Our objective is the estimation of voter transitions between two consecutive parliamentary elections. Usually, such analyses have been based either on individual survey data or on aggregated data. To move beyond these methods and their respective problems, we propose the application of so-called hybrid models, which combine aggregate and…

As a boy I spent many hours skipping stones across the surface of the water on the shore of Lake Michigan. The challenge was to get as many skips or as much distance as possible. Zero skips was a bust. One or two skips was disappointing, three or four skips was mediocre, and six or more skips was exhilarating. The angle of the stone with respect…

A method based on oblique projection is presented for construction of sundials. The derived formulas are classical, but usage of vectors and projections renders a coherent presentation rather than a number of special cases. The presented work is aimed to be useful for those taking a beginning module on vector algebra.

As education systems adapt to evolving societal and technological demands, mathematics curricula must also evolve. Recent trends highlight challenges such as declines in student performance and gaps between intended learning goals and real-world applications. Integrating competencies like data literacy, computational thinking, and problem-solving…

In Singapore, where primary and secondary students routinely top standardized worldwide mathematics examinations, a paradox emerges: when reaching university, many struggle to apply their skills critically in real-world contexts. This commentary examines the challenges and strategies involved in teaching quantitative reasoning (QR) to…

This article offers some less-than-rigorous explanations for the notion of degrees of freedom, and for the particular formulae to be used when computing those values.

In 1961, Barbara Ringer published "Study No. 31: Renewal of Copyright," where she determined the renewal rate for fiscal year 1932 U.S. publications. In that study, she concludes that the renewal rate for Class A works for FY 1932 was 7 percent. This paper seeks to reassess Ringer's study by analyzing the copyright registrations for 1932…

Dynamic measurement modeling (DMM) is a recent framework for measuring developing constructs whose manifestation occurs after an assessment is administered (e.g., learning capacity). Empirical studies have suggested that DMM may improve consequential validity of test scores because DMM learning capacity estimates were shown to be much less related…

Given two 2-level factors of interest, a 2[superscript 2] split-plot design (a) takes each of the 2 [superscript 2] = 4 possible factorial combinations as a treatment, (b) identifies one factor as `whole-plot,' (c) divides the experimental units into blocks, and (d) assigns the treatments in such away that all units within the same block receive…

This study investigated when the Bayesian cue combination of piloting and path integration occurs in human homing behaviors. The Bayesian cue combination was hypothesized to occur in estimating the home location or self-localization. In Experiment 1, the participants learned the locations of 5 objects (1 located at the learning position) in the…

From ancient times, the different features of planets and moons have created a huge interest. Aristarchus was one of the first to study the relative relations among Earth, Moon, and Sun. This interest has remained until today, and therefore it is always relevant to make this knowledge more appealing to the younger generations. Nowadays, smartphone…

The purpose of this study was to determine the validity and reliability of the Power Walker® 610(PW) pedometer for step counting in children. The study sample was composed of 30 boys and 22 girls, from 8-13 years old. Participants were equipped with both a PW and a Digiwalker® SW-200(DW) pedometers and walked 400 m around an outdoor athletic track…

Teaching writing strategies based on writing processes has attracted wide attention as a method for developing writing skills. The writing process can be generally defined as a sequence of subtasks, such as planning, formulation, and revision. Therefore, instructor feedback is often given based on sequence patterns of those subtasks. For such…

Representations of the fingers are embodied in our cognition and influence performance in enumeration tasks. Among deaf signers, the fingers also serve as a tool for communication in sign language. Previous studies in normal hearing (NH) participants showed effects of embodiment (i.e., embodied numerosity) on tactile enumeration using the fingers…

Developing computational thinking (CT) skills at a young age is critical for preparing preschool children to engage with the technologies that have become central to nearly every occupation and for improving achievements in STEM, literacy, and other disciplines. This paper builds on foundational research in early childhood math and CT by reporting…