Looking for closed forms for an integral depending on one parameter, we obtain integral identities and new integral presentations of Catalan numbers. Wallis formula appears as an important tool.

A simple and direct method for measuring the absorption of carbon dioxide by two different substances is described. Lithium hydroxide has been used for decades to remove the gas from enclosed living spaces, such as spacecraft and submarines. The ratio of the mass of carbon dioxide absorbed to the mass of lithium hydroxide used obtained from this…

Engagement influences participation, progression and retention in game-based e-learning (GBeL). Therefore, GBeL systems should engage the players in order to support them to maximize their learning outcomes, and provide the players with adequate feedback to maintain their motivation. Innovative engagement monitoring solutions based on players'…

Receiver operating characteristic curve (ROC) analysis was used to investigate the ability of early numeracy curriculum-based measures (EN-CBM) administered in preschool to predict performance below the 25th and 40th percentiles on a quantity discrimination measure in kindergarten. Areas under the curve derived from a sample of 279 students ranged…

Oklahoma is one of 16 states electing to use an A-F letter grade as an indicator of school quality. On the surface, letter grades are an attractive policy instrument for school improvement; they are seemingly clear, simple, and easy to interpret. Evidence, however, on the use of letter grades as an instrument to rank and improve schools is scant…

Computational thinking has been gaining new impetus in the academic community and in K-12 level education. Scratch is a visual programming environment that can be utilized to teach and learn introductory computing concepts. There are some studies investigating the effectiveness of Scratch for K-12 level education. However, studies that have been…

New high-frequency multimodal data collection technologies and machine learning analysis techniques could offer new insights into learning, especially when students have the opportunity to generate unique, personalized artifacts, such as computer programs, robots, and solutions engineering challenges. To date most of the work on learning analytics…

This article presents a systematic review of research related to the use of robotics construction kits (RCKs) in P-12 learning in the STEM disciplines for typically developing children. The purpose of this review is to configure primarily qualitative and mixed methods findings from studies meeting our selection and quality criterion to answer the…

In recent years, teachers' increased workloads have become an issue for policy, and have been multiply pointed out, deriving as they do from peripheral duties such as paperwork, in academic research as well. However, these mentions have not been based on sufficiently solid proof. Here, this paper compares teacher working hours surveys extant from…

This report documents the first-year of implementing Cycle-based Budgeting at Jefferson County Public Schools (Louisville, KY). To address the limitations of incremental budgeting and zero-based budgeting, a Cycle-based Budgeting model was developed and implemented in JCPS. Specifically, each new program needs to submit an on-line budget request…

This research was designed to investigate the conceptualisations and thinking strategies Indigenous Australian students use in counting tasks. Eighteen Aboriginal students, in years 1 to 11 at a remote community school, were interviewed using standard counting tasks and a "counting" task that involved fetching "maku" (witchetty…

This study compared 5 scoring methods in terms of their statistical assumptions. They were then used to score the Teacher Observation of Classroom Adaptation Checklist, a measure consisting of 3 subscales and 21 Likert-type items. The 5 methods used were (a) sum/average scores of items, (b) latent factor scores with continuous indicators, (c)…

The purpose of this study was to examine the cognitive predictors of calculations and number line estimation with whole numbers and fractions. At-risk 4th-grade students (N = 139) were assessed on 7 domain-general abilities (i.e., working memory, processing speed, concept formation, language, attentive behavior, and nonverbal reasoning) and…

This study compared 5 scoring methods in terms of their statistical assumptions. They were then used to score the Teacher Observation of Classroom Adaptation Checklist, a measure consisting of 3 subscales and 21 Likert-type items. The 5 methods used were (a) sum/average scores of items,(b) latent factor scores with continuous indicators, (c)…

The purpose of this study is to investigate teachers' understanding and knowledge of computational estimation, and teaching practice toward to computational estimation. There are six fifth-grade elementary teachers who participated in this study; three teachers with mathematics/ science major and three teachers with non-mathematics/science major.…