Compared to the use of the word "average" in the media and in everyday conversations, an average is used very precisely in mathematics. This is complicated by the fact that there are three different types of averages: means, medians, and modes. As with other concepts, scaffolding understanding of mathematical averages is important. Such…

When examinees' test-taking motivation is questionable, practitioners must determine whether careless responding is of practical concern and if so, decide on the best approach to filter such responses. As there has been insufficient research on these topics, the objectives of this study were to: a) evaluate the degree of underestimation in the…

In this paper, the hypothesis that Developmental Dyscalculia (DD) is a characteristic of Down syndrome (DS) is proposed. Implications for the hypothesis are addressed: If it were to be confirmed that DS implies DD, what would be the consequences for the mathematics education of learners with DS? The use of prosthetic devices to overcome the…

The Dijkstra's algorithm is an algorithm that determines the shortest paths needed to go from a starting node to any node in a graph. In this article, the process and results of an activity that included route formation among the provinces in the Aegean region using Dijkstra's algorithm are shared. The activity was designed based on a mathematical…

Statistical mediation analysis allows researchers to identify the most important mediating constructs in the causal process studied. Identifying specific mediators is especially relevant when the hypothesized mediating construct consists of multiple related facets. The general definition of the construct and its facets might relate differently to…

A software to calculate the net charge and to predict the isoelectric point (pI) of a polypeptide is developed in this work using the graphical programming language LabVIEW. Through this instrument the net charges of the ionizable residues of the chains of the proteins are calculated at different pH values, tabulated, pI is predicted and an Excel…

Cognitive diagnosis models (CDMs) are an increasingly popular method to assess mastery or nonmastery of a set of fine-grained abilities in educational or psychological assessments. Several inference techniques are available to quantify the uncertainty of model parameter estimates, to compare different versions of CDMs, or to check model…

This article develops some ideas concerning the "big picture" of how using computers might fundamentally change learning, with an emphasis on mathematics (and, more generally, STEM education). I develop the big-picture model of "computation as a new literacy" in some detail and with concrete examples of sixth grade students…

Piecewise GMM with unknown turning points is a new procedure to investigate heterogeneous subpopulations' growth trajectories consisting of distinct developmental phases. Unlike the conventional PGMM, which relies on theory or experiment design to specify turning points a priori, the new procedure allows for an optimal location of turning points…

In this paper, we reconstruct matrices from their minors, and give explicit formulas for the reconstruction of matrices of orders 2 × 3, 2 × 4, 2 × n, 3 × 6 and m × n. We also formulate the Plücker relations, which are the conditions of the existence of a matrix related to its given minors.

Understanding how struggling students approach math is vital to designing effective math lessons. Many low achieving students rely on a weak knowledge of procedures and attempt calculations without adequate consideration of the problem. We investigated how enabling or preventing premature calculations affected learning math. Students were…

Whenever classification decisions are made on educational tests, such as pass/fail, or basic, proficient, or advanced, the consistency and accuracy of those decisions should be estimated and reported. Methods for estimating the reliability of classification decisions made on the basis of educational tests are well-established (e.g., Rudner, 2001;…

A national survey of physics faculty was conducted to investigate the prevalence and nature of computational instruction in physics courses across the United States. 1246 faculty from 357 unique institutions responded to the survey. The results suggest that more faculty have some form of computational teaching experience than a decade ago, but it…

Parallel analysis (PA) assesses the number of factors in exploratory factor analysis. Traditionally PA compares the eigenvalues for a sample correlation matrix with the eigenvalues for correlation matrices for 100 comparison datasets generated such that the variables are independent, but this approach uses the wrong reference distribution. The…

Contrast analysis is a relatively simple but effective statistical method for testing theoretical predictions about differences between group means against the empirical data. Despite its advantages, contrast analysis is hardly used to date, perhaps because it is not implemented in a convenient manner in many statistical software packages. This…