Teachers strive to engage students in rich and varied experiences involving exploration. These experiences should be accessible to all types of learners (e.g., visual, kinesthetic, mathematically inclined), offering multiple pathways for engagement at different levels of sophistication and accommodating both conceptual and computational…

Getting students to think about the relationships between area and perimeter beyond the formulas for these measurements is never easy. An interesting, nonroutine, and accessible problem that will stimulate such thoughts is the Lattice Octagon problem. A "lattice polygon" is a polygon whose vertices are points of a regularly spaced array.…

This study examined Advanced Placement Calculus students' mathematical understanding of rate of change, after studying four years of college preparatory (integrated or single-subject) mathematics. Students completed the Precalculus Concept Assessment (PCA) and two open-ended tasks with questions about rates of change. After adjusting for prior…

Developmental coordination disorder (DCD) is a heterogeneous disorder, which is often co-morbid with learning disabilities. However, mathematical problems have rarely been studied in DCD. The aim of this study was to investigate the mathematical problems in children with various degrees of motor problems. Specifically, this study explored if the…

In recent years, the idea of language influencing the cognitive development of an understanding of place value has received increasing attention. This study explored the influence of using explicit number names on pre-kindergarten and kindergarten students' ability to rote count, read two-digit numerals, model two-digit numbers, and identify the…

We tested children in Grades 1 to 5, as well as college students, on a number line estimation task and examined latencies and errors to explore the cognitive processes involved in estimation. The developmental trends in estimation were more consistent with the hypothesized shift from logarithmic to linear representation than with an account based…

Both adults and young children possess powerful statistical computation capabilities--they can infer the referent of a word from highly ambiguous contexts involving many words and many referents by aggregating cross-situational statistical information across contexts. This ability has been explained by models of hypothesis testing and by models of…

These proceedings contain the papers of the 7th International Conference on Educational Technologies 2020 (ICEduTech 2020), which has been organised by the International Association for Development of the Information Society and co-organised by the University of São Paulo ("Universidade de São Paulo"), Brazil, from 5 to 7 February 2020.…

We consider a version of an optimal stopping problem, in which a customer is presented with a finite set of items, one by one. The customer is aware of the number of items in the finite set and the minimum and maximum possible value of each item, and must purchase exactly one item. When an item is presented to the customer, she or he observes its…

This paper provides practical guidance for researchers who are designing and analyzing studies that randomize schools--which comprise three levels of clustering (students in classrooms in schools)--to measure intervention effects on student academic outcomes when information on the middle level (classrooms) is missing. This situation arises…

Consider a discrete bivariate random variable (X, Y) with possible values x[subscript 1], x[subscript 2],..., x[subscript I] for X and y[subscript 1], y[subscript 2],..., y[subscript J] for Y. Further suppose that the corresponding families of conditional distributions, for X given values of Y and of Y for given values of X are available. We…

In the framework of the Italian National Plan "Lauree Scientifiche" (PLS) in collaboration with secondary schools, we have investigated the mechanical paradox of the double cone. We have calculated the geometric condition for obtaining an upward movement. Based on this result, we have built a mechanical model with a double cone made of aluminum…

We derive the energy levels associated with the even-parity wavefunctions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical example of a modification of the usual harmonic oscillator potential, with emphasis on the modification of the…

We describe a method for the accurate calculation of bound-state and resonance energies for one-dimensional potentials. We calculate the shape resonances for symmetric two-barrier potentials and compare them with those coming from the Siegert approximation, the complex scaling method and the box-stabilization method. A comparison of the…

Accurate time measurement is essential to temporal analysis in sport. This study aimed to (a) develop a new method for time computation from surveyed trajectories using a high-end global navigation satellite system (GNSS), (b) validate its precision by comparing GNSS with photocells, and (c) examine whether gate-to-gate times can provide more…