Computational modeling and thinking skill sets were previously relegated to computer scientists and programmers. As a result, computational tools are largely unfamiliar to K-12 science teachers and students. Using Mathematical and Computational Thinking and Developing and Using Models were included in the "Next Generation Science…

Sampling distributions are fundamental for statistical inference, yet their abstract nature poses challenges for students. This research investigates the development of high school students' conceptions of sampling distribution through informal significance tests with the aid of digital technology. The study focuses on how technological tools…

Determining the error of measurement is a necessity for researchers engaged in bench chemistry, chemistry education research (CER), and a multitude of other fields. Discussions regarding what constructs measurement error entails and how to best measure them have occurred, but the critiques about traditional measures have yielded few alternatives.…

The selection of an appropriate booklet design is an important element of large-scale assessments of student achievement. Two design properties that are typically optimized are the "balance" with respect to the positions the items are presented and with respect to the mutual occurrence of pairs of items in the same booklet. The purpose…

Tossing a fair coin 1000 times can have an unexpected result. In the activities presented here, players keep track of the accumulated total for heads and tails after each toss, noting which player is in the lead or whether the players are tied. The winner is the player who was in the lead for the higher number of turns over the course of the game.…

This paper describes the utility of using simulated, rather than real, student solutions to problems within a peer-assessment setting and whether this approach can be used as a means of improving performance in chemical calculations. The study involved a small cohort of students, of two levels, who carried out a simulated peer-assessment as a…

In this paper we examine ways to conceptualize and address potential bias that can arise when the mechanism for missing outcome data is at least partially associated with treatment assignment, an issue we refer to as treatment confounded missingness (TCM). In discussing TCM, we bring together concepts from the methodological literature on missing…

It is common to assume during a statistical analysis of a multiscale assessment that the assessment is composed of several unidimensional subtests or that it has simple structure. Under this assumption, the unidimensional and multidimensional approaches can be used to estimate item parameters. These two approaches are equivalent in parameter…

A "Framework for K-12 Science Education" identified eight practices as "essential elements of the K-12 science and engineering curriculum" (NRC 2012, p. 49). Most of the practices, such as Developing and Using Models, Planning and Carrying Out Investigations, and Analyzing and Interpreting Data, are well known among science…

Despite the widespread popularity of growth curve analysis, few studies have investigated robust growth curve models. In this article, the "t" distribution is applied to model heavy-tailed data and contaminated normal data with outliers for growth curve analysis. The derived robust growth curve models are estimated through Bayesian…

The most common question the author's students ask is, "When will I ever use this in real life?" To address this question in her geometry classes, the author sought to create a project that would incorporate a real-world business situation with their lesson series on the surface area and volume of three-dimensional objects--specifically, prisms,…

The process-component approach has become quite popular for examining many psychological concepts. A typical example is the model with internal restrictions on item difficulty (MIRID) described by Butter (1994) and Butter, De Boeck, and Verhelst (1998). This study proposes a hierarchical generalized random-situation random-weight MIRID. The…

The objective of this paper is to measure the efficiency of high schools in Tunisia. We use a statistical data envelopment analysis (DEA)-bootstrap approach with quasi-fixed inputs to estimate the precision of our measure. To do so, we developed a statistical model serving as the foundation of the data generation process (DGP). The DGP is…

On the 2009 AP[c] Statistics Exam, students were asked to create a statistic to measure skewness in a distribution. This paper explores several of the most popular student responses and evaluates which statistic performs best when sampling from various skewed populations. (Contains 8 figures, 3 tables, and 4 footnotes.)

This article describes a mathematical biology workshop given to secondary school teachers of the Danville area in Virginia, USA. The goal of the workshop was to enable teams of teachers with biology and mathematics expertise to incorporate lesson plans in mathematical modelling into the curriculum. The biological focus of the activities is the…