The celebrated Basel Problem, that of finding the infinite sum 1 + 1/ 4 + 1/9 + 1/16 + ..., was open for 91 years. In 1735 Euler showed that the sum is pi[superscript 2]/6. Dozens of other solutions have been found. We give one that is short and elementary.

The content validity ratio (Lawshe) is one of the earliest and most widely used methods for quantifying content validity. To correct and expand the table, critical values in unit steps and at multiple alpha levels were computed. Implications for content validation are discussed. (Contains 2 tables and 1 figure.)

An emerging literature demonstrates that relevance interventions, which ask students to produce written reflections on how what they are learning relates to their lives, improve student learning outcomes. As part of a randomized evaluation of a relevance intervention (N = 1,978 students from 82 ninth-grade classes), we used Complier Average Causal…

Working memory capacities are associated with mathematical development. Many studies have tried to improve working memory abilities through training. Furthermore, the central executive has been shown to be the component of working memory, which is the most strongly related to numerical and arithmetical skills. Therefore, we developed a training…

The authors of this article strongly advocate for a change to the current Australian model of primary education in order to, among other things, establish the concrete practicalities of systematic mathematics thinking thereby limiting the "re-teaching" time required of secondary school mathematics teachers; bring a clear focus to the…

The subject of the research is to build methodologies to evaluate the student knowledge by testing. The author points to the importance of feedback about the mastering level in the learning process. Testing is considered as a tool. The object of the study is to create the test system models for defence practice problems. Special attention is paid…

We studied the processes involved in synthesis writing, focusing on planning, editing and self-regulation strategies. The aims of the study were a) to analyse the temporal distribution of cognitive strategies and self-regulation across the different phases of writing, b) to identify different writing approaches (i.e., profiles), and c) to…

This study analyzed the relationship between benchmark scores from two curriculum-based measurement probes in mathematics (M-CBM) and student performance on a state-mandated high-stakes test. Participants were 298 students enrolled in grades 7 and 8 in a rural southeastern school. Specifically, we calculated the criterion-related and predictive…

Studies comparing mathematical abilities of children with autism spectrum disorder (ASD) and typically developing children are hitherto scarce, inconclusive, and mainly focusing on elementary school children or adolescents. The present study wants to gain insight into the foundation of mathematics by looking at preschool performances. Five early…

This research report presents the final year results of a three-year research project on computational thinking (CT). The project, funded by the National Science Foundation, involved training teachers in grades four through six to implement Scalable Game Design and LEGO® EV3 robotics during afterschool clubs. Thirty teachers and 531 students took…

Item response models typically assume that the item characteristic (step) curves follow a logistic or normal cumulative distribution function, which are strictly monotone functions of person test ability. Such assumptions can be overly-restrictive for real item response data. We propose a simple and more flexible Bayesian nonparametric IRT model…

State education budgets have shrunk since the economic recession of 2007-09. During the 2012-13 school year 35 states provided less funding for education than they had five years earlier (Leachman, Albares, Masterson, & Wallace, 2016; Levin et al., 2012; Oliff, Mai, & Leachman, 2012). As a result, districts across the country are seeking…

Texas's higher education plan, 60x30TX, calls for undergraduate student loan debt to not exceed 60 percent of first-year wages for graduates of Texas public institutions by 2030 (earning a certificate, associate's, or bachelor's). The Texas Higher Education Coordinating Board (THECB) calculates the total undergraduate debt of a graduate as all…

The What Works Clearinghouse (WWC) systematic review process is the basis of many of its products, enabling the WWC to use consistent, objective, and transparent standards and procedures in its reviews, while also ensuring comprehensive coverage of the relevant literature. The WWC systematic review process consists of five steps: (1) Developing…

This volume focuses on the implications of digital technologies for educators and educational decision makers that are not widely represented in the literature. The chapters contained in the volume are based on the presentations at the 2020 edition of the CELDA conference and cover multiple developments in the field such as deploying learning…