skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Revising Word Problems to Address UDL and Standards
Mathematics assessments should allow all students opportunities to demonstrate their knowledge and skills as problem solvers. Looking at textbook word problems, we share a process for revising them using Universal Design for Learning.  more » « less
Award ID(s):
2101026
PAR ID:
10329097
Author(s) / Creator(s):
; ; ; ; ;
Date Published:
Journal Name:
Mathematics Teacher: Learning and Teaching PK-12
Volume:
115
Issue:
4
ISSN:
0025-5769
Page Range / eLocation ID:
252 to 264
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Bogdanović; Iva; Lorenz, Katharina (Ed.)
    PIXE analysis was conducted on p8 fisher brand filter paper samples soaked in elemental standard solutions to determine the minimum detectable levels of Al, Si, P, S, Cl, K, Ca, Cr, Fe, Ni, Cu, and Se. All samples were analyzed with beam parameters of 2 µC incident charge, and beam current of less than 2 nA at 2 MeV beam energy. Minimum detectable levels were obtained by analyzing the x-ray spectrum in the GeoPIXE analysis package, and the data for each element would be averaged over all collected spectra. The minimum detectable level in parts per million was found to be on average 9.59 for Al, 4.6 for Si, 3.23 for P, 2.27 for S, 1.82 for Cl, 1.15 for K, 0.88 for Ca, 0.51 for Cr, 0.07 for Mn, 0.54 for Fe, 1.59 for Ni, 2.0 for Zn, 1.55 for Cu, and 6.5 for Se. Minimal deviation from the averaged values was observed, except in cases where samples contained high concentrations of elements with overlapping X-ray energies. 
    more » « less
  2. The effects of various branches geometry and dimensions such as length, thickness, and width for H-, U-, O-, YH- and YU-shaped alnico structures on coercivity (Hci) using micromagnetic simulation for coherent rotation and curling modes are investigated. The simulation results suggest that the H-shaped structure needs long and short branch length for the coherent rotation and curling, respectively, regardless of branch thickness and width to realize high Hci. Short branch length with thin thickness and short width are recommended for both rotations for the U- and O-shaped structures. Lastly, both Y-shaped structures need branch with long length, thin thickness, and mid-long width for the coherent rotation, but short width for the YH-shaped and mid-long width for the YU-shaped regardless of length and thickness for curling are desired. Furthermore, among the five studied structures, H- or YH-shaped structure for coherent rotation and O-shaped structure for curling are highly recommended for fabrication to realize a high Hci. 
    more » « less
  3. Regularization plays a key role in improving the prediction of emotions using attributes such as arousal, valence and dominance. Regularization is particularly important with deep neural networks (DNNs), which have millions of parameters. While previous studies have reported competitive performance for arousal and dominance, the prediction results for valence using acoustic features are significantly lower. We hypothesize that higher regularization can lead to better results for valence. This study focuses on exploring the role of dropout as a form of regularization for valence, suggesting the need for higher regularization. We analyze the performance of regression models for valence, arousal and dominance as a function of the dropout probability. We observe that the optimum dropout rates are consistent for arousal and dominance. However, the optimum dropout rate for valence is higher. To understand the need for higher regularization for valence, we perform an empirical analysis to explore the nature of emotional cues conveyed in speech. We compare regression models with speakerdependent and speaker-independent partitions for training and testing. The experimental evaluation suggests stronger speaker dependent traits for valence. We conclude that higher regularization is needed for valence to force the network to learn global patterns that generalize across speakers. 
    more » « less
  4. The distance matrix of a dataset X of n points with respect to a distance function f represents all pairwise distances between points in X induced by f. Due to their wide applicability, distance matrices and related families of matrices have been the focus of many recent algorithmic works. We continue this line of research and take a broad view of algorithm design for distance matrices with the goal of designing fast algorithms, which are specifically tailored for distance matrices, for fundamental linear algebraic primitives. Our results include efficient algorithms for computing matrix-vector products for a wide class of distance matrices, such as the l1 metric for which we get a linear runtime, as well as a quadratic lower bound for any algorithm which computes a matrix-vector product for the l_infty case. Our upper bound results have many further downstream applications, including the fastest algorithm for computing a relative error low-rank approximation for the distance matrix induced by l1 and l2 functions and the fastest algorithm for computing an additive error lowrank approximation for the l2 metric, in addition to applications for fast matrix multiplication among others. We also give algorithms for constructing distance matrices and show that one can construct an approximate l2 distance matrix in time faster than the bound implied by the Johnson-Lindenstrauss lemma. 
    more » « less
  5. Abstract Public health intervention to contain the ongoing COVID-19 pandemic significantly differed by country since the SARS-CoV-2 spread varied regionally in time and in scale. Since vaccinations were not available until the end of 2020 non-pharmaceutical interventions (NPIs) remained the only strategies to mitigate the pandemic spread at that time. Belarus in Europe is one of a few countries with a high Human Development Index where no lockdowns have ever been implemented and only limited NPIs have taken place for a period of time. Therefore, the Belarusian case was evaluated and compared in terms of the mortality burden. Since the COVID-19 mortality was low, the excess overall mortality was studied for Belarus. Since no overall mortality data have been reported past June 2020 the analysis was complemented by the study of Google Trends funeral-related search queries up until August 2021. Depending on the model, the Belarusian mortality for June of 2020 was 29 to 39% higher than otherwise expected with the corresponding estimated excess death was from 2953 to 3690 while the reported COVID-19 mortality for June 2020 was only 157 cases. The Belarusian excess mortality for June 2020 was higher than for all neighboring countries with an excess of 5% for Poland, 5% for Ukraine, 8% for Russia, 11% for Lithuania and 11% for Latvia. The relationship between Google Trends and mortality time series was studied using Granger’s test and the results were statistically significant. The results for Google Trends searches did vary by key phrase with the largest excess of 138% for April 2020 and 148% for September 2020 was observed for a key phrase “coffin”, while the largest excess of 218% for January 2021 was observed for “funeral services”. In summary, there are indications of the excess overall mortality in Belarus, which is larger than the reported COVID-19-related mortality. 
    more » « less