This study considers probability models as tools for both making informal statistical inferences and building stronger conceptual connections between data and chance topics in teaching statistics. In this paper, we aim to explore pre-service mathematics teachers' use of probability models for a chance game, where the sum of two dice matters in…

In most school achievement research, the relationships between achievement and explanatory variables follow the Newton and Einstein concept/principle and the viewpoint of the macro-observer: Deterministic measures based on the mean value of a sufficiently large number of schools. What if the relationships between achievement and explanatory…

We represent the main stages of the process of mathematical modelling as fuzzy sets in the set of the linguistic labels of negligible, low intermediate, high and complete success by students in each of these stages and we use the total possibilistic uncertainty as a measure of students' modelling capacities. A classroom experiment is also…

Conjoint choice experiments are used widely in marketing to study consumer preferences amongst alternative products. We develop a class of choice models, belonging to the class of Poisson race models, that describe a "random utility" which lends itself to a process-based description of choice. The models incorporate a dependence structure which…

Darwinian selection by consequences was instantiated in a computational model that consisted of a repertoire of behaviors undergoing selection, reproduction, and mutation over many generations. The model in effect created a digital organism that emitted behavior continuously. The behavior of this digital organism was studied in three series of…

A computer program to perform a Monte Carlo simulation of counting experiments was written. The program was based on a mathematical derivation which started with counts in a time interval. The time interval was subdivided to form a binomial distribution with no two counts in the same subinterval. Then the number of subintervals was extended to…

The CODE Theory of Visual Attention (CTVA) is a mathematical model explaining the effects of grouping by proximity and distance upon reaction times and accuracy of response with regard to elements in the visual display. The predictions of the theory agree quite acceptably in one and two dimensions (CTVA-2D) with the experimental results (reaction…

The purpose of this paper is to present problems (and solutions) from the areas of marketing, population planning, system reliability, and mathematics to show how a computer simulation can be used as a problem-solving strategy in probability. Examples using BASIC and two methods of generating random numbers are given. (Author/MP)

Discusses ways to simulate a probability problem of interest to middle school students in which students calculate the average number of packets of trading cards purchased to obtain a complete set of cards. Simulations utilize a spinner, a table of random numbers, and a computer. Includes the BASIC program utilized in the simulation. (MDH)

The purpose of this article is to identify the difficulty of learning materials in the network by using learner's portfolio in the asynchronous learning system. Asynchronous learning takes the advantage of information technology that records the learning portfolio of the learner. The data of the learning portfolio reflects the characteristics of…

This document contains the second volume of the proceedings of the 30th Annual Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 60 research reports by presenters with last names beginning between Abr…