mathematica[TM] environment: a user-friendly interface with buttons functionalities and on-line help allows…

The concept of Arithmetic Story Grammar is introduced. Arithmetic Story Grammar maintains that any equation containing a single operand tells, in and of itself, a complete story with a setting, plot, theme, and resolution. Multiple-operand equations differ from their single-operand siblings only in the number of actions undertaken and the number…

One aim of this report is to show and emphasize that in the computational approaches to most of today's pressing and challenging scientific and technological problems, the mathematical aspects cannot and should not be considered in isolation. Following an introductory chapter, chapter 2 discusses a number of typical problems leading to…

Using the analogy of temperature measurement, the Rasch model is presented with arguments for its adoption as the basic scaling technique for achievement measures. Three extensions of the Rasch model for more complex testing are developed. Test development for the British national assessment program and the promise of item banking are also…

We noticed that when workers try to explain their mathematical practices to inquisitive outsiders, breakdowns in communication arise. We present here an example in which a worker spontaneously uses metaphors and models to facilitate explanation and communication. We analyse these, drawing on Lakoff & Johnson (1999) and Lakoff & Nunez…

This paper presents information on a course entitled "Mathematics and Technology" which was created at the University of Montreal and was taught once during the winter term of 2001. The students in the course were for the most part future high school teachers. Several applications of mathematics in technology are introduced and students…

Discusses simulation program to aid in the design of enzyme kinetic experimentation (includes sample runs). Concentration versus time profiles of any subset or all nine states of reactions can be displayed with/without simulated instrumental noise, allowing the user to estimate the practicality of any proposed experiment given known instrument…

Discusses a mathematical model for mastery learning. The model includes measures of a motivational factor and the specific ability of a learner with respect to content being learned. The model also contains a variable reflecting prior learning. Assumptions/limitations are discussed, and research questions raised. (Author/JN)

Describes a one-dimensional model for an ideal gas to study development of disordered motion in Newtonian mechanics. A Monte Carlo procedure for simulation of the statistical ensemble of an ideal gas with fixed total energy is developed. Compares both approaches for a pseudoexperimental foundation of statistical mechanics. (Author/JN)

Describes the use of a microcomputer in studying a model experiment (Brownian particles colliding with thermal particles). A flow chart and program for the experiment are provided. Suggests that this experiment may foster a deepened understanding through mutual dialog between the student and computer. (SK)

Shows that the experiment of the ancient Greek mathematician and geographer, Eratosthenes, can be replicated and used to teach geographic concepts. Eratosthenes calculated the most accurate ancient measurement of earth based on fundamental mathematics concepts and earth-sun relations. Includes instructions, illustrations, graphs, and historical…

The evolution of ideas about the concept of chaos is surveyed. Discussed are chaos in deterministic, dynamic systems; order in dissipative systems; and thermodynamics and irreversibility. Included are logistic and bifurcation maps to illustrate points made in the discussion. (CW)

Presents an example of a proof to the mathematical problem of the sum of the cubes of the digits. Provides a Pascal program to search for these results. (MVL)

Outlines differences between classical statistics and exploratory data analysis. Provides examples in the use of the exploratory techniques. (YP)