Empirical research has documented how children's early counting develops into an increasingly abstract process, and initial counting procedures are reified as children develop and use more sophisticated counting. In this development, the learning of different oral counting sequences that allow children to count in steps bigger than one is seen as…

Considerable recent work suggests that mathematical abilities in children correlate with the ability to estimate numerosity. Does math correlate only with numerosity estimation, or also with other similar tasks? We measured discrimination thresholds of school-age (6- to 12.5-years-old) children in 3 tasks: numerosity of patterns of relatively…

Individuals with agrammatic Broca's aphasia experience difficulty when processing reversible non-canonical sentences. Different accounts have been proposed to explain this phenomenon. The Trace Deletion account (Grodzinsky, 1995, 2000, 2006) attributes this deficit to an impairment in syntactic representations, whereas others (e.g., Caplan,…

Partially compensatory models may capture the cognitive skills needed to answer test items more realistically than compensatory models, but estimating the model parameters may be a challenge. Data were simulated to follow two different partially compensatory models, a model with an interaction term and a product model. The model parameters were…

Who will make a better estimate concerning the number of jelly beans in a jar, a single person or a group of people? On one side of the debate is the notion that a person would make a better decision because he or she uses unique knowledge that the group may not possess. On the opposite side of the argument is the claim that because of their…

Computational thinking (CT) parallels the core practices of science, technology, engineering, and mathematics (STEM) education and is believed to effectively support students' learning of science and math concepts. However, despite the synergies between CT and STEM education, integrating the two to support synergistic learning remains an important…

One influence contributing to this trend may be the imprecise use of mathematics language. Educators may not interpret mathematics as a second (or third) language for children, when, in fact, all children are mathematical-language learners (Barrow, 2014). The numerals, symbols, and terms that explain mathematics concepts and procedures are…

Growth curve modeling provides a general framework for analyzing longitudinal data from social, behavioral, and educational sciences. Bayesian methods have been used to estimate growth curve models, in which priors need to be specified for unknown parameters. For the covariance parameter matrix, the inverse Wishart prior is most commonly used due…

In this theoretical paper, I consider reversibility as a defining characteristic of mathematics. Inverse pairs of formalized operations, such as multiplication and division, provide obvious examples of this reversibility. However, there are exceptions, such as multiplying by 0. If we are to follow Piaget's lead in defining mathematics as the…

In the domain of "Counting & Cardinality," Common Core State Standards indicate that by the time students leave kindergarten, they should know the names and sequence of number words up to 100, be able to count to determine the number of objects in a small set (up to 20), and make comparisons between small sets of objects (National…

We present a logistic function of a monotonic polynomial with a lower asymptote, allowing additional flexibility beyond the three-parameter logistic model. We develop a maximum marginal likelihood based approach to estimate the item parameters. The new item response model is demonstrated on math assessment data from a state, and a computationally…

This study aims to demonstrate how the average speed of a light-emitting toy car may be determined using a smartphone's light sensor. The freely available Android smartphone application, "AndroSensor," was used for the experiment. The classroom experiment combines complementary physics knowledge of optics and kinematics to find the…

Numerous computational and spectroscopic studies have demonstrated the decisive role played by nonadiabatic coupling in photochemical reactions. Nonadiabatic coupling drives photochemistry when potential energy surfaces are nearly degenerate at avoided crossings or truly degenerate at unavoided crossings. The dynamics induced by nonadiabatic…

Representations of numerical value have been assessed by using bounded (e.g., 0-1,000) and unbounded (e.g., 0-?) number-line tasks, with considerable debate regarding whether 1 or both tasks elicit unique cognitive strategies (e.g., addition or subtraction) and require unique cognitive models. To test this, we examined how well a mixed log-linear…

The purpose of the current study was to investigate how combinations of different epoch durations and cut-points affect the estimations of sedentary time and physical activity in adolescents. Accelerometer data from 101 adolescents were derived and 30 combinations were used to estimate sedentary time, light, moderate, vigorous, and combined…