Different moments in the participatory stage of the secondary students’ abstraction of mathematical conceptions

This study provides support to the characteristics of participatory and anticipatory stages in secondary school pupils’ abstraction of mathematical conceptions. We carried out clinical task-based interviews with 71 secondary-school pupils to obtain evidence of the different constructed mathematical conceptions (Participatory Stage) and how they were used (Anticipatory Stage). We distinguish two moments in the Participatory Stage based on the coordination of information from particular cases by activity-effect reflection which, in some cases, lead to a change of focus enabling secondary-school pupils to achieve a reorganization of their knowledge. We argue that (a) the capacity of perceiving regularities in sets of particular cases is a characteristic of activity-effect reflection in the abstraction of mathematical conceptions in secondary school, and (b) the coordination of information by pupils provides opportunities for changing the attention-focus from the particular results to the structure of properties.

A strongly magnetized pulsar within the grasp of the milky way’s supermassive black hole

The center of our Galaxy hosts a supermassive black hole, Sagittarius (Sgr) A∗. Young, massive stars within 0.5 pc of Sgr A∗ are evidence of an episode of intense star formation near the black hole a few million years ago, which might have left behind a young neutron star traveling deep into Sgr A∗’s gravitational potential. On 2013 April 25, a short X-ray burst was observed from the direction of the Galactic center. With a series of observations with the Chandra and the Swift satellites, we pinpoint the associated magnetar at an angular distance of 2.4±0.3 arcsec from Sgr A∗, and refine the source spin period and its derivative (P = 3.7635537(2) s and ˙ P = 6.61(4) × 10−12 s s−1), confirmed by quasi simultaneous radio observations performed with the Green Bank Telescope and Parkes Radio Telescope, which also constrain a dispersion measure of DM = 1750 ± 50 pc cm−3, the highest ever observed for a radio pulsar. We have found that this X-ray source is a young magnetar at ≈0.07–2 pc from Sgr A∗. Simulations of its possible motion around Sgr A∗ show that it is likely (∼90% probability) in a bound orbit around the black hole. The radiation front produced by the past activity from the magnetar passing through the molecular clouds surrounding the Galactic center region might be responsible for a large fraction of the light echoes observed in the Fe fluorescence features.

Developing pre-service teachers’ noticing of students’ understanding of the derivative concept

This research study examines the development of the ability of pre-service teachers to notice signs of students’ understanding of the derivative concept. It analyses preservice teachers’ interpretations of written solutions to problems involving the derivative concept before and after participating in a teacher training module. The results indicate that the development of this skill is linked to pre-service teachers’ progressive understanding of the mathematical elements that students use to solve problems. We have used these results to make some suggestions for teacher training programmes.

High-Resolution N2 Adsorption Isotherms at 77.4 K: Critical Effect of the He Used During Calibration

Accurate characterization of the microporous structure in porous solids is of paramount importance for several applications such as energy and gas storage, nanoconfinement reactions, and so on. Among the different techniques for precise textural characterization, high-precision gas adsorption measurement of probe molecules at cryogenic temperatures (e.g., N2 at 77.4 K and Ar at 87.3 K) is the most widely used, after appropriate calibration of the sample holder with a probe gas, which does not experience physisorption processes. Although traditionally helium has been considered not to be adsorbed in porous solids at cryogenic temperatures, here we show that even at 77.4 K (high above its boiling temperature, 4 K) the use of He in the calibration step can give rise to erroneous interpretations when narrow micropores/constrictions are present.

The X-ray outburst of the Galactic Centre magnetar SGR J1745−2900 during the first 1.5 year

In 2013 April a new magnetar, SGR 1745−2900, was discovered as it entered an outburst, at only 2.4 arcsec angular distance from the supermassive black hole at the centre of the Milky Way, Sagittarius A*. SGR 1745−2900 has a surface dipolar magnetic field of ∼2 × 1014 G, and it is the neutron star closest to a black hole ever observed. The new source was detected both in the radio and X-ray bands, with a peak X-ray luminosity LX ∼ 5 × 1035 erg s−1. Here we report on the long-term Chandra (25 observations) and XMM–Newton (eight observations) X-ray monitoring campaign of SGR 1745−2900 from the onset of the outburst in 2013 April until 2014 September. This unprecedented data set allows us to refine the timing properties of the source, as well as to study the outburst spectral evolution as a function of time and rotational phase. Our timing analysis confirms the increase in the spin period derivative by a factor of ∼2 around 2013 June, and reveals that a further increase occurred between 2013 October 30 and 2014 February 21. We find that the period derivative changed from 6.6 × 10−12 to 3.3 × 10−11 s s−1 in 1.5 yr. On the other hand, this magnetar shows a slow flux decay compared to other magnetars and a rather inefficient surface cooling. In particular, starquake-induced crustal cooling models alone have difficulty in explaining the high luminosity of the source for the first ∼200 d of its outburst, and additional heating of the star surface from currents flowing in a twisted magnetic bundle is probably playing an important role in the outburst evolution.

Students’ understanding of the function-derivative relationship when learning economic concepts

The aim of this study is to characterise students’ understanding of the function-derivative relationship when learning economic concepts. To this end, we use a fuzzy metric (Chang 1968) to identify the development of economic concept understanding that is defined by the function-derivative relationship. The results indicate that the understanding of these economic concepts is linked to students’ capacity to perform conversions and treatments between the algebraic and graphic registers of the function-derivative relationship when extracting the economic meaning of concavity/convexity in graphs of functions using the second derivative.