Seeking to leverage students' interests into mathematical tasks and noticing how their students excitedly discussed the NCAA's Division 1-A football rankings every year, the authors devised a mathematical modeling task in which students could use mathematics to justify their rankings. The task takes students on a journey to consider the complexity…

The teaching quality evaluation of college teachers is an important indicator of school evaluation, performance assessment and teacher promotion. However, the existing evaluation methods are only limited to the formal evaluation of teaching behavior, and have not achieved objective, reasonable and scientific evaluation results. The purpose of this…

The National Council of Teachers of Mathematics (NCTM, 2014) highlights that effective teaching practices promote students' reasoning and sense making through various problem-solving strategies. Rather than telling students what to do and how to solve problems, teachers are expected to engage learners in accessible real-life problem situations…

The OSeMOSYS project offers open-access energy modeling to a wide audience. Its relative simplicity makes it appealing for academic research and governmental organizations to study the impacts of policy decisions on an energy system in the context of possibly severe greenhouse gases emissions limitations. OSeMOSYS is a tool that enhances the…

The subject of the research is to build methodologies to evaluate the student knowledge by testing. The author points to the importance of feedback about the mastering level in the learning process. Testing is considered as a tool. The object of the study is to create the test system models for defence practice problems. Special attention is paid…

Sensitivity analysis is the study of how the different input variations of a mathematical model influence the variability of its output. In this paper, we review the principle of global and local sensitivity analyses of a complex black-box system. A simulated case of application is given at the end of this paper to compare both approaches.…

Structural balance theory (SBT) has maintained a venerable status in the psychological literature for more than 5 decades. One important problem pertaining to SBT is the approximation of structural or generalized balance via the partitioning of the vertices of a signed graph into "K" clusters. This "K"-balance partitioning problem also has more…

When using linear models for cluster-correlated or longitudinal data, a common modeling practice is to begin by fitting a relatively simple model and then to increase the model complexity in steps. New predictors might be added to the model, or a more complex covariance structure might be specified for the observations. When fitting models for…

Smaller universities may produce research which is on a par with larger, elite establishments. This is confirmed by a recently developed mathematical model, supported by data from British and French higher education research-evaluation exercises. The detailed nature of the UK system, in particular, allows quantification of the notion of critical…

Focuses on methods of generating and evaluating hypertext. Highlights include historical landmarks; nonlinearity; literary hypertext; models of hypertext; manual, automatic, and semi-automatic generation of hypertext; mathematical models for hypertext evaluation, including computing coverage and correlation; human factors in evaluation; and…

Suggests a method for analyzing structure and process in prose using algorithms based on graph theory and rules based in syntax. Describes application of the method to essays written by 52 fourteen year old pupils on a newly learned topic in chemistry. (Author/GC)

Illustrates the use of latent growth modeling (LGM) as an analytical tool in program evaluation using the hypothetical example of a high school drug prevention program. Demonstrates the use of LGM in assessing longitudinal impact and in incorporating predictors of status and growth into a model. Highlights advantages and limitations of LGM. (SLD)

Based on seminal work by Lord and Hambleton, Swaminathan, and Rogers, this article is an analytical, graphical, and conceptual reminder that item response theory (IRT) parameter invariance only holds for perfect model fit in multiple populations or across multiple conditions and is thus an ideal state. In practice, one attempts to quantify the…

A longitudinal program evaluation approach used in the Vermont system of care for children and adolescents is described. The method focuses on movement between residential placements and compares system functioning to service system values using a person-level longitudinal database. This methodology can be useful in a number of fields. (SLD)

Presents three mathematical models for the evolution over time of the proportion of minorities in an academic department or similarly selected group of constant size. Analyzes both the steady-state and time-dependent behavior of the proportion of minorities and suggests a method of evaluating the fairness of a department's hiring history.…