It is shown that quantum systems of identical particles can be treated as different when they are in well-differentiated states. This simplifying assumption allows for the consideration of quantum systems isolated from the rest of the universe and justifies many intuitive statements about identical systems. However, it is shown that this…

Gamma-family measures are bivariate ordinal correlation measures that form a family because they all reduce to Goodman and Kruskal's gamma in the absence of ties (1954). For several gamma-family indices, more than one variance estimator has been introduced. In previous research, the "consistent" variance estimator described by Cliff and…

Considering a dyad as a dynamic system whose current state depends on its past state has allowed researchers to investigate whether and how partners influence each other. Some researchers have also focused on how differences between dyads in their interaction patterns are related to other differences between them. A promising approach in this area…

How do we estimate the number of objects in a set? Two types of visual representations might underlie this ability--an unsegmented visual image or a segmented collection of discrete objects. We manipulated whether individual objects were isolated from each other or grouped into pairs by irrelevant lines. If number estimation operates over an…

In standard treatments of probability, Pr(A[vertical bar]B) is defined as the ratio of Pr(A[intersection]B) to Pr(B), provided that Pr(B) greater than 0. This account of conditional probability suggests a psychological question, namely, whether estimates of Pr(A[vertical bar]B) arise in the mind via implicit calculation of…

We compute closed forms for two multiparameter families of definite integrals, thus obtaining combinatorial formulas. As a consequence, a surprising formula is derived between a definite integral and an improper integral for the same parametric function.

How well we are attuned to the statistics of our environment is a fundamental question in understanding human behaviour. It seems particularly important to be able to provide accurate assessments of the probability with which negative events occur so as to guide rational choice of preventative actions. One question that arises here is whether or…

Two types of calculation processes have been distinguished in the literature: approximate processes are supposed to rely heavily on the non-verbal quantity system, whereas exact processes are assumed to crucially involve the verbal system. These two calculation processes were commonly distinguished by manipulation of two factors in addition…

Vehicles holding at traffic lights is a typical queuing problem. At crossings the vehicles experience delay in both directions. Longer periods with green lights in one direction are disadvantageous for the vehicles coming from the other direction. The total delay for getting through the traffic point is what counts. This article presents an…

The persistently low college attainment rates of youth from poor families are partly attributable to their uncertainty about college affordability. The current federal financial aid system does not provide specific information about college costs until just before college enrollment and the information is only available to students completing a…

The present study examined whether multiple opportunities to learn math were associated with smaller socioeconomic status (SES) disparities in fifth-grade math achievement using data from the NICHD Study of Early Child Care and Youth Development (SECCYD; N = 1,364). High amounts of procedural math instruction were associated with higher…

How to compute and report subscores for a test that was originally designed for reporting scores on a unidimensional scale has been a topic of interest in recent years. In the research reported here, we describe an application of multidimensional item response theory to identify a subscore structure in a test designed for reporting results using a…

Enabling learning through meaningful classroom experiences has always been a challenge for teachers. Bringing about a balance of the "conceptual" and the "hands-on", along with contextual embeddedness in problem-solving situations, broadly characterises the experience of development and trials of three Design and Technology…

The purpose of this study was to determine the efficacy of specific, individualized training for students with different levels of mathematical difficulties. Fifty-four students, with either severe or mild math difficulties, were assigned to individualized training or to a control condition. Ten students with severe math difficulties…

Scratch, a visual programming language, was used in many studies in computer science education. Most of them reported positive results by integrating Scratch into K-12 computer courses. However, the object-oriented concept, one of the important computational thinking skills, is not represented well in Scratch. Alice, another visual programming…