This study compared five common multilevel software packages via Monte Carlo simulation: HLM 7, M"plus" 7.4, R (lme4 V1.1-12), Stata 14.1, and SAS 9.4 to determine how the programs differ in estimation accuracy and speed, as well as convergence, when modeling multiple randomly varying slopes of different magnitudes. Simulated data…

This article investigates the effect of kinesthetic educational game on students' mental computation speed. A Solomon four-group design was used to avoid the influence of pretest-posttest design. In order to determine which grade is appropriate for this game, a pilot study was conducted with 30 students. As for the main study, 123 students…

Within the past few years there has been an increasing emphasis on making computer science (CS) more accessible for all K-12 students. In 2013 there were 12 states that allowed CS courses to count towards high school graduation, and in 2018 that number had grown to 35 states plus the District of Columbia (Code.org, 2018). Due to the increasing…

Case studies appear prominently in political science, sociology, and other social science fields. A scholar employing a case study research design in an effort to estimate causal effects must confront the question, how should cases be selected for analysis? This question is important because the results derived from a case study research program…

Without a doubt, fractions prove to be a stumbling block for many children. Researchers have suggested a variety of explanations for why this is the case. The introduction of symbolization and operations before the development of conceptual understanding of fractions, a lack of understanding of the role of the numerator and denominator, and an…

A simple molecular dynamics experiment is described to demonstrate transport properties for the undergraduate physical chemistry laboratory. The AMBER package is used to monitor self-diffusion in "n"-hexane. Scripts (available in the Supporting Information) make the process considerably easier for students, allowing them to focus on the…

Working memory (WM) is used for storing information in a highly accessible state so that other mental processes, such as reasoning, can use that information. Some WM tasks require that participants not only store information, but also reason about that information to perform optimally on the task. In this study, we used visual WM tasks that had…

Very recently, in the "Australian Association of Mathematics Teachers (AAMT)/Australian Industry Group quantitative report" (2014), concerns were raised that school mathematics is lacking real world application. This report highlighted the gaps between school mathematics and the requirements of the workplace. After interviewing industry…

This brief "Math for Real" article introduces Ohanna, a seventh grader who lives in New York City and regularly takes the bus to get around the city. Ohanna pays $2.50 per bus ride when using her MetroCard. She earns a 5% bonus when she refills the card with a minimum of $5.00. For example, if she adds $10.00 on her MetroCard, her…

This investigation presents students with the challenge of determining the total number of eggs in a photograph of a stack of egg trays. The perspective of the photograph does not allow students to count all the individual eggs in the top tray but does allow them to see the number of eggs in one row and one column of the top tray. During this…

We report on interview results from a classroom teaching experiment in a Number and Operations course for prospective elementary teachers. Improving the number sense of this population is an important goal for mathematics teacher education, and researchers have found this goal to be difficult to accomplish. In earlier work, we devised a local…

This article explores how integrating computational tools into a general chemistry laboratory course can influence student perceptions of programming and investigates relationships among student perceptions, prior experience, and student outcomes.

Reduction is one of the key techniques used for problem-solving in computer science. In particular, in the theory of computation and complexity (TCC), mapping and polynomial reductions are used for analysis of decidability and computational complexity of problems, including the core concept of NP-completeness. Reduction is a highly abstract…

For decades, students have been encouraged to use "Please Excuse My Dear Aunt Sally" as a means of learning the order of operations. Teachers unfamiliar with the Aunt Sally mnemonic are perhaps more familiar with a mnemonic such as PEMDAS. Each mnemonic is intended to convey "parentheses, exponents, multiplication, division,…

To assess the direct and indirect effect of an intervention, multilevel 2-1-1 studies with intervention randomized at the upper (class) level and mediator and outcome measured at the lower (student) level are frequently used in educational research. In such studies, the mediation process may flow through the student-level mediator (the within…