The Experts below are selected from a list of 81 Experts worldwide ranked by ideXlab platform
Meixia Ding - One of the best experts on this subject based on the ideXlab platform.
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teaching of the Associative Property a natural classroom investigation
Investigations in Mathematics Learning, 2019Co-Authors: Eli Barnett, Meixia DingAbstract:ABSTRACTIn this study we investigate the teaching of the Associative Property in a natural classroom setting through observation of classroom video of several elementary math classes in a large urb...
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transferring specialized content knowledge to elementary classrooms preservice teachers learning to teach the Associative Property
International Journal of Mathematical Education in Science and Technology, 2018Co-Authors: Meixia Ding, Kayla HeffernanAbstract:This study explores how preservice teachers (PSTs) transfer the intended specialized content knowledge (SCK) to elementary classrooms. Focusing on the case of the Associative Property of multiplication, we compared three PSTs’SCK during enacted lessons in fourth grade classrooms with their own learning in professional development (PD) settings. Findings revealed the PSTs’ successes and challenges in unpacking an example task, especially in areas of making connections between concrete and abstract representations and asking deep questions that target quantitative interactions. Factors that may have supported or hindered PSTs’ SCK transfer include the complex nature of teacher knowledge, the PD effort and the outside factors such as the support from textbooks and cooperating teachers. Implications for teacher education and directions for future research are discussed.
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developing preservice elementary teachers specialized content knowledge the case of Associative Property
International Journal of STEM Education, 2016Co-Authors: Meixia DingAbstract:Specialized content knowledge (SCK) is a type of mathematical content knowledge specifically needed for teaching. This type of knowledge, although serving as a critical component for preservice teacher education, is often challenging to develop with preservice elementary teachers (PTs). The purpose of this study is to investigate PTs’ development of SCK for teaching fundamental mathematical ideas in a university methods course. Focusing on the case of the Associative Property (AP) of multiplication, the author as the course instructor identified three instructional opportunities (a formal introduction and two delayed revisits) to stress two SCK components, representations, and explanations. PTs’ learning progresses were assessed through three diagnostic tests (a pretest, a mid-term exam, and a final exam) and two prompts, which informed the upcoming lesson design. Meanwhile, the course instructor conducted ongoing reflections on PTs’ learning, which also informed the corresponding lessons. It was found that PTs initially generated abstract number sentences without reasoning about the contexts of word problems. This representational sequence indicates a symbol precedence view. When prompted for explanations, PTs focused on individual numbers rather than quantitative relationships, and they could not consistently apply the basic meaning of multiplication for reasoning. The methods course, when designed to address these issues, promoted PTs’ SCK development. At the end of the course, the majority of PTs were able to generate number sentences based on the word problem structures and provided reasonable explanations; however, the methods course also faced dilemmas due to PTs’ robust symbol precedence view and the tension between PTs’ learning and children’s learning. Very few studies have explored ways to support PTs’ knowledge growth in SCK, especially for teaching fundamental mathematical ideas. This study, by carefully documenting the successes and challenges in developing PTs’ SCK, contributes to the existing literature. Based on our findings, this study highlights the importance of stressing basic meanings so as to develop PTs’ explanation skills. Meanwhile, to develop PTs’ representation skills, university instructors should be aware of the tension between PTs’ and children’s learning as manifested by PTs’ symbol precedence view. Finally, to support PTs’ SCK growth, it is also important to emphasize the role of elementary textbooks.
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supporting meaningful initial learning of the Associative Property cross cultural differences in textbook presentations
Jornal Internacional de Estudos em Educação Matemática, 2015Co-Authors: Meixia Ding, Xiaobao Li, Mary Margaret Capraro, Robert M CapraroAbstract:The purpose of this paper is to examine how Chinese and U.S. textbooks present the Associative Property of multiplication (AP) to support student’s initial learning. For all of the identified worked examples, we analyzed the nature of context and the purpose of using word problems and illustrations. There were important cross-cultural differences in textbook presentations. The U.S. reform textbook did not explicitly introduce AP; the U.S. traditional textbooks introduced AP and applied it to computation while the accompanying word problems and illustrations did not help students understand AP. In contrast, the Chinese textbook introduced AP through a word problem context while seamlessly incorporating sense making of AP. Our findings of cross-cultural differences suggest alternative approaches for grounding fundamental mathematical ideas in word problems and illustrations to support students’ meaningful initial learning.
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preservice elementary teachers knowledge for teaching the Associative Property of multiplication a preliminary analysis
The Journal of Mathematical Behavior, 2013Co-Authors: Meixia Ding, Xiaobao Li, Mary Margaret CapraroAbstract:Abstract This study examines preservice elementary teachers’ (PTs) knowledge for teaching the Associative Property (AP) of multiplication. Results reveal that PTs hold a common misconception between the AP and commutative Property (CP). Most PTs in our sample were unable to use concrete contexts (e.g., pictorial representations and word problems) to illustrate AP of multiplication conceptually, particularly due to a fragile understanding of the meaning of multiplication. The study also revealed that the textbooks used by PTs at both the university and elementary levels do not provide conceptual support for teaching AP of multiplication. Implications of findings are discussed.
Yan Zhang - One of the best experts on this subject based on the ideXlab platform.
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preparation of hydrophobic association polyacrylamide in a new micellar copolymerization system and its hydrophobically Associative Property
Macromolecules, 2008Co-Authors: Jian Wang, Yan ZhangAbstract:This paper describes for the first time the combination of a polymerizable surfactant, sodium 2-acrylamido-dodecane sulfonate (NaAMC12S), and a hydrophobic monomer to prepare water-soluble associating polymer via a new micellar process. In this method, the hydrophobic monomer, N-dodecylacrylamide (C12AM) or N,N-didodecylacrylamide (DiC12AM), was first solubilized within NaAMC12S micelles, whereas the hydrophilic monomer acrylamide (AM) was dissolved in the aqueous continuous medium. The micellar copolymerization, therefore, resulted in a ternary hydrophobic association polyacrylamide (HAPAM), namely, C12AM/NaAMC12S/AM or DiC12AM/ NaAMC12S/AM. The chemical structures of these ternary copolymers were characterized with Fourier transform infrared (FTIR) spectroscopy, and their hydrophobic Associative behavior as well as the relationship between microstructure and hydrophobic Associative Property was studied by a combination of the fluorescence probe technique and viscosimetry. The experimental result shows, ...
Mary Margaret Capraro - One of the best experts on this subject based on the ideXlab platform.
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supporting meaningful initial learning of the Associative Property cross cultural differences in textbook presentations
Jornal Internacional de Estudos em Educação Matemática, 2015Co-Authors: Meixia Ding, Xiaobao Li, Mary Margaret Capraro, Robert M CapraroAbstract:The purpose of this paper is to examine how Chinese and U.S. textbooks present the Associative Property of multiplication (AP) to support student’s initial learning. For all of the identified worked examples, we analyzed the nature of context and the purpose of using word problems and illustrations. There were important cross-cultural differences in textbook presentations. The U.S. reform textbook did not explicitly introduce AP; the U.S. traditional textbooks introduced AP and applied it to computation while the accompanying word problems and illustrations did not help students understand AP. In contrast, the Chinese textbook introduced AP through a word problem context while seamlessly incorporating sense making of AP. Our findings of cross-cultural differences suggest alternative approaches for grounding fundamental mathematical ideas in word problems and illustrations to support students’ meaningful initial learning.
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preservice elementary teachers knowledge for teaching the Associative Property of multiplication a preliminary analysis
The Journal of Mathematical Behavior, 2013Co-Authors: Meixia Ding, Xiaobao Li, Mary Margaret CapraroAbstract:Abstract This study examines preservice elementary teachers’ (PTs) knowledge for teaching the Associative Property (AP) of multiplication. Results reveal that PTs hold a common misconception between the AP and commutative Property (CP). Most PTs in our sample were unable to use concrete contexts (e.g., pictorial representations and word problems) to illustrate AP of multiplication conceptually, particularly due to a fragile understanding of the meaning of multiplication. The study also revealed that the textbooks used by PTs at both the university and elementary levels do not provide conceptual support for teaching AP of multiplication. Implications of findings are discussed.
Anthony J. Michaels - One of the best experts on this subject based on the ideXlab platform.
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Lightweight Internet of Things Encryption Using Galois Extension Field Arithmetic
Proceedings - IEEE 2018 International Congress on Cybermatics: 2018 IEEE Conferences on Internet of Things Green Computing and Communications Cyber Ph, 2018Co-Authors: Jason M. Mcginthy, Anthony J. MichaelsAbstract:This paper provides a cryptographic extension to related work on the use of Galois Extension Field techniques [1] to combine multiple output streams from independent pseudorandom number generators (PRNGs), modified for use in low-power stream-cipher cryptographic applications. The core extension field techniques are shown to be computationally efficient, scalable, and support a variety of contextual variations that make them suited for improving cryptography on low power Internet of Things (IoT) devices. This paper focuses specifically on the use in scalable, multi-party cryptographic algorithms, with a focus on the invertible transforms that may be applied in the extension field to rapidly encrypt and decrypt data. A key benefit of this technique is the ability to exploit the Associative Property of the underlying arithmetic to interchange the order of parties encrypting or decrypting the data stream without limitation, making the technique highly versatile, meeting a number of IoT use cases. Testing has shown that this technique passes NIST's test suite for randomness indicating that the produced ciphertext is indistinguishable from a randomly generated sequence. MSP430 implementations in C indicate that this encryption scheme is faster and more energy efficient than AES. 1. Motivation The pervasive nature of the Internet is having a profound impact on everyday lives. Experts claim that the number of Internet of Things (IoT) devices is going to grow well over 50 billion devices by 2020 [2]. Many of these items will improve quality of life such as thermostats [3] and garage doors [4], but the IoT will be an integral part of healthcare [5], smart cities [6], and other future innovations. The proliferation of this new hyper-connected technology has in many cases outpaced the concern over securing devices. In 2016, unsecured and poorly secured IoT devices were used in a large distributed, denial of service (DDoS) attack, named Mirai, taking out major companies', such as Twitter, Spotify, Netflix, Amazon, Tumblr, Reddit, and PayPal, services and websites [7]. Unfortunately, many IoT devices are designed for cost, and security is either ignored or implemented poorly [8]. Therefore as the IoT boom continues, security must be of critical importance as these devices will handle personal and private information of users and surroundings. One crucial area of security is encryption. Encryption is used to ensure that any data transmitted should only be accessible by the intended recipient. However, due to the resource limitations of many IoT devices (limited power, memory, computational ability) current encryption techniques are not feasible for these platforms. This paper presents a lightweight, yet simple and effective encryption technique suitable for IoT and wireless sensor network (WSN) devices. Cryptographic techniques are constantly being researched by both industry and academia. Past competitions such as eSTREAM [9] have been held to help discover new stream ciphers for use in resource constrained devices. However, there is resistance to using new algorithms due to concerns over weak ciphers such as A5/X [10] or implementation errors which have accounted for lack of security in other encryption techniques such as RC4 in WPA [11]. Much of the world uses Advanced Encryption Standard (AES) because it is well understood and has been proven secure over the test of time, but it is not the most energy efficient solution for resource constrained devices. Therefore, the focus and goal of this paper is to provide a reasonable level of multi-party security/data cover for very little cost. Moreover, the ability for every user to provide their own pseudorandom number generator (PRNG) (and not disclose the details of the generation process) enables abstraction of the stream encryption process. The overall contribution for this paper is the presentation of an extremely efficient cryptographic technique that also enables independent multi-party data encryption and decryp-tion. The rest of the paper is organized as follows: Section 2 highlights past and current encryptions techniques, while some background on stream-based cryptographic techniques using Galois Extension Fields will be presented in Section 3. Results based on tests for randomness are discussed in Section 4, software implementation and verification results are presented in Section 5, followed by specific use case examples in Section 6 and conclusions in Section 7. 2. Background Most cryptographic algorithms, such as AES, Data Encryption Standard (DES), and Rivest-Shamir-Adleman (RSA) [12], rely on a series of number theoretic transforms that ensure the underlying security of the data encrypted in case of observation by a non-approved third party who 74
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Lightweight Internet of Things Encryption Using Galois Extension Field Arithmetic
2018 IEEE International Conference on Internet of Things (iThings) and IEEE Green Computing and Communications (GreenCom) and IEEE Cyber Physical and , 2018Co-Authors: Jason M. Mcginthy, Anthony J. MichaelsAbstract:This paper provides a cryptographic extension to related work on the use of Galois Extension Field techniques [1] to combine multiple output streams from independent pseudorandom number generators (PRNGs), modified for use in low-power stream-cipher cryptographic applications. The core extension field techniques are shown to be computationally efficient, scalable, and support a variety of contextual variations that make them suited for improving cryptography on low power Internet of Things (IoT) devices. This paper focuses specifically on the use in scalable, multi-party cryptographic algorithms, with a focus on the invertible transforms that may be applied in the extension field to rapidly encrypt and decrypt data. A key benefit of this technique is the ability to exploit the Associative Property of the underlying arithmetic to interchange the order of parties encrypting or decrypting the data stream without limitation, making the technique highly versatile, meeting a number of IoT use cases. Testing has shown that this technique passes NIST's test suite for randomness indicating that the produced ciphertext is indistinguishable from a randomly generated sequence. MSP430 implementations in C indicate that this encryption scheme is faster and more energy efficient than AES.
Jian Wang - One of the best experts on this subject based on the ideXlab platform.
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preparation of hydrophobic association polyacrylamide in a new micellar copolymerization system and its hydrophobically Associative Property
Macromolecules, 2008Co-Authors: Jian Wang, Yan ZhangAbstract:This paper describes for the first time the combination of a polymerizable surfactant, sodium 2-acrylamido-dodecane sulfonate (NaAMC12S), and a hydrophobic monomer to prepare water-soluble associating polymer via a new micellar process. In this method, the hydrophobic monomer, N-dodecylacrylamide (C12AM) or N,N-didodecylacrylamide (DiC12AM), was first solubilized within NaAMC12S micelles, whereas the hydrophilic monomer acrylamide (AM) was dissolved in the aqueous continuous medium. The micellar copolymerization, therefore, resulted in a ternary hydrophobic association polyacrylamide (HAPAM), namely, C12AM/NaAMC12S/AM or DiC12AM/ NaAMC12S/AM. The chemical structures of these ternary copolymers were characterized with Fourier transform infrared (FTIR) spectroscopy, and their hydrophobic Associative behavior as well as the relationship between microstructure and hydrophobic Associative Property was studied by a combination of the fluorescence probe technique and viscosimetry. The experimental result shows, ...
