The three target articles presented in this special issue converged on an emerging theme: the importance of spatial proportional reasoning. They suggest that the ability to map between symbolic fractions (like 1/5) and nonsymbolic, spatial representations of their sizes or "magnitudes" may be especially important for building robust…

Test score distributions of schools or demographic groups are often summarized by frequencies of students scoring in a small number of ordered proficiency categories. We show that heteroskedastic ordered probit (HETOP) models can be used to estimate means and standard deviations of multiple groups' test score distributions from such data. Because…

In 2 studies (Ns = 55 and 54), the authors examined a basic form of conceptual understanding of rational number arithmetic, the direction of effect of decimal arithmetic operations, at a level of detail useful for informing instruction. Middle school students were presented tasks examining knowledge of the direction of effects (e.g., "True or…

Counting is an evolutionarily recent cultural invention of the human species. In order for humans to have conceived of counting in the first place, certain representational and logical abilities must have already been in place. The focus of this article is the origins and nature of those fundamental mechanisms that promoted the emergence of the…

The natural numbers may be our simplest, most useful, and best-studied abstract concepts, but their origins are debated. I consider this debate in the context of the proposal, by Gallistel and Gelman, that natural number system is a product of cognitive evolution and the proposal, by Carey, that it is a product of human cultural history. I offer a…

We address the challenging task of "computational natural language inference," by which we mean bridging two or more natural language texts while also providing an explanation of how they are connected. In the context of question answering (i.e., finding short answers to natural language questions), this inference connects the question…

Wollack, Cohen, and Eckerly (2015) suggested the "erasure detection index" (EDI) to detect fraudulent erasures for individual examinees. Wollack and Eckerly (2017) extended the EDI to detect fraudulent erasures at the group level. The EDI at the group level was found to be slightly conservative. This paper suggests two modifications of…

Patient safety is a priority in healthcare today. Good clinician numeracy in doctors contributes to patient safety, since it is essential for accuracy in prescribing, and in data interpretation. Evidence, however, suggests that although doctors are assumed to be highly numerate, they often make errors in drug dose calculation and struggle to…

This quantitative research analyzes the impact of the Web Application for the Educational Process on Compound Interest (WAEPCI) considering the machine learning and data science. The sample is composed of 46 students who studied the Financial Mathematics course in a Mexican university during the 2017 school year. WAEPCI presents the calculation of…

Incorporating computational thinking (CT) ideas into core subjects, such as mathematics and science, is one way of bringing early computer science (CS) education into elementary school. Minimal research has explored how teachers can translate their knowledge of CT into practice to create opportunities for their students to engage in CT during…

In this study, it was aimed to teach the addition and subtraction to a student with dyscalculia who is in third grade at elementary school. Before preparing individualized program, the student was given a pretest to measure about his level of the subject. The instruction was carried out in a room in the school, with a time of 40 minutes per day in…

In this study we investigated the effects of two naturalistic 2- to 4-year-old children's intervention programs aimed at promoting children's Spontaneous Focusing On Numerosity (SFON) and early numerical skills. The study consisted of a quasi-experimental, pretest-posttest design with a delayed posttest and an active control group participating in…

We examined the type of errors on multiplication and division computation problems of 326 rising fifth graders enrolled in four elementary schools in Northern Portugal. We further examined whether there was a difference in the number of errors across age and whether there was an association between students' performance on number knowledge and…

Teachers around the world have started teaching programming at the K-9 level, some due to the formal introduction of programming in the national curriculum, others without such pressure and on their own initiative. In this study, we attempted to understand which skills -- both CT-related and general -- are developed among pupils in the process of…

The purpose of this descriptive case study was to develop pre-service chemistry teachers' Technological Pedagogical Science Knowledge (TPASK) through novel computational chemistry modules. The study consisted of two phases starting with designing a computational chemistry based learning environment followed by a case study where students'…