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The purpose of this study is to investigate secondary teacher candidates’ experience of mathematical modeling task design. In the study, 54 teacher candidates in a university-based teacher education program created modeling tasks and scoring rubrics. Next, the participants pilot-tested the tasks with students and had the opportunity to revise the original tasks and rubrics based on student responses. The data included participants’ statements, in which they described and reflected on the design and revision process of modeling tasks. The study describes six didactic revision strategies in revising modeling tasks and identifies five emerging pedagogical ideas from revising tasks and rubrics. The study also discusses the way modeling task design activities have the potential to support teacher candidates’ learning through a bottom-up modeling curriculum in teacher education.

Wide field planetary camera 2 (WFPC2) exposures are already some 20 years older than Gaia epoch observations, or future James Webb Space Telescope observations. As such, they offer an unprecedented time baseline for high-precision proper-motion studies, provided the full astrometric potential of these exposures is reached. We have started such a project with the work presented here being its first step. We explore geometric distortions beyond the well-known ones published in the early 2000 s. This task is accomplished by using the entire database of WFPC2 exposures in filters F555W, F606W and F814W and three standard astrometric catalogs: Gaia EDR3, 47 Tuc and ωCen. The latter two were constructed using Hubble Space Telescope observations made with cameras other than WFPC2. We explore a suite of centering algorithms, and various distortion maps in order to understand and quantify their performance. We find no high-frequency systematics beyond the 34th-row correction, down to a resolution of 10 pixels. Low-frequency systematics starting at a resolution of 50 pixels are present at a level of 30–50 millipix (1.4–2.3 mas) for the PC and 20–30 millipix (2–3 mas) for the WF chips. We characterize these low-frequency systematics by providing correction maps and updated cubic-distortion coefficients for each filter.

This study investigates how pre-service teachers use their knowledge of technology, mathematics, and pedagogy to create video lessons using portable interactive whiteboards. The TPACK framework was used to identify the different types of knowledge pre-service teachers rely on as they create their videos. Results indicate pre-service teachers’ effective use of conveyance technology, pedagogical techniques, and mathematical representations using technology. Their videos portray their process of coordinating their TPACK. Recommendations are made for teacher educators to integrate technology in activities that aim to develop pre-service teachers’ comfort and confidence with technological tools for teaching and learning. © 2021 ATE and CCNY.

Background: Attenuation correction (AC) using CT transmission scanning enables the accurate quantitative analysis of dedicated cardiac SPECT. However, AC is challenging for SPECT-only scanners. We developed a deep learning-based approach to generate synthetic AC images from SPECT images without AC. Methods: CT-free AC was implemented using our customized Dual Squeeze-and-Excitation Residual Dense Network (DuRDN). 172 anonymized clinical hybrid SPECT/CT stress/rest myocardial perfusion studies were used in training, validation, and testing. Additional body mass index (BMI), gender, and scatter-window information were encoded as channel-wise input to further improve the network performance. Results: Quantitative and qualitative analysis based on image voxels and 17-segment polar map showed the potential of our approach to generate consistent SPECT AC images. Our customized DuRDN showed superior performance to conventional network design such as U-Net. The averaged voxel-wise normalized mean square error (NMSE) between the predicted AC images by DuRDN and the ground-truth AC images was 2.01 ± 1.01%, as compared to 2.23 ± 1.20% by U-Net. Conclusions: Our customized DuRDN facilitates dedicated cardiac SPECT AC without CT scanning. DuRDN can efficiently incorporate additional patient information and may achieve better performance compared to conventional U-Net. © 2021, American Society of Nuclear Cardiology.

A Skolem sequence can be thought of as a labelled path where two vertices with the samelabelarethatdistanceapart.Thisconcepthasnaturallybeengeneralizedto labellingsofothergraphs,butalwaysusingatmosttwoofanyintegerlabel.Giventhat more than two vertices can be mutually distance d apart, wedefine a new generalization of aSkolemsequenceongraphsthatwecallaproperSkolemlabelling.Thisbrings rise tothequestion;use to proper Skolemlabel a graph?"This will be known as the Skolem number of the graph. In this paper we give the Skolem number for cycles and grid graphs,while also providing other related results along the way. Published by Digital Commons@Georgia Southern, 2021. © 2021 Georgia Southern University. All rights reserved.

A rokudoku-pair square is an order-6 sudoku Latin square for both 2 x 3 and 3 x 2 tiling regions simultaneously. We count the distinct rokudoku-pair squares as well as orbits under the action of a suitable group. Our arguments employ group actions and list colorings of graphs. As an application we determine which rokudoku-pair squares are based on groups. © 2021. All Rights Reserved.

This paper will discuss the correlation between the SAT and the Math Inventory Test. Many school districts adopted the Math Inventory as a tool to measure student growth from grades kindergarten through high school. The Math Inventory is a computer-administered test that gives students math problems spanning from counting to high school level math. When completed, the students are given a quantile measure, much like a Lexile score for reading skill. The purpose of this study is to figure out if success on the Math Inventory is a good indicator for performing well on the SAT. For most high schools around the United States, objectives and lessons are aligned with those of the SAT. The goal of high school teachers is for students to excel on the SAT so that they can go to college, which means the tests used in middle school should be aligned with that goal. If the Math Inventory is not, then it might not be a very good use of school time and resources. Data was analyzed from the 2017-2018 school year from ten different high schools in an urban school district to determine the correlation between Math Inventory score, and the math score/sub scores of SAT/PSAT. The value of the Pearson’s correlation coefficient is used to suggest a fairly moderate positive relationship between these two variables. © 2021, International Journal of Information and Education Technology. All rights reserved.

The increasing number of technological devices available in schools, aligned with curriculum guidance, set an expectation for mathematics teachers to incorporate these devices into their teaching. This qualitative study investigated prospective teachers’ use of TPACK and mathematical action technologies as they created screencast video lessons using iPads. Results showed prospective teachers’ effective use of pedagogical techniques and the screencast app as an amplifier tool, according to the amplifier-reorganizer metaphor. Half of the participants used mathematics technology to confirm and expand the results they had found without technology. The other half had mathematics technology integrated into their solution exercising the balance among TPACK components. For some, their use of the mathematical tool had the potential of expanding the mathematical repertoire of virtual students. We conclude by making recommendations for teacher educators to implement cycles of learning for pre-service teachers to design, enact, and reflect upon the creation of screencast video lessons. © 2021, Association for Educational Communications & Technology.

This paper is a sequel to [8] where we introduced an invariant, called canonical degree, of Cohen–Macaulay local rings that admit a canonical ideal. Here to each such ring R with a canonical ideal, we attach a different invariant, called bi-canonical degree, which in dimension 1 appears also in [12] as the residue of R. The minimal values of these functions characterize specific classes of Cohen–Macaulay rings. We give a uniform presentation of such degrees and discuss some computational opportunities offered by the bi-canonical degree. © 2019 Elsevier Inc.