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,…

To explain children's difficulties learning fraction arithmetic, Braithwaite et al. (2017) proposed FARRA, a theory of fraction arithmetic implemented as a computational model. The present study tested predictions of the theory in a new domain, decimal arithmetic, and investigated children's use of conceptual knowledge in that domain. Sixth and…

A quick survey of physics textbooks shows that many (Knight, Young, and Serway for example) cover estimation, significant digits, precision versus accuracy, and uncertainty in the first chapter. Estimation "Fermi" questions are so useful that there has been a column dedicated to them in "TPT" (Larry Weinstein's "Fermi…

Recent years have seen a surge of calls for personalization of education. Automatised adaptivity in serious games has been advocated as a potential instantiation of such calls. Yet little is known about the extent to which personalised learning through automatised adaptivity poses an advantage for language learning over generalised teacher-led…

Being able to estimate quantity is important in everyday life and for success in the STEM disciplines. However, people have difficulty reasoning about magnitudes outside of human perception (e.g., nanoseconds, geologic time). This study examines patterns of estimation errors across temporal and spatial magnitudes at large scales. We evaluated the…

Recursion is one of the most difficult programming topics for students. In this paper, an instructional method is proposed to enhance students' understanding of recursion tracing. The proposal is based on the use of rules to translate linear recursion algorithms into equivalent, iterative ones. The paper has two main contributions: the…

Assessment data from the United States and international reports of student achievement indicate that upper elementary students are failing to meet basic levels of proficiency in fractions and writing, and that this is particularly prevalent with students with or at-risk for learning disabilities in mathematics. Proficiency with fractions has been…

The capture-mark-release-recapture method provides a simple way to estimate population size. However, when used as part of ecological sampling, this method does not easily allow an opportunity to evaluate the accuracy of the calculation because the actual population size is unknown. Here, we describe a method that can be used to measure the…

This study tested whether second graders use benchmark-based strategies when solving a number line estimation (NLE) task. Participants were assigned to one of three conditions based on the availability of benchmarks provided on the number line. In the bounded condition, number lines were only bounded at both sides by 0 and 200, while the midpoint…

Even in primary school, mathematics achievement depends upon the efficiency of cognitive, metacognitive and self-regulatory processes. Thus, for pupils to carry out a computation, such as a written calculation, metacognitive mechanisms play a crucial role, since children must employ self-regulation to assess the precision of their own thinking and…

This study investigated the roles of different executive function (EF) components (inhibition, shifting, and working memory) in 2-step arithmetic word problem solving. A sample of 139 children aged 8 years old and regularly attending the 3rd grade of primary school were tested on 6 EF tasks measuring different EF components, a reading task and a…

The purpose of the present study was to examine factors that influence strategic flexibility in computational estimation for Chinese- and Canadian-educated adults. Strategic flexibility was operationalized as the percentage of trials on which participants chose the problem-based procedure that best balanced proximity to the correct answer with…

Curriculum-based measurement of oral reading (CBM-R) is used to index the level and rate of student growth across the academic year. The method is frequently used to set student goals and monitor student progress. This study examined the diagnostic accuracy and quality of growth estimates derived from pre-post measurement using CBM-R data. A…

In order for simulations and games to be effective for learning, instructional designers must verify that the underlying computational models being used have an appropriate degree of fidelity to the conceptual models of their real-world counterparts. A simulation/game that provides incorrect feedback is likely to promote misunderstanding and…

This study presents an efficient approach to personalized mispronunciation detection of Taiwanese-accented English. The main goal of this study was to detect frequently occurring mispronunciation patterns of Taiwanese-accented English instead of scoring English pronunciations directly. The proposed approach quickly identifies personalized…