1,663 research outputs found
Tools or crutches? Apparatus as a sense-making aid in mathematics teaching with children with moderate learning difficulties
This paper challenges a view of concrete materials as abstracts used within a rigid instructional sequence that particular children are perceived to require or not, as the case may be. Focussing on mathematics teaching, it contends that it is more useful to consider the function of these materials as tools, artefacts used flexibly and selectively by pupils to make sense of mathematics, rather than as crutches, devices which may support procedural competency in mathematics but with no guarantees of understanding
High-Resolution Simulations of Cosmic Microwave Background non-Gaussian Maps in Spherical Coordinates
We describe a new numerical algorithm to obtain high-resolution simulated
maps of the Cosmic Microwave Background (CMB), for a broad class of
non-Gaussian models. The kind of non-Gaussianity we account for is based on the
simple idea that the primordial gravitational potential is obtained by a
non-linear but local mapping from an underlying Gaussian random field, as
resulting from a variety of inflationary models. Our technique, which is based
on a direct realization of the potential in spherical coordinates and fully
accounts for the radiation transfer function, allows to simulate non-Gaussian
CMB maps down to the Planck resolution (), with
reasonable memory storage and computational time.Comment: 9 pages, 5 figures. Submitted to ApJ. A version with higher quality
figures is available at http://www.pd.infn.it/~liguori/content.htm
'I like it instead of maths' : how pupils with moderate learning difficulties in Scottish primary special schools intuitively solved mathematical word problems
This study shows how a group of 24 children in three Scottish primary schools for pupils with moderate learning difficulties responded to word problems following their teachers' introduction to the principles of Cognitively Guided Instruction (CGI). CGI is a professional development programme in mathematics instruction based on constructivist principles developed at the University of Wisconsin-Madison. The study found that the sample group of pupils were able to develop their understanding of mathematical concepts through actively engaging in word problems without prior explicit instruction and with minimal teacher adjustments. The pupils' conceptual understandings demonstrated by their solution strategies within CGI activities were generally not consistent with classroom records of assessment. The results were encouraging in illustrating the capacity of the sample group of pupils with moderate learning difficulties to reveal their mathematical thinking and considers the importance of this insight for instructional decision making
The jeely nursery, letting the children lead: final report to the robertson trust
This is the final report written at the conclusion of a three year Robertson Trust funded project at the Jeely Nursery in Castlemilk, Glasgow, 2007 to 2010. The project purpose was to meet the particular needs of children vulnerable to highly adverse social and economic circumstances, including those living with parental addiction. The aim was to develop a collaborative strategy which would, by involving children, nursery staff and parents together, help to build enduring resources for the emotional resilience needed by children to overcome adversity and improve their chances of achieving educational success. The well validated premise underpinning the child-led pedagogy, Special Playtime, is that early negative attachment experiences can be transformed through direct positive experience with trained staff. The report examines the project using a three dimensional conceptual framework located in the literature on attachment, resilience and child-led pedagogy and focuses on the manner in which the several and differing relationships within the project interacted with and sustained each other
Kurtosis and Large--Scale Structure
We discuss the non--linear growth of the excess kurtosis parameter of the
smoothed density fluctuation field ,
S_4\equiv[\lan\delta^{\,4}\ran-3\lan\delta^{\,2}\ran^2]/
\lan\delta^{\,2}\ran^3 in an Einstein--de Sitter universe. We assume Gaussian
primordial density fluctuations with scale--free power spectrum and analyze the dependence of on primordial spectral index ,
after smoothing with a Gaussian filter. As already known for the skewness ratio
, the kurtosis parameter is a {\it decreasing function} of , both in
exact perturbative theory and in the Zel'dovich approximation. The parameter
provides a powerful statistics to test different cosmological scenarios.Comment: 11 pages in Latex (plus 1 figure), SISSA 127/93/
Lensing dispersion of supernova flux: a probe of nonlinear structure growth
The scatter in the apparent magnitude of type Ia supernovae induced by
stochastic gravitational lensing is highly dependent on the nonlinear growth of
cosmological structure. In this paper, we show that such a dependence can
potentially be employed to gain significant information about the mass
clustering at small scales. While the mass clustering ultimately hinges on
cosmology, here we demonstrate that, upon obtaining more precise observational
measurements through future cosmological surveys, the lensing dispersion can
very effectively be used to gain information on the poorly understood
astrophysical aspects of structure formation, such as the clumpiness of dark
matter halos and the importance of gas physics and star formation into shaping
the large-scale structure. In order to illustrate this point we verify that
even the tentative current measurements of the lensing dispersion performed on
the Supernova Legacy Survey sample favor a scenario where virialized structures
are somewhat less compact than predicted by body cosmological simulations.
Moreover, we are also able to put lower limits on the slope of the
concentration-mass relation. By artificially reducing the statistical
observational error we argue that with forthcoming data the stochastic lensing
dispersion will allow one to importantly improve constraints on the baryonic
physics at work during the assembly of cosmological structure.Comment: 13 pages, 6 figures. Accepted for publication by MNRA
Letting the children lead: the jeely nursery - a first interim report to the robertson trust
This is the first interim report undertaken for the Robertson Trust (RT) of an ongoing project developed by the Jeely Nursery (JN) in Castlemilk Glasgow 2007 â 2010. The Robertson Trust funding has enabled the JN to initiate a radical multi faceted programme of development focussed on children living in highly adverse socioeconomic conditions who may in addition be subject to the negative effects of living in families coping with substance abuse. They represent one of the most vulnerable groups of children in contemporary society. The task ahead for the nursery staff is complex, challenging and long term, requiring a high degree of consistency and commitment to both professional and personal growth. There is no question that the challenge is understood and accepted at all levels; that commitment to the project is well established and that a high level of motivation is sustained in spite of a number of difficult circumstances occurring over the year, unrelated to the project
Constraining Primordial Magnetic Fields with Future Cosmic Shear Surveys
The origin of astrophysical magnetic fields observed in galaxies and clusters
of galaxies is still unclear. One possibility is that primordial magnetic
fields generated in the early Universe provide seeds that grow through
compression and turbulence during structure formation. A cosmological magnetic
field present prior to recombination would produce substantial matter
clustering at intermediate/small scales, on top of the standard inflationary
power spectrum. In this work we study the effect of this alteration on one
particular cosmological observable, cosmic shear. We adopt the semi-analytic
halo model in order to describe the non-linear clustering of matter, and feed
it with the altered mass variance induced by primordial magnetic fields. We
find that the convergence power spectrum is, as expected, substantially
enhanced at intermediate/small angular scales, with the exact amplitude of the
enhancement depending on the magnitude and power-law index of the magnetic
field power spectrum. We use the predicted statistical errors for a future
wide-field cosmic shear survey, on the model of the ESA Cosmic Vision mission
\emph{Euclid}, in order to forecast constraints on the amplitude of primordial
magnetic fields as a function of the spectral index. We find that the amplitude
will be constrained at the level of nG for , and at the
level of nG for . The latter is at the same level of
lower bounds coming from the secondary emission of gamma-ray sources, implying
that for high spectral indices \emph{Euclid} will certainly be able to detect
primordial magnetic fields, if they exist. The present study shows how
large-scale structure surveys can be used for both understanding the origins of
astrophysical magnetic fields and shedding new light on the physics of the
pre-recombination Universe. (abridged)Comment: 24 pages, 9 figures. To appear on JCA
CoMaLit - II. The scaling relation between mass and Sunyaev-Zel'dovich signal for Planck selected galaxy clusters
We discuss the scaling relation between mass and integrated Compton parameter
of a sample of galaxy clusters from the all-sky {\it Planck} Sunyaev-Zel'dovich
catalogue. Masses were measured with either weak lensing, caustics techniques,
or assuming hydrostatic equilibrium. The retrieved - relation
does not strongly depend on the calibration sample. We found a slope of
1.4-1.9, in agreement with self-similar predictions, with an intrinsic scatter
of per cent. The absolute calibration of the relation can not be
ascertained due to systematic differences of 20-40 per cent in mass
estimates reported by distinct groups. Due to the scatter, the slope of the
conditional scaling relation, to be used in cosmological studies of number
counts, is shallower, 1.1-1.6. The regression methods employed account
for intrinsic scatter in the mass measurements too. We found that Planck mass
estimates suffer from a mass dependent bias.Comment: 14 pages, 7 figures; v2: 17 pages, 11 figures; MNRAS in press,
results unchanged; extended discussion of the Planck calibration sample;
added discussion of conditional vs symmetric scaling relations and of mixture
of Gaussian functions as distribution of the independent variable; products
from the CoMaLit series at http://pico.bo.astro.it/~sereno/CoMaLi
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