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…

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…

Randomized experiments are commonly used to evaluate the effectiveness of educational interventions. The goal of the present investigation is to develop small-sample corrections for multiple contrast hypothesis tests (i.e., F-tests) such as the omnibus test of meta-regression fit or a test for equality of three or more levels of a categorical…

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…

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 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)

The interest in developmental sequences and learning hierarchies is growing. One approach to the study of such sequences is to gather data on several variables, each of which corresponds to a stage, step, or phase in the sequence and to examine the associations between the variables as displayed in a contingency table. If the variables are…

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)

The logic and procedures underlying a disturbance term regression test of logical consistency for structural models are reviewed for recursive and nonrecursive designs. It is shown that in a simple three-variable, complete mediational case the test procedure is mathematically equivalent to a part correlation. (Author/LMO)

When the experimental units are measured twice, and the response variable is dichotomous, the equality of the two proportions is usally assessed by Mc Nemar's (1947) test. In this paper, Bayesian methods are presented for testing hypotheses regarding the two success probabilities in light of complete and incomplete data. (Author/BW)

The form of the Johnson-Neyman region of significance is shown to be determined by the statistic for testing the null hypothesis that the population within-group regressions are parallel. Results are obtained for both simultaneous and nonsimultaneous regions of significance. (Author)

The G index is a measure of the similarity between individuals over dichotomous items. Some tests for the G-index are described. For each case an example is included. (Author/GK)

This paper demonstrates that multiple comparison tests using a pooled error term are dependent on the circularity assumption and shows how to compute tests which are insensitive (robust) to this assumption. (Author/GK)

If the null hypothesis of a one-sample test of multivariate means is rejected, the dimension of the line joining the population centroid and the hypothesized centroid can be interpreted with a linear function, using a discriminant function and the correlation of each dependent variable with a discriminant score. (Author/BW)