Investigates the introduction of mathematical modeling into the mathematics assessment program of the International Baccalaureate Diploma. Considers structured and open modeling in the pre-university mathematics program. Discusses influences of the use of hand-held technology on mathematical modeling and teacher and assessor beliefs about modeling…

Considers transitions from naive realism to formal mathematical modeling, using a Direct Manipulation Environment for Newtonian Mechanics. Highlights include a case study of pre-university students in the United Kingdom; the interplay of mathematical reasoning, modes of interaction with technology, and setting; and comparisons between direct…

Suggests ways for using data from championship tennis as a means for exploring probabilistic models, especially binomial probability. Examples include the probability of winning a service point and the probability of winning a service game using data from tables and graphs. (AIM)

Presents classroom vignettes in which middle grade students with developmentally different views of geometry stimulate each other's reasoning by externalizing mental images through modeling and discourse. (KHR)

Focused on two fifth graders in the Netherlands and studied two approaches to working with models in primary mathematics education: providing models versus designing models in coconstruction. Findings suggest that understanding may be improved by models students made themselves, and that students of this age are able to design models working…

Investigates problems of modeling and application based on a paradigmatic case study of a classroom situation in which students deal with functions within a computer-aided learning environment. Analysis of the case study shows that computer-supported operating with functions as objects does not automatically lead to a better understanding of the…

Discusses the changed roles of mathematics and novel representations that emerge from the ubiquity of computational models. Considers the implications for learning mathematics. Contends that a central component of knowledge required in modern societies involves the development of a meta-epistemological stance. Maps out implications for the design…

Aims for students to use a combination of stochastic ideas to simulate a basketball tournament. Uses the TI-83 calculator in the activity to simulate the binomial distribution. (KHR)

Counters arguments of Donald N. McClosky on formalism in the social sciences and claims he fails to identify important arguments that justify the practices he criticizes. Agrees that, although exposing accepted methods to critical examination is useful, this broad attack implies the rejection of good social science as well as bad. (NL)

Using several data sets, the relative performance of the beta binomial model and two more general strong true score models in estimating several indices of classification consistency is examined. It appears that the beta binomial model can provide inadequate fits to raw score distributions compared to more general models. (TJH)

The mean and variance of the statistic psi-star, which is useful for measuring agreement between two raters and allows for tests of significance in the case of large samples, are considered. Results may also be applied for the "G" index of J. W. Holley and J. P. Guilford (1964). (SLD)

The Dutch Identity is presented as a useful tool for expressing the basic equations of item response models that relate the manifest probabilities to the item response functions and the latent trait distribution. Ways in which the identity may be exploited are suggested and illustrated. (SLD)

Statistical properties of person fit indices are reviewed as indicators of the extent to which a person's score pattern is in agreement with a measurement model. Distribution of a fit index and ability-free fit evaluation are discussed. The null distribution was simulated for a test of 20 items. (SLD)

An approach to scoring reading comprehension based on the concept of the testlet is described, using models developed for items in multiple categories. The model is illustrated using data from 3,866 examinees. Application of testlet scoring to multiple category models developed for individual items is discussed. (SLD)

Information functions are used to find the optimum ability levels and maximum contributions to information for estimating item parameters in three commonly used logistic item response models. Implications are discussed for applications such as adaptive testing and test construction. (SLD)