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Articles 1 - 23 of 23
Full-Text Articles in Physical Sciences and Mathematics
Functional Singular Spectrum Analysis, Hossein Haghbin, Seyed Morteza Najibi, Rahim Mahmoudvand, Jordan Trinka, Mehdi Maadooliat
Functional Singular Spectrum Analysis, Hossein Haghbin, Seyed Morteza Najibi, Rahim Mahmoudvand, Jordan Trinka, Mehdi Maadooliat
Mathematical and Statistical Science Faculty Research and Publications
In this paper, we develop a new extension of the singular spectrum analysis (SSA) called functional SSA to analyze functional time series. The new methodology is constructed by integrating ideas from functional data analysis and univariate SSA. Specifically, we introduce a trajectory operator in the functional world, which is equivalent to the trajectory matrix in the regular SSA. In the regular SSA, one needs to obtain the singular value decomposition (SVD) of the trajectory matrix to decompose a given time series. Since there is no procedure to extract the functional SVD (fSVD) of the trajectory operator, we introduce a computationally …
Triple Oxygen Isotope Constraints On Atmospheric O2 And Biological Productivity During The Mid-Proterozoic, Peng Liu, Jingjin Liu, Aoshaung Ji, Christopher T. Reinhard, Noah J. Planavsky, Dmitri Babikov, Raymond G. Najjar, James F. Kasting
Triple Oxygen Isotope Constraints On Atmospheric O2 And Biological Productivity During The Mid-Proterozoic, Peng Liu, Jingjin Liu, Aoshaung Ji, Christopher T. Reinhard, Noah J. Planavsky, Dmitri Babikov, Raymond G. Najjar, James F. Kasting
Chemistry Faculty Research and Publications
Reconstructing the history of biological productivity and atmospheric oxygen partial pressure (pO2) is a fundamental goal of geobiology. Recently, the mass-independent fractionation of oxygen isotopes (O-MIF) has been used as a tool for estimating pO2 and productivity during the Proterozoic. O-MIF, reported as Δ′17O, is produced during the formation of ozone and destroyed by isotopic exchange with water by biological and chemical processes. Atmospheric O-MIF can be preserved in the geologic record when pyrite (FeS2) is oxidized during weathering, and the sulfur is redeposited as sulfate. Here, sedimentary sulfates from …
2d Covalent Organic Frameworks With An Incorporated Manganese Complex For Light Driven Carbon Dioxide Reduction, Denan Wang, Daniel Streater, Yun Peng, Jier Huang
2d Covalent Organic Frameworks With An Incorporated Manganese Complex For Light Driven Carbon Dioxide Reduction, Denan Wang, Daniel Streater, Yun Peng, Jier Huang
Chemistry Faculty Research and Publications
Covalent organic frameworks (COFs) have emerged as a novel class of crystalline porous photocatalytic materials due to their unique properties such as large surface area, tunable porosity, and rigid structure. In this work, we report the direct incorporation of a manganese CO2 molecular catalyst (MC) into COFs (Mn−TTA-COF) and the evaluation of its capability as photocatalyst for visible light driven CO2 reduction to form CO. We found that the photocatalytic activity of Mn−TTA-COF is quite low, which mainly results from the elimination of the CO ligand in the Mn MC upon light illumination, rendering its short duration in …
Identification Of An Intermediate Species Along The Nitrile Hydratase Reaction Pathway By Epr Spectroscopy, Wasantha Lankathilaka Karunagala Pathiranage, Natalie Gumataotao, Adam T. Fiedler, Richard C. Holz, Brian Bennett
Identification Of An Intermediate Species Along The Nitrile Hydratase Reaction Pathway By Epr Spectroscopy, Wasantha Lankathilaka Karunagala Pathiranage, Natalie Gumataotao, Adam T. Fiedler, Richard C. Holz, Brian Bennett
Physics Faculty Research and Publications
A new method to trap catalytic intermediate species was employed with Fe-type nitrile hydratase from Rhodococcus equi TG328-2 (ReNHase). ReNHase was incubated with substrates in a 23% (w/w) NaCl/H2O eutectic system that remained liquid at −20 °C, thereby permitting the observation of transient species that were present at electron paramagnetic resonance (EPR)-detectable levels in samples frozen while in the steady state. FeIII-EPR signals from the resting enzyme were unaffected by the presence of 23% NaCl, and the catalytic activity was ∼55% that in the absence of NaCl at the optimum pH of 7.5. …
Examination Of The Catalytic Role Of The Axial Cystine Ligand In The Co-Type Nitrile Hydratase From Pseudonocardia Thermophila Jcm 3095, Irene Anyango Ogutu, Martin St. Maurice, Brian Bennett, Richard C. Holz
Examination Of The Catalytic Role Of The Axial Cystine Ligand In The Co-Type Nitrile Hydratase From Pseudonocardia Thermophila Jcm 3095, Irene Anyango Ogutu, Martin St. Maurice, Brian Bennett, Richard C. Holz
Physics Faculty Research and Publications
The strictly conserved αSer162 residue in the Co-type nitrile hydratase from Pseudonocardia thermophila JCM 3095 (PtNHase), which forms a hydrogen bond to the axial αCys108-S atom, was mutated into an Ala residue. The αSer162Ala yielded two different protein species: one was the apoform (αSerA) that exhibited no observable activity, and the second (αSerB) contained its full complement of cobalt ions and was active with a kcat value of 63 ± 3 s−1 towards acrylonitrile at pH 7.5. The X-ray crystal structure of was determined at 1.85 Å resolution and contained no detectable …
Spectrumsdt: A Program For Parallel Calculation Of Coupled Rotational-Vibrational Energies And Lifetimes Of Bound States And Scattering Resonances In Triatomic Systems, Igor Gayday, Alexander Teplukhin, Jonathan Moussa, Dmitri Babikov
Spectrumsdt: A Program For Parallel Calculation Of Coupled Rotational-Vibrational Energies And Lifetimes Of Bound States And Scattering Resonances In Triatomic Systems, Igor Gayday, Alexander Teplukhin, Jonathan Moussa, Dmitri Babikov
Chemistry Faculty Research and Publications
We present SpectrumSDT – a program for calculations of energies and lifetimes of bound rotational-vibrational states below and scattering resonances above the dissociation threshold on a global potential energy surface of a triatomic system, which may include stable molecules, weekly-bound van-der-Waals complexes, and unbound atom + diatom scattering systems. Large-amplitude vibrational motion is treated explicitly using hyper-spherical coordinates. Three options for the rotational-vibrational interaction are supported: uncoupled (symmetric top rotor), partially coupled (to include interaction between several nearest states only) and full-coupled (vibrating asymmetric-top rotor). In addition to energies and lifetimes, SpectrumSDT is able to integrate ro-vibrational wave functions over …
Workers’ Attitudes Toward Increased Surveillance During And After The Covid-19 Pandemic, Jessica Vitak, Michael Zimmer
Workers’ Attitudes Toward Increased Surveillance During And After The Covid-19 Pandemic, Jessica Vitak, Michael Zimmer
Computer Science Faculty Research and Publications
Amid the Covid-19 pandemic, the transition of many offices to remote work has led to new ways for employers to track workers’ movements, behavior, and productivity. Through their SSRC-funded research, Jessica Vitak and Michael Zimmer surveyed remote workers in the US about perceptions of current workplace monitoring practices. They argue that worker concerns about reductions in privacy and independence at work might have negative outcomes on worker productivity, satisfaction, and well-being.
Dissecting Monomer-Dimer Equilibrium Of An Rnase P Protein Provides Insight Into The Synergistic Flexibility Of 5’ Leader Pre-Trna Recognition, Danyun Zeng, Ainur Abzhanova, Benjamin P. Brown, Nicholas J. Reiter
Dissecting Monomer-Dimer Equilibrium Of An Rnase P Protein Provides Insight Into The Synergistic Flexibility Of 5’ Leader Pre-Trna Recognition, Danyun Zeng, Ainur Abzhanova, Benjamin P. Brown, Nicholas J. Reiter
Chemistry Faculty Research and Publications
Ribonuclease P (RNase P) is a universal RNA-protein endonuclease that catalyzes 5’ precursor-tRNA (ptRNA) processing. The RNase P RNA plays the catalytic role in ptRNA processing; however, the RNase P protein is required for catalysis in vivo and interacts with the 5’ leader sequence. A single P RNA and a P protein form the functional RNase P holoenzyme yet dimeric forms of bacterial RNase P can interact with non-tRNA substrates and influence bacterial cell growth. Oligomeric forms of the P protein can also occur in vitro and occlude the 5’ leader ptRNA binding interface, presenting a challenge in accurately defining …
Electronic Structures And Spectroscopic Signatures Of Diiron Intermediates Generated By O2 Activation Of Nonheme Iron(Ii)–Thiolate Complexes, Danushka M. Ekanayake, Dao Pham, Andrew L. Probst, Joshua R. Miller, Cordina V. Popescu, Adam T. Fiedler
Electronic Structures And Spectroscopic Signatures Of Diiron Intermediates Generated By O2 Activation Of Nonheme Iron(Ii)–Thiolate Complexes, Danushka M. Ekanayake, Dao Pham, Andrew L. Probst, Joshua R. Miller, Cordina V. Popescu, Adam T. Fiedler
Chemistry Faculty Research and Publications
The activation of O2 at thiolate–ligated iron(II) sites is essential to the function of numerous metalloenzymes and synthetic catalysts. Iron–thiolate bonds in the active sites of nonheme iron enzymes arise from either coordination of an endogenous cysteinate residue or binding of a deprotonated thiol-containing substrate. Examples of the latter include sulfoxide synthases, such as EgtB and OvoA, that utilize O2 to catalyze tandem S–C bond formation and S-oxygenation steps in thiohistidine biosyntheses. We recently reported the preparation of two mononuclear nonheme iron–thiolate complexes (1 and 2) that serve as structural active-site models of substrate-bound EgtB …
Covalent Immobilization Of Molecular Complexes On Metal-Organic Frameworks Towards Robust And Highly Efficient Heterogeneous Water Oxidation Catalysts, Xiangming Liang, Sizhou Yang, Junyi Yang, Wanjun Sun, Xiangyang Li, Baochun Ma, Jier Huang, Jiangwei Zhang, Lele Duan, Yong Ding
Covalent Immobilization Of Molecular Complexes On Metal-Organic Frameworks Towards Robust And Highly Efficient Heterogeneous Water Oxidation Catalysts, Xiangming Liang, Sizhou Yang, Junyi Yang, Wanjun Sun, Xiangyang Li, Baochun Ma, Jier Huang, Jiangwei Zhang, Lele Duan, Yong Ding
Chemistry Faculty Research and Publications
The major challenges to practical implementation of efficient noble metal based molecular water oxidation catalysts are their stability and recycle ability. Herein, noble metal Ru based molecular water oxidation catalysts were covalently anchored in MOFs through “amide bond” as bridges, which leads to the formation of high-efficiency and robust heterogeneous catalysts for water oxidation reaction. We show that the efficiency for CeIV-driven water oxidation was significantly enhanced by 120 times when the Ru molecules were immobilized on the frameworks of MIL-101(Cr). The relationship between recycle stability and the structure of the Ru complexes covalently anchored in MOFs was …
Catalytic Transfer Deuteration And Hydrodeuteration: Emerging Techniques To Selectively Transform Alkenes And Alkynes To Deuterated Alkanes, Zoua Pa Vang, Samuel J. Hintzsche, Joseph R. Clark
Catalytic Transfer Deuteration And Hydrodeuteration: Emerging Techniques To Selectively Transform Alkenes And Alkynes To Deuterated Alkanes, Zoua Pa Vang, Samuel J. Hintzsche, Joseph R. Clark
Chemistry Faculty Research and Publications
Increasing demand for deuterium-labeled organic molecules has spurred a renewed interest in selective methods for deuterium installation. Catalytic transfer deuteration and transfer hydrodeuteration are emerging as powerful techniques for the selective incorporation of deuterium into small molecules. These reactions not only obviate the use of D2 gas and pressurized reaction setups but provide new opportunities for selectively installing deuterium into small molecules. Commercial or readily synthesized deuterium donors are typically employed as easy-to-handle reagents for transfer deuteration and hydrodeuteration reactions. In this minireview, recent advances in the catalytic transfer deuteration and hydrodeuteration of alkenes and alkynes for the selective …
Characterizations And Reliability Measures Of The Generalized Log Burr Xii Distribution, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Azeem Ali, Sedigheh Mirzaei Salehabadi, Munir Ahmad
Characterizations And Reliability Measures Of The Generalized Log Burr Xii Distribution, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Azeem Ali, Sedigheh Mirzaei Salehabadi, Munir Ahmad
Mathematical and Statistical Science Faculty Research and Publications
In this paper, we derive the generalized log Burr XII (GLBXII) distribution [2] from the generalized Burr-Hatke differential equation. We characterize the GLBXII distribution via innovative techniques. We derive various reliability measures (series and parallel). We also authenticate the potentiality of the GLBXII model via economics applications. The applications of characterizations and reliability measures of the GLBXII distribution in different disciplines of science will be profitable for scientists.
Efficient Method For An Approximate Treatment Of The Coriolis Effect In Calculations Of Quantum Dynamics And Spectroscopy, With Application To Scattering Resonances In Ozone, Igor Gayday, Dmitri Babikov
Efficient Method For An Approximate Treatment Of The Coriolis Effect In Calculations Of Quantum Dynamics And Spectroscopy, With Application To Scattering Resonances In Ozone, Igor Gayday, Dmitri Babikov
Chemistry Faculty Research and Publications
A numerical approach is developed to capture the effect of rotation–vibration coupling in a practically affordable way. In this approach only a limited number of adjacent rotational components are considered to be coupled, while the couplings to other rotational components are neglected. This partially coupled (PC) approach permits to reduce the size of Hamiltonian matrix significantly, which enables the calculations of ro-vibrational states above dissociation threshold (scattering resonances) for large values of total angular momentum. This method is employed here to reveal the role of the Coriolis effect in the ozone formation reaction at room temperature, dominated by large values …
In Situ Activated Co3–XNiXO4 As A Highly Active And Ultrastable Electrocatalyst For Hydrogen Generation, Kailu Guo, Yantao Wang, Junfeng Huang, Min Lu, Hua Li, Yong Peng, Pinxian Xi, Haoli Zhang, Jier Huang, Siyu Lu, Cailing Xu
In Situ Activated Co3–XNiXO4 As A Highly Active And Ultrastable Electrocatalyst For Hydrogen Generation, Kailu Guo, Yantao Wang, Junfeng Huang, Min Lu, Hua Li, Yong Peng, Pinxian Xi, Haoli Zhang, Jier Huang, Siyu Lu, Cailing Xu
Chemistry Faculty Research and Publications
The spinel Co3O4 has emerged as a promising alternative to noble-metal-based electrocatalysts for electrochemical water electrolysis in alkaline medium. However, pure Co3O4, despite having high activity in anodic water oxidation, remains inactive toward the hydrogen evolution reaction (HER). Here, a Ni-doped Co3O4(Co3–xNixO4) prepared by a simple method exhibits favorable HER activity and stability (>300 h, whether in 1 M KOH or the realistic 30 wt % KOH solution) after in situ electrochemical activation, outperforming almost all of the oxide-based electrocatalysts. More …
Rapid Entry Into Masters In Computing Program For Non-Majors, Gary S. Krenz, Thomas Kaczmarek, John C. Moyer
Rapid Entry Into Masters In Computing Program For Non-Majors, Gary S. Krenz, Thomas Kaczmarek, John C. Moyer
Mathematical and Statistical Science Faculty Research and Publications
The COSMIC: Change Opportunity - Start Masters in Computing graduate curriculum initiative strives to provide a rapid entry pathway to a professional Master of Science (MS) degree for individuals who do not have an undergraduate degree in computing, but who wish to cross over to a career in the computing field. The goal of our curriculum is to minimize the time students spend preparing for graduate study and maximize experiences relevant for work after graduation. The COSMIC curriculum initiative is similar in concept to other post-baccalaureate conversion programs. However, customization of the COSMIC bridge course and curriculum pathway makes it …
Needles In A Haystack: How Pooling Can Control Error Rates In Noisy Tests, Arockia David Roy Kulandai, J. Stella, John Rose, Thomas Schwarz
Needles In A Haystack: How Pooling Can Control Error Rates In Noisy Tests, Arockia David Roy Kulandai, J. Stella, John Rose, Thomas Schwarz
Computer Science Faculty Research and Publications
Testing many individuals for a reasonably rare condition using imperfect, time consuming, and expensive tests can be facilitated by pooling. Pooling groups samples from different individuals that are then tested for the existence of a pathogen. An individual is diagnosed as a carrier if a threshold of the tests to which the individual contributed samples is positive. Our assumptions dictate a testing strategy that is not adaptive, with the exception of retesting positively diagnosed persons individually. Pooling is a standard proposal to stretch the supply of test kits. We show that it can also be used to control the false …
Comparing Generic And Community-Situated Crowdsourcing For Data Validation In The Context Of Recovery From Substance Use Disorders, Sabirat Rubya, Joseph Numainville, Svetlana Yarosh
Comparing Generic And Community-Situated Crowdsourcing For Data Validation In The Context Of Recovery From Substance Use Disorders, Sabirat Rubya, Joseph Numainville, Svetlana Yarosh
Computer Science Faculty Research and Publications
Targeting the right group of workers for crowdsourcing often achieves better quality results. One unique example of targeted crowdsourcing is seeking community-situated workers whose familiarity with the background and the norms of a particular group can help produce better outcome or accuracy. These community-situated crowd workers can be recruited in different ways from generic online crowdsourcing platforms or from online recovery communities. We evaluate three different approaches to recruit generic and community-situated crowd in terms of the time and the cost of recruitment, and the accuracy of task completion. We consider the context of Alcoholics Anonymous (AA), the largest peer …
Laser Cooling Of Antihydrogen Atoms, C. J. Baker, W. Bertsche, A. Capra, C. Carruth, C. L. Cesar, M. Charlton, A. Christensen, R. Collister, A. Cridland Mathad, S. Eriksson, A. Evans, N. Evetts, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, P. Grandemange, P. Granum, J. S. Hangst, W. N. Hardy, M. E. Hayden, D. Hodgkinson, E. D. Hunter, C. A. Isaac, M. A. Johnson, J. M. Jones, S. A. Jones, S. Jonsell, A. Khramov, P. Knapp, L. Kurchaninov, N. Madsen, D. Maxwell, J. T. K. Mckenna, S. Menary, J. M. Michan, T. Momose, P. S. Mullan, K. Olchanski, A. Olin, J. Peszka, A. Powell, P. Pusa, C. O. Rasmussen, F. Robicheaux, R. L. Sacramento, M. Sameed, E. Sarid, D. M. Silveira, D, M. Starko, C. So, G. Stutter, Timothy Tharp, A. Thibeault, R. I. Thompson, D. P. Van Der Werf, J. S. Wurtele
Laser Cooling Of Antihydrogen Atoms, C. J. Baker, W. Bertsche, A. Capra, C. Carruth, C. L. Cesar, M. Charlton, A. Christensen, R. Collister, A. Cridland Mathad, S. Eriksson, A. Evans, N. Evetts, J. Fajans, T. Friesen, M. C. Fujiwara, D. R. Gill, P. Grandemange, P. Granum, J. S. Hangst, W. N. Hardy, M. E. Hayden, D. Hodgkinson, E. D. Hunter, C. A. Isaac, M. A. Johnson, J. M. Jones, S. A. Jones, S. Jonsell, A. Khramov, P. Knapp, L. Kurchaninov, N. Madsen, D. Maxwell, J. T. K. Mckenna, S. Menary, J. M. Michan, T. Momose, P. S. Mullan, K. Olchanski, A. Olin, J. Peszka, A. Powell, P. Pusa, C. O. Rasmussen, F. Robicheaux, R. L. Sacramento, M. Sameed, E. Sarid, D. M. Silveira, D, M. Starko, C. So, G. Stutter, Timothy Tharp, A. Thibeault, R. I. Thompson, D. P. Van Der Werf, J. S. Wurtele
Physics Faculty Research and Publications
The photon—the quantum excitation of the electromagnetic field—is massless but carries momentum. A photon can therefore exert a force on an object upon collision1. Slowing the translational motion of atoms and ions by application of such a force2,3, known as laser cooling, was first demonstrated 40 years ago4,5. It revolutionized atomic physics over the following decades6,7,8, and it is now a workhorse in many fields, including studies on quantum degenerate gases, quantum information, atomic clocks and tests of fundamental physics. However, this technique has not yet been applied to antimatter. Here we …
Four Isotope-Labeled Recombination Pathways Of Ozone Formation, Dmitri Babikov, Elizaveta Grushnikova, Igor Gayday, Alexander Teplukhin
Four Isotope-Labeled Recombination Pathways Of Ozone Formation, Dmitri Babikov, Elizaveta Grushnikova, Igor Gayday, Alexander Teplukhin
Chemistry Faculty Research and Publications
A theoretical approach is developed for the description of all possible recombination pathways in the ozone forming reaction, without neglecting any process a priori, and without decoupling the individual pathways one from another. These pathways become physically distinct when a rare isotope of oxygen is introduced, such as 18O, which represents a sensitive probe of the ozone forming reaction. Each isotopologue of O3 contains two types of physically distinct entrance channels and two types of physically distinct product wells, creating four recombination pathways. Calculations are done for singly and doubly substituted isotopologues of ozone, eight rate coefficients …
A New Extended Alpha Power Transformed Family Of Distributions: Properties, Characterizations And An Application To A Data Set In The Insurance Sciences, Zubair Ahmad, Eisa Mahmoudi, Gholamhossein Hamedani
A New Extended Alpha Power Transformed Family Of Distributions: Properties, Characterizations And An Application To A Data Set In The Insurance Sciences, Zubair Ahmad, Eisa Mahmoudi, Gholamhossein Hamedani
Mathematical and Statistical Science Faculty Research and Publications
Heavy tailed distributions are useful for modeling actuarial and financial risk management problems. Actuaries often search for finding distributions that provide the best fit to heavy tailed data sets. In the present work, we introduce a new class of heavy tailed distributions of a special sub-model of the proposed family, called a new extended alpha power transformed Weibull distribution, useful for modeling heavy tailed data sets. Mathematical properties along with certain characterizations of the proposed distribution are presented. Maximum likelihood estimates of the model parameters are obtained. A simulation study is provided to evaluate the performance of the maximum likelihood …
Unraveling A Trifecta Of Weak Non-Covalent Interactions: The Dissociation Energy Of The Anisole-Ammonia 1:1 Complex, John L. Loman, James T. Makuvaza, Damian L. Kokkin, Scott A. Reid
Unraveling A Trifecta Of Weak Non-Covalent Interactions: The Dissociation Energy Of The Anisole-Ammonia 1:1 Complex, John L. Loman, James T. Makuvaza, Damian L. Kokkin, Scott A. Reid
Chemistry Faculty Research and Publications
The anisole-ammonia 1:1 complex is a challenge for both experiment and theory. Early studies supported a non-planar structure, involving a trifecta of weak non-covalent interactions: N-H/O, N-H/π, and C-H/N. The calculated structure and binding energy of the complex proved remarkably sensitive to the level of theory employed. Here, we report the first experimental measurement of the ground state dissociation energy of the complex, and derive an excited (S1) state dissociation energy that is in excellent agreement with the cutoff observed in the experimental excitation spectrum. Results are compared with previous predictions and new calculations based on benchmarked Density …
Characterizations Of The Discrete Lindley And Discrete Poisson-Lindley Distributions, Gholamhossein G. Hamedani, Mahrokh Najaf
Characterizations Of The Discrete Lindley And Discrete Poisson-Lindley Distributions, Gholamhossein G. Hamedani, Mahrokh Najaf
Mathematical and Statistical Science Faculty Research and Publications
Certain characterizations of the discrete Lindley and discrete Poisson-Lindley distributions, originally introduced by Bakouch, Jazi and Nadarjah (2014) and Sankaran (1970), respectively, are presented. Al-Babtain, Gemeay and Afify (2020) revisited these distributions and provided estimation methods and actuarial measures as well as their applications in medicine. This short note is intended to complete, in some way, Al-Babtain, Gemeay and Afify (2020)’s work. It should be mentioned that the probability mass functions reported in the two papers mentioned above are not correct. In this note, it will be explained why they are not correct.
Exploring Prospective 1-8 Teachers' Number And Operation Sense In The Context Of Fractions, Marta T. Magiera, Leigh A. Van Den Kieboom
Exploring Prospective 1-8 Teachers' Number And Operation Sense In The Context Of Fractions, Marta T. Magiera, Leigh A. Van Den Kieboom
Mathematical and Statistical Science Faculty Research and Publications
This exploratory study examined prospective elementary teachers’ (PSTs’) number and operation sense (NOS) in the context of solving problems with fractions. Drawing on the existing literature, we identified seven skills that characterize fraction-related NOS. We analyzed 230 responses to 23 tasks completed by 10 PSTs for evidence of PSTs’ use of different fraction-related NOS skills. The analysis revealed that PSTs did not use all seven fraction-related NOS skills to the same extent. PSTs’ responses documented their frequent reasoning about the meaning of symbols and formal mathematical language in the context of fractions. To a lesser extent, PSTs’ responses documented their …