In this paper, we explore the role that examples play as mathematicians formulate conjectures, and we describe and exemplify one particular example-related activity that we observed in interviews with thirteen mathematicians. During our interviews, mathematicians productively used examples as they formulated conjectures, particularly by creating…

Children vary in the extent to which their development is shaped by particular experiences (e.g. maltreatment, social support). This variation raises a question: Is there no single level of plasticity that maximizes biological fitness? One influential hypothesis states that when different levels of plasticity are optimal in different environmental…

There has been an ongoing debate of which physical labs or virtual labs are better. To resolve this issue, a remote lab provides an online lab that can do real experiments to obtain real data from a distant physical lab. Instead of relying on a remote lab, this article suggests that students collect experimental data locally with low-cost data…

A fundamental aspect of statistical inference is representation of real-world data using statistical models. This article analyzes students' articulations of statistical models and modeling during their first steps in making informal statistical inferences. An integrated modeling approach (IMA) was designed and implemented to help students…

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…

This study investigated the effects of applying mathematical modeling on revising students' preconception of the process of optimizing area enclosed by a string of a fixed length. A group of 28 high school pre-calculus students were immersed in modeling activity that included direct measurements, data collecting, and formulating algebraic…

A quiet methodological revolution, a modeling revolution, has occurred over the past several decades, almost without discussion. In contrast, the 20th century ended with contentious argument over the utility of null hypothesis significance testing (NHST). The NHST controversy may have been at least partially irrelevant, because in certain ways the…

A new framework is offered that uses multilevel logistic regression (MLR) to analyze data from "visual world" eyetracking experiments used in psycholinguistic research. The MLR framework overcomes some of the problems with conventional analyses, making it possible to incorporate time as a continuous variable and gaze location as a categorical…

Comments on articles by Botvinick et al. and Jacob et al. M. M. Botvinick, T. S. Braver, D. M. Barch, C. S. Carter, and J. D. Cohen (2001) implemented their conflict-monitoring hypothesis of cognitive control in a series of computational models. The authors of the current article first demonstrate that M. M. Botvinick et al.'s (2001)…

The online deployment of Technology Engineered online Student Ratings of Instruction (SRIs) by colleges and universities in the United States has dynamically changed the deployment of course evaluation. This research investigation is the fourth part of a post hoc study that analytically and psychometrically examines the design, reliability, and…

A theorem is developed to show that the Kruskal-Wallis test (W. Kruskal and W. Wallis, 1952) (KWt) can be used validly to test a hypothesis about location under much less restrictive conditions than required by the recently accepted, mathematically correct shift model. The specific null hypothesis for which the KWt can be used validly is…

A binomial test for hierarchical dependency is presented. The null hypothesis is that all members of a population who possess a certain skill are a subset of the members who possess another skill. The model, assumptions, formula derivations, and procedures for the test are explained. An illustrative hypothesis is provided. (Author/LMO)

Challenge studies can be used to see whether there is a causal relationship between an agent of interest and a response. An approach based on union-intersection testing is presented that allows researchers to examine observations on a single subject and test the hypothesis of interest. An application using psychological data is presented. (SLD)

Means of identifying sources of rejection of hypotheses regarding linear multivariate statistical models are discussed. Problems with the use of a global test using Roy's largest root criterion and means of solving them are presented, along with a practical application of the techniques. (TJH)

A method for externally constraining certain distances in multidimensional scaling configurations is introduced and illustrated. The method is described in detail and several examples are presented. (Author/JKS)