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Gestures are one of the ways in which mathematical cognition is embodied and have been elevated as a potentially important semiotic device in the teaching of mathematics. As such, a better understanding of gestures used during mathematics instruction (including frequency of use, types of gestures, how they are used, and the possible relationship between gestures and student performance) would inform mathematics education. We aim to understand teachers’ gestures in the context of early algebra, particularly in the teaching of the equal sign. Our findings suggest that the equal sign is a relatively rich environment for gestures, which are used in a variety of ways. Participating teachers used gestures frequently to support their teaching about the equal sign. Furthermore, the use of gestures varied depending on the particular conception of the equal sign the instruction aimed to promote. Finally, teacher gesture use in this context is correlated with students’ high performance on an early algebra assessment.more » « lessFree, publicly-accessible full text available May 8, 2025
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We experimentally demonstrate that we can detect correlated errors in a twin-field quantum key distribution (TFQKD) system by using a technique that is related to self-consistent tomography. We implement a TFQKD system based on a fiber-Sagnac loop, in which Alice and Bob encode information in the phase of weak coherent states that propagate in opposite directions around the loop. These states interfere as they exit the loop and are detected by a third party, Charlie, who reports the results of their measurements to Alice and Bob. We find that it is possible for Alice and Bob to detect correlated state-preparation and measurement errors while trusting only their own individual states, and without trusting Charlie’s measurements.
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Abstract We face complex global issues such as climate change that challenge our ability as humans to manage them. Models have been used as a pivotal science and engineering tool to investigate, represent, explain, and predict phenomena or solve problems that involve multi-faceted systems across many fields. To fully explain complex phenomena or solve problems using models requires both systems thinking (ST) and computational thinking (CT). This study proposes a theoretical framework that uses modeling as a way to integrate ST and CT. We developed a framework to guide the complex process of developing curriculum, learning tools, support strategies, and assessments for engaging learners in ST and CT in the context of modeling. The framework includes essential aspects of ST and CT based on selected literature, and illustrates how each modeling practice draws upon aspects of both ST and CT to support explaining phenomena and solving problems. We use computational models to show how these ST and CT aspects are manifested in modeling.
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Gresalfi, M. ; Horn, I. S. (Ed.)There is broad belief that preparing all students in preK-12 for a future in STEM involves integrating computing and computational thinking (CT) tools and practices. Through creating and examining rich “STEM+CT” learning environments that integrate STEM and CT, researchers are defining what CT means in STEM disciplinary settings. This interactive session brings together a diverse spectrum of leading STEM researchers to share how they operationalize CT, what integrated CT and STEM learning looks like in their curriculum, and how this learning is measured. It will serve as a rich opportunity for discussion to help advance the state of the field of STEM and CT integration.more » « less
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https://doi.org/https://doi.dx.org/10.22318/icls2020.1479 https://repository.isls.org//handle/1/6353Gresalfi, M. ; Horn, I. S. (Ed.)There is broad belief that preparing all students in preK-12 for a future in STEM involves integrating computing and computational thinking (CT) tools and practices. Through creating and examining rich “STEM+CT” learning environments that integrate STEM and CT, researchers are defining what CT means in STEM disciplinary settings. This interactive session brings together a diverse spectrum of leading STEM researchers to share how they operationalize CT, what integrated CT and STEM learning looks like in their curriculum, and how this learning is measured. It will serve as a rich opportunity for discussion to help advance the state of the field of STEM and CT integration.more » « less