Taylor series play a ubiquitous role in calculus courses, and their applications as approximants to functions are widely taught and used everywhere. However, it is not common to present the students with other types of approximations besides Taylor polynomials. These notes show that polynomials construed to satisfy certain boundary conditions at…

We discuss the limits of the equation of the period of a simple pendulum, T[subscript s] = 2[pi][square root]l/g, frequently used in high-school and university classrooms to measure the acceleration of gravity. We evaluate the relative error in determining the acceleration of gravity with this simple equation instead of a more realistic one,…

R and Python are commonly used software languages for data analytics. Using these languages as the course software for the introductory course gives students practical skills for applying statistical concepts to data analysis. However, the reliance upon the command line is perceived by the typical nontechnical introductory student as sufficiently…

It is expected that children increasingly learn to identify errors throughout their schooling process and even before it. As a further step, however, some scholars have suggested how a culture of error should be implemented in the classroom for the student to be able not only to locate errors but also, and above all, to learn from them. Yet the…

The articles presented in this Special Issue provide evidence for many statistically significant relationships among error scores obtained from the Kaufman Test of Educational Achievement, Third Edition (KTEA)-3 between various groups of students with and without disabilities. The data reinforce the importance of examiners looking beyond the…

When it comes to L1 and L2 differences in second-language writing, some researchers are not fully convinced that there is a fundamental difference. However, when comparing L1 and L2 writing, many would agree that macro- and micro-level writing characteristics exist and overlap (Eckstein and Ferris 2018). This article identifies some of the…

In online educational systems we can easily collect and analyze extensive data about student learning. Current practice, however, focuses only on some aspects of these data, particularly on correctness of students answers. When a student answers incorrectly, the submitted wrong answer can give us valuable information. We provide an overview of…

Lying is a deliberate attempt to transmit messages that mislead others. Analysis of language behaviors holds great promise as an objective method of detecting deception. The current study reports on the frequency of use and acoustic nature of "um" and "like" during laboratory-elicited lying versus truth-telling. Results obtained using a…

This article characterizes and measures errors in the 2010 National Research Council (NRC) assessment of research-doctorate programs in geography. This article provides a conceptual model for data-based sources of uncertainty and reports on a quantitative assessment of NRC research data uncertainty for a particular geography doctoral program.…

Teachers all over the world are aware that students struggle with fractional concepts and with elementary algebra. Support for this assertion can be found in a variety of research reports. The National Assessment of Educational Progress (NAEP), a United States report, indicates that students have recurrently demonstrated a lack of proficiency in…

Large corpora such as the British National Corpus and the COBUILD Corpus and Collocations Sampler are now accessible, free of charge, online and can be usefully incorporated into a process writing approach to help develop students' writing skills. This article aims to familiarize readers with these resources and to show how they can be usefully…

Studies that examine the impacts of education interventions on key student, teacher, and school outcomes typically collect data on large samples and on many outcomes. In analyzing these data, researchers typically conduct multiple hypothesis tests to address key impact evaluation questions. Tests are conducted to assess intervention effects for…

There is variability in the estimation of an equating transformation because common-item parameters are obtained from responses of samples of examinees. The most commonly used standard error of equating quantifies this source of sampling error, which decreases as the sample size of examinees used to derive the transformation increases. In a…

Interactions between (multiple indicator) latent variables are rarely used because of implementation complexity and competing strategies. Based on 4 simulation studies, the traditional constrained approach performed more poorly than did 3 new approaches-unconstrained, generalized appended product indicator, and quasi-maximum-likelihood (QML). The…

Answers to theoretical questions about the place of input in a formal second language acquisition model are dependent on a distinction between two kinds of learner hypotheses. Type-N hypotheses require "negative evidence" for testing, while Type-P hypotheses are tested on the basis of "positive data" alone. (Author/CB)