This summary of nine studies provides information about evidence-based practices for Tier 2 interventions and how to use Response to Intervention (RTI) in mathematics. It gives a critical technical analysis and review of research on RTI and multi-tiered instructional systems. In an earlier Center on Instruction publication, the authors described…

Obtaining an accurate microscopic description of water structure and dynamics is of great interest to molecular biology researchers and in the physics and quantum chemistry simulation communities. This dissertation describes efforts to apply quantum Monte Carlo methods to this problem with the goal of making progress toward a fully "ab initio"…

A fundamental goal of educational research is identifying students' current stage of skill mastery (complete/partial/none). In recent years a number of cognitive diagnosis models have become a popular means of estimating student skill knowledge. However, these models become difficult to estimate as the number of students, items, and skills grows.…

In educational research, a fundamental goal is identifying which skills students have mastered, which skills they have not, and which skills they are in the process of mastering. As the number of examinees, items, and skills increases, the estimation of even simple cognitive diagnosis models becomes difficult. We adopt a faster, simpler approach:…

This paper aims to highlight the significance of a particular aspect of magnitude processing, namely counting and subitizing or the rapid enumeration of small sets of items, for learning. Emphasis is laid on the historical roots and the conceptual framework as well as on studies on pre-verbal and school-age children. Evidence of the potential…

This paper describes how to calculate measurement uncertainties using as a practical example the assessment of the thickness of ping-pong balls and their material density. The advantages of a randomized experiment are also discussed. This experiment can be reproduced in the physics laboratory for undergraduate students. (Contains 7 tables, 1…

Images formed from light rays refracting a spherical surface are often introduced in textbooks using the paraxial approximation. Incoming rays propagating from the object meeting the surface of a transparent medium at a given point for which the angle is larger than 15 degrees with respect to the normal are not described accurately from the…

The dipole radiation from an oscillating charge is treated using the Hamiltonian approach to electrodynamics where the concept of cavity modes plays a central role. We show that the calculation of the radiation field can be obtained in a closed form within this approach by emphasizing the role of coherence between the cavity modes, which is…

Fluency with basic number facts is vital for students' progress in mathematics. Not only does it contribute to students' facility with mental computation and algorithms, but an understanding of numbers and their properties builds a foundation for future mathematical work including algebra. There are many activities that can help students…

A bivariate lognormal model for the distribution of the response times on a test by a pair of test takers is presented. As the model has parameters for the item effects on the response times, its correlation parameter automatically corrects for the spuriousness in the observed correlation between the response times of different test takers because…

The estimation of fetal birth weight is an important factor in the management of high risk pregnancies. The information and knowledge gained through this study, comparing a combination of various fetal parameters using computer assisted analysis, will help the obstetrician to screen the high risk pregnancies, monitor the growth and development,…

This article uses photographs as a springboard for mathematical inquiry to encourage readers to see patterns and relationships that they can think about and extend in a mathematically playful way. Herein, two photographs are presented along with a discussion of the meaning of slopes and their relationship to gradient and pitch. (Contains 6…

The capital accumulation ratio (CAR) is commonly used in academic research as a measure of household portfolio quality. This study tested whether a higher initial CAR impacts change in wealth over a decade among households in the accumulation life cycle stage. Meeting the 25% CAR guideline resulted in a 28.1% increase in net worth between 1994 and…

The mythology surrounding Hercules has been a part of human culture for over 2,500 years. In ancient Greek mythology, Eurystheus assigns various labors to Hercules, who has to perform them in order to cleanse his soul. This article treats one of the more famous labors, the fifth labor: The Augean Stables. The labor is provided verbatim from…

A comprehensive understanding of biological functions requires new systemic perspectives, such as those provided by systems biology. Systems biology approaches are hypothesis-driven and involve iterative rounds of model building, prediction, experimentation, model refinement, and development. Developments in computer science are allowing for ever…