To rule out the need for a two-parameter item response theory (IRT) model during item analysis by Rasch models, it is important to check the Rasch model's assumption that all items have the same item discrimination. Biserial and polyserial correlation coefficients measuring the association between items and restscores are often used in an informal…

This article first notes the misinterpretation of a common thought experiment, and the misleading comment that "systems tend to flow from less probable to more probable macrostates". It analyses the experiment, generalizes it and introduces a new tool of investigation, the simplectic structure. A time-symmetric model is built upon this structure,…

We propose a laboratory learning pathway, suitable for secondary school up to introductory undergraduate level, employing the VnR dynamic modelling software. It is composed of three increasingly complex activities dealing with experimental work, model design and discussion. (Contains 4 footnotes, 1 table and 5 figures.)

Students of Architecture and Building Engineering Degrees work with Computer Aided Design systems daily in order to design and model architectonic constructions. Since this kind of software is based on the creation and transformation of geometrical objects, it seems to be a useful tool in Maths classes in order to capture the attention of the…

The reactions by Ridley and Shaw-Ridley (EJ832451) and Lichtenberg (EJ832452) to the authors' meta-analysis on the effects of experience on judgment accuracy add positively to what is hoped will become an ever more focused discourse on this most basic question: How can mental health clinical decision making be improved? In this rejoinder, the…

This paper suggests two new, related methods for estimating a test-score equating relationship from small samples of test takers. These methods do not require the estimated equating transformation to be linear. Instead, they constrain the estimated equating curve to pass through 2 prespecified end-points and a middle point determined from the…

Estimating the difficulty level of math word problems is an important task for many educational applications. Identification of relevant and irrelevant sentences in math word problems is an important step for calculating the difficulty levels of such problems. This paper addresses a novel application of text categorization to identify two types of…

A heuristic approach to explaining of the Black-Scholes option pricing model in undergraduate classes is described. The approach draws upon the method of protocol analysis to encourage students to "think aloud" so that their mental models can be surfaced. It also relies upon extensive visualizations to communicate relationships that are…

The 2009 college football season is here, but there has been a continuing controversy swirling over how the Football Bowl Subdivision (FBS) selects its national champion. College football uses a multi-criterion decision matrix (MCDM) evaluation technique to determine which two teams will play for the national championship. We analyzed the BCS…

Second-order latent growth curve models (S. C. Duncan & Duncan, 1996; McArdle, 1988) can be used to study group differences in change in latent constructs. We give exact formulas for the covariance matrix of the parameter estimates and an algebraic expression for the estimation of slope differences. Formulas for calculations of the required sample…

At the heart of the recent focus on mathematics has been an increased emphasis on developing students' "number sense." Ironically, although growing as a force in the education literature, number sense has not been clearly defined for teachers. Teachers need specific support in understanding how to develop number sense in students, to…

The unifying theme of models was incorporated into a required Science Capstone course for pre-service elementary teachers based on national standards in science and mathematics. A model of a teeter-totter was selected for use as an example of a functional model for gathering data as well as a visual model of a mathematical equation for developing…

Water chemistry is central to aquarium design, and it provides many potential applications for discussion in undergraduate chemistry and engineering courses. Marine aquaria and their life support systems feature many chemical processes. A life support system consists of the entire recirculation system, as well as the habitat tank and all ancillary…

This article proposes a new model of human concept learning that provides a rational analysis of learning feature-based concepts. This model is built upon Bayesian inference for a grammatically structured hypothesis space--a concept language of logical rules. This article compares the model predictions to human generalization judgments in several…

Despite its great importance, many students and even their teachers still cannot recognize the relevance of models to build up physical knowledge and are unable to develop qualitative explanations for mathematical expressions that exist within physics. Thus, it is not a surprise that analogies play an important role in science education, since…