2,704 research outputs found

### Always Improving: Turning Test Responses into Learning Opportunities

By using summative assessment scores and authentic student work samples, teachers can transform test
grades into further opportunities for student growth. This practice allows students to continue to hone their
mathematical skills, even after the test is finished. The procedures described include the incorporation of
technology and "math talk" to transform everyday classroom tests into unique learning opportunities. Through
the responses of their peers, students gain a clearer understanding of how to successfully respond to written
response questions

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### Making Use of District and School Data

This paper describes how districts can better use their extensive student databases and other existing data to explore questions of interest. School districts are required to maintain a wealth of student information in electronic data systems and other formats. The meaningfulness of the data depends to a large degree on whether they can understand the information and use it to guide their efforts. The considerations and guidelines presented here are organized into six components which include identifying the broad area, creating specific questions, roles and trust, sample and methodology, presentation of results, and outcomes and further directions. Two examples are used throughout the paper to illustrate each component. One is from a study of high school mathematics in an urban school district, the other is from a teacher-initiated effort to better understand studentsâ€™ perceptions of their middle school. Recommendations are offered throughout for encouraging effective data use in decision-making. Accessed 8,252 times on https://pareonline.net from May 16, 2012 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right

### TriMinimal Parametrization of the Neutrino Mixing Matrix

Current experimental data on neutrino mixing are very well described by
TriBiMaximal mixing. Accordingly, any phenomenological parametrization of the
MNSP matrix must build upon TriBiMaximal mixing. We propose one particularly
natural parametrization, which we call "TriMinimal". The three small deviations
of the PDG angles from their TriBiMaximal values, and the PDG phase,
parametrize the TriMinimal mixing matrix. As an important example of the
utility of this new parametrization, we present the simple resulting
expressions for the flavor-mixing probabilities of atmospheric and
astrophysical neutrinos. As no foreseeable experiment will be sensitive to more
than second order in the small parameters, we expand these flavor probabilities
to second order.Comment: Typos corrected, references added, title changed; matches version
appearing in PRL 100, 111801 (2008)

### X - Ray Flares and Their Connection With Prompt Emission in GRBs

We use a wavelet technique to investigate the time variations in the light
curves from a sample of GRBs detected by Fermi and Swift. We focus primarily on
the behavior of the flaring region of Swift-XRT light curves in order to
explore connections between variability time scales and pulse parameters (such
as rise and decay times, widths, strengths, and separation distributions) and
spectral lags. Tight correlations between some of these temporal features
suggest a common origin for the production of X-ray flares and the prompt
emission.Comment: 7th Huntsville Gamma-Ray Burst Symposium, GRB 2013: paper 15 in eConf
Proceedings C130414

### On the rigidity of back-to-back top quark pairs in e^+e^- annihilation

We consider the effect of gluon radiation on the energy of top/antitop quarks
and on the anticollinearity of top-antitop quark pairs produced in $e^+e^-$
annihilation. Our results are presented in terms of the $E_q$-dependence of the
$t\bar tg$ cross section and the dependence on the cosine of the opening angle
$\theta_{12}$ between top and antitop for a center of mass energy of
$\sqrt{q^2}=500 GeV$. We then go on to determine mean values for the top
quark's energy as well as its longitudinal and transverse projections, and for
the deviation of $\sin\theta_{12}$ and $\cos\theta_{12}$ from the
anticollinearity limits $\sin\theta_{12}=0$ and $\cos\theta_{12}=-1$. For a
center of mass energy of $500 GeV$ we obtain $=248.22 GeV$, $=247.24
GeV$ and $=4.70 GeV$. Thus, at this energy gluon radiation causes a total
average energy loss of 0.71% of the top quark's energy. The average energy loss
in the longitudinal direction is 1.06% and the average energy gain in the
transverse direction is 1.88%. These percentage figures go up to 3.77%, 5.19%
and 6.06%, respectively, at 1000\GeV. For the mean of the acollinearity angle
$\bar\theta_{12}=180^0-\theta_{12}$ we obtain $=1.25^0$ at
$500 GeV$, the value of which goes up to $4.62^0$ at $1000 GeV$. From an
analysis of the transverse momentum of the top we find that the mean transverse
momentum of the top stays close to the mean total momentum of the gluon in the
energy range from threshold to $1000 GeV$ showing that the gluon momentum has a
large mean transverse component in this energy range.Comment: 17 pages, 7 postscript figures, to appear in Nucl. Phys.

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