This article offers an engaging student activity that allows them to make a connection between seemingly different topics of drug testing procedure, logistic model, and iterations.

The ability to apply existing knowledge in new situations and settings is clearly a vital skill that all students need to develop. Nowhere is this truer than in the rapidly developing world of Web-based learning, which is characterized by non-sequential courses and the absence of an effective cross-subject guidance system. As a result, questions…

This article presents the results of two studies on using an innovative pedagogical strategy in teaching mathematical modelling and applications to engineering students. Both studies are dealing with introducing non-traditional contexts for engineering students in teaching/learning of mathematical modelling and applications: environment and…

This study analyzed the processes used by students when engaged in modeling activities and examined how students' abilities to solve modeling problems changed over time. Two student populations, one experimental and one control group, participated in the study. To examine students' modeling processes, the experimental group participated in an…

This paper explores the public awareness that there presently exists a crisis in mathematics education and a "dumbing down" of the curriculum, examines the nature of this crisis and argues that there has been a lowering of cultural, pedagogical and cognitive expectations with respect to most learners. The notion of cognitive development in…

The goal of this paper is to demonstrate the infrastructural nature of many modern conceptual technologies. The focus of this paper is on conceptual tools associated with elementary types of data modeling. We intend to show a variety of ways in which these conceptual tools not only express thinking, but also mold and shape thinking. And those ways…

In current curriculum materials for middle school students in the US, data and chance are considered as separate topics. They are then ideally brought together in the minds of high school or university students when they learn about statistical inference. In recent studies we have been attempting to build connections between data and chance in the…

This paper provides a microanalysis of one Algebra I teacher's instruction to explore the advantages that are afforded us by coordinating two perspectives to document and account for the teacher's mathematical understandings. We use constructs associated with Stein, Grover and Henningsen's domain of mathematical didactics and Realistic Mathematics…

Math-education reformers encourage the incorporation of mathematical modeling activities into K-12 curricula. Many of the purported educational benefits derive from the authenticity of the activities-how well they reflect the everyday and occupational mathematical practices of adults. But a paucity in the literature of observational descriptions…

This paper deals with a prey-predator model incorporating a prey refuge and harvesting of the predator species. A mathematical analysis shows that prey refuge plays a crucial role for the survival of the species and that the harvesting effort on the predator may be used as a control to prevent the cyclic behaviour of the system. The optimal…

The existing vector formalism method for thermodynamic relationship maintains tractability and uses accessible mathematics, which can be seen as a diverting and entertaining step into the mathematical formalism of thermodynamics and as an elementary application of matrix algebra. The method is based on ideas and operations apt to improve the…

Interpretation of emergent variables on the basis of structure coefficients (zero order correlations between original and emergent variables) is potentially very misleading and should be avoided in favor of interpretation on the basis of scoring coefficients. This is most apparent in multiple regression analysis and its special case, two-group…

How common patterns of rater errors may be detected in a large-scale performance assessment setting is discussed. Common rater effects are identified, and a scaling method that can be used to detect them in operational data sets is presented. Simulated data sets are generated to exhibit each of these rater effects. The three continua that depict…

These FORTRAN programs and MATHEMATICA routines were developed in the course of a research project titled "Achievement and Assessment in School Science: Modeling and Mapping Ability and Performance." Their use is described in other publications from that project, including "Latent Traits or Latent States? The Role of Discrete Models…

Statistical significance is often misinterpreted to mean replicability or generalizability of results, although a statistically significant difference does not equal a reliable difference. Sample splitting procedures may be a more accurate way of estimating research result generalizability. This type of cross-validation involves randomly dividing…