In this paper we report on findings from a study of 5-to-6-year-old children's ways of structuring part-part-whole relations using finger patterns. We focused our analysis on data from interviews with 28 children who during their last year of preschool learned to enact a structural approach. We used this data set to analyze their different ways of…

Subitizing, a quick apprehension of the numerosity of a small set of items, has been found to explain students' number understanding when counting. We utilized a constructivist teaching experiment methodology to investigate how the counting and subitizing activity of one student, Diego, related to his number understanding (described by his…

Biochemistry is about structure and function, but it is also about data and this is where computers come in. From my time as a graduate student and post doc, whenever I encountered data I thought, "I can work this up by hand, but I think a computer could do a better job." Since that time, I have been working at the interface of…

Simulations concerning the distributional assumptions of coefficient alpha are contradictory. To provide a more principled theoretical framework, this article relies on the Fréchet-Hoeffding bounds, in order to showcase that the distribution of the items play a role on the estimation of correlations and covariances. More specifically, these bounds…

By around the age of 5½, many children in the United States judge that numbers never end, and that it is always possible to add 1 to a set. These same children also generally perform well when asked to label the quantity of a set after one object is added (e.g., judging that a set labeled "five" should now be "six"). These…

One common score reported from diagnostic classification assessments is the vector of posterior means of the skill mastery indicators. As with any assessment, it is important to derive and report estimates of the reliability of the reported scores. After reviewing a reliability measure suggested by Templin and Bradshaw, this article suggests three…

One of the easily accessible results in elementary fluid mechanics is the so-called Torricelli's theorem (or law), which states that the velocity U[subscript th] of the fluid exiting from an orifice at depth "h" from the free surface of a container filled with fluid, is the same as the velocity of a free-falling body from rest over a…

Test scoring models vary in their generality, some even adjust for examinees answering multiple-choice items correctly by accident (guessing), but no models, that we are aware of, automatically adjust an examinee's score when there is internal evidence of cheating. In this study, we use a combination of jackknife technology with an adaptive robust…

Kim and Opfer (2017) found that number-line estimates increased approximately logarithmically with number when an upper bound (e.g., 100 or 1000) was explicitly marked (bounded condition) and when no upper bound was marked (unbounded condition). Using procedural suggestions from Cohen and Ray (2020), we examined whether this logarithmicity might…

One commonly used compromise standard-setting method is the Beuk (1984) method. A key assumption of the Beuk method is that the emphasis given to the pass rate and the percent correct ratings should be proportional to the extent that the panelists agree on their ratings. However, whether the slope of Beuk line reflects the emphasis that panelists…

The purpose of this study was to compare 12 commonly-used nonoverlap methods with each other and with the results of visual analysis. Data were obtained from 25 studies focused on embedded instruction and schema-based instruction and included a total of 101 graphs. Treatment effect estimates using 12 nonoverlap methods were calculated for each…

The aim of this article is to advise readers that natural numbers may be introduced as ordinal numbers or cardinal numbers and that there is an ongoing discussion about which come first. In addition, through several examples, the authors demonstrate that in the process of answering the question "How many?" one may, if convenient, use…

This article compares cut scores from two variations of the Hofstee and Beuk methods, which determine cut scores by resolving inconsistencies in panelists' judgments about cut scores and pass rates, with the Angoff method. The first variation uses responses to the Hofstee and Beuk percentage correct and pass rate questions to calculate cut scores.…

The present study aimed at clarifying the various shortcomings of the Cohen's criteria for the interpretation of the values of the practical significance indicators. The hypothetical data were used for two experimental and control groups and calculating the paired-samples t-test. To clarify the inadequacy of Cohen's criteria in interpreting…

Kim and Opfer (2017) found that number-line estimates increased approximately logarithmically with number when an upper bound (e.g., 100 or 1000) was explicitly marked (bounded condition) and when no upper bound was marked (unbounded condition). Using procedural suggestions from Cohen and Ray (2020), we examined whether this logarithmicity might…