Implantación de las matemáticas en la educación secundaria obligatoria: un análisis en el contexto internacional

Hace ahora cinco años que comenzó a implantarse la educación secundaria obligatoria en algunos centros de diferentes lugares. Desde entonces, el número de estudiantes y de centros que se han incorporado a esta etapa educativa ha ido creciendo progresivamente. Tenemos ya alguna experiencia que nos permite hacer un primer balance de sus características más relevantes y sus efectos en relación con la enseñanza y el aprendizaje de las matemáticas y de las condiciones en las que se ha ido poniendo en marcha.

Reflexión sobre los fines de la educación matemática

La delimitación de finalidades es un dato esencial para cualquier plan de formación: por ello, las finalidades de un currículo de matemáticas lo caracterizan en su extensión y alcance, y constituyen parte determinante en el proceso de su planificación.

Evaluación en educación matemática y sus efectos

La construcción de la didáctica de las matemáticas como área de conocimiento científico trata de romper con la ilusión de transparencia que emerge del dominio de realidad configurado por los hechos didácticos. En este trabajo analizaremos la transparencia de los hechos didácticos a partir de diferentes investigaciones llevadas a cabo en esta área de conocimiento. En ellas se muestra cómo el análisis epistemológico de los objetos matemáticos de enseñanza es una condición necesaria para poder interpretar racionalmente los hechos y fenómenos didácticos.

Análisis de los conocimientos probabilísticos del profesorado de educación primaria

Algunos profesores presentan dificultades para enseñar probabilidad, sobre todo en países en los que la incorporación de esta materia en el currículo es reciente y la preparación durante la formación inicial es escasa, como es el caso de Chile. Para diseñar programas de intervención que den lugar a una enseñanza idónea, se realiza un estudio exploratorio sobre el conocimiento didáctico-matemático para enseñar probabilidad, fundamentado en el modelo del Conocimiento Didáctico-Matemático (CDM). Con este propósito se ha administrado el Cuestionario CDM-Probabilidad a 93 profesores, cuyos resultados han puesto de manifiesto varios errores y dificultades, evidenciando la presencia de heurísticas y sesgos probabilísticos. Se concluye que es necesaria una mayor especialización del profesorado en todas las facetas de su conocimiento didáctico-matemático: conocimiento común del contenido, conocimiento ampliado del contenido y conocimiento especializado.

Sobre la finitud de las series de potencias infinitas de tipo geometrico-polinomiales

Una investigación que inicie a mediados del ano 2004, para tratar de encontrar como pudieron hacer los matemáticos de fines del siglo XVII, para encontrar la suma de algunas series de potencias infinitas.

Electron impact excitation of Ar XVII

Energies for the lowest 49 levels among the 1s(2) and 1snl (n = 2-5) configurations of Ar XVII have been calculated using the GRASP code of Dyall et al. (1989, Comput. Phys. Comm., 55, 424). Additionally, radiative rates, oscillator strengths, and line strengths are calculated for all electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions among these levels. Furthermore, collision strengths have also been calculated for all the 1176 transitions among the above 49 levels using the Dirac Atomic R-matrix Code (DARC) of Norrington & Grant (2005, Comput. Phys. Commun., in preparation), over a wide energy range up to 580 Ryd. Resonances have been resolved in the threshold region, and effective collision strengths have been obtained over a wide temperature range up to log T-e = 7.2 K. Comparisons are made with the limited results available in the literature, and the accuracy of the data is assessed. Our energy levels are estimated to be accurate to better than 0.1%, whereas results for other parameters are probably accurate to better than 20%.

Radiative rates for transitions in Fe XVII

Energies of the lowest 157 levels belonging to the (1s(2)) 2s(2)2p(6), 2s(2)p(5)3l, 2s(2)2p(5)4l, 2s(2)2p(5)4l, 2s2p(5)5l, 2s2p(6)4l and 2s2p(6)5l configurations of Fe XVII have been calculated using the GRASP code of Dyall et al. (1989). Additionally, radiative rates, oscillator strengths, and line strengths are calculated for all electric dipole (E I), magnetic dipole (M I), electric quadrupole (E2), and magnetic quadrupole (M2) transitions among these levels. Comparisons are made with the results already available in the literature, and the accuracy of the data is assessed. Our energy levels are expected to be accurate to better than M whereas results for other parameters are probably accurate to better than 20%.

Energy levels and radiative rates for transitions in Ni XIII-Ni XVI

Energy levels and radiative rates for fine-structure transitions in nickel ions (Ni XIII-XVI) have been calculated using the GRASP code. Configuration interaction and relativistic effects have been included, and comparisons are made with available data. Energy levels and radiative rates are tabulated for transitions among the 48, 43, 32, and 84 levels of Ni XIII, Ni XIV, Ni XV, and Ni XVI, respectively. The energy levels are assessed to be accurate to better than 5% for a majority of levels, while oscillator strengths for all strong transitions are accurate to better than 20%. (C) 2003 Published by Elsevier Inc.

Oscillator strengths for transitions in C-like ions between K XIV and Mn XX

Energy levels and oscillator strengths (transition probabilities) have been calculated for transitions among 46 fine-structure levels of the (1s(2)) 2s(2) 2p(2), 2s2p(3),2p(4), 2s(2)2p3s, 2s(2) 2p3p and 2s(2)2p3d configurations of C-like K XIV, Sc XVI, Ti XVII, V XVIII, Cr XIX and Mn XX using the GRASP code. Configuration interaction and relativistic effects have been included while generating the wavefunctions. Calculated values of energy levels agree within 3% with the experimentally compiled results, and the length and velocity forms of oscillator strengths agree within 20% for a majority of allowed transitions.

Energy levels, radiative rates, and collision strengths for transitions in Fe XVII

Energy levels and radiative rates have been calculated for fine-structure transitions among the lowest 89 levels of the (1s(2)) 2s(2)2p(6), 2s(2) 2p(5) 3 l, 2s(2) 2p(5) 4l, 2s2p(6) 3 l, and 2s2p(6)4l configurations of Fe XVII using the GRASP code of Dyall et al. Collision strengths have also been calculated, for transitions among the lowest 55 levels, using the recently developed Dirac atomic R-matrix code (DARC) of Norrington & Grant. The results are compared with those available in the literature, and the accuracy of the data is assessed.

Emission lines of Na-like ions in spectra obtained with the Solar EUV Research Telescope and Spectrograph (SERTS)

Theoretical emission-line ratios involving transitions in the 236-412 Angstrom wavelength range are presented for the Na-like ions Ar viii, Cr xiv, Mn xv, Fe xvi, Co xvii, Ni xviii and Zn xx. A comparison of these with an extensive data set of the solar active region, quiet-Sun, subflare and off-limb observations, obtained during rocket flights by the Solar EUV Research Telescope and Spectrograph (SERTS), reveals generally very good agreement between theory and experiment. This indicates that most of the Na-like ion lines are reliably detected in the SERTS observations, and hence may be employed with confidence in solar spectral analyses. However, the features in the SERTS spectra at 236.34 and 300.25 Angstrom, originally identified as the Ni xviii 3p (2) P-3/2 -3d (2) D- 3/2 and Cr xiv 3p (2) P-3/2 -3d (2) D-5/2 transitions, respectively, are found to be due to emission lines of Ar xiii (236.34 Angstrom) and possibly S v or Ni vi (300.25 Angstrom). The Co xvii 3s (2) S-3p (2) P-3/2 line at 312.55 Angstrom is always badly blended with an Fe xv feature at the same wavelength, but Mn xv 3s (2) S-3p (2) P-1/2 at 384.75 Angstrom may not always be as affected by second-order emission from Fe xii 192.37 Angstrom as previously thought. On the other hand, we find that the Zn xx 3s (2) S-3p (2) P-3/2 transition can sometimes make a significant contribution to the Zn xx/Fe xiii 256.43- Angstrom blend, and hence care must be taken when using this feature as an Fe xiii electron density diagnostic. A line in the SERTS-89 active region spectrum at 265.00 Angstrom has been re-assessed, and we confirm its identification as the Fe xvi 3p (2) P-3/2 -3d (2) D-3/2 transition.

Inner-shell photoexcitation of Fe XV and Fe XVI

The configuration-interaction method as implemented in the computer code CIV3 is used to determine energy levels, electric dipole radiative transition wavelengths, oscillator strengths and transition probabilities for inner-shell excitation of transitions in Fe XV and Fe XVI. Specifically, transitions are considered of the type 1s(2) 2s(2) 2p(6) 3s(2) -1s(2) 2s(2) 2p(5) 3l3l' 3l" (l, l' and l" = s,p or d) in FeXV and 1s(2) 2s(2) 2p(6) 3s- 1s(2) 2s(2) 2p(5) 3l3l' (l and l' = s,p or d) in FeXVI, using the relativistic Breit-Pauli approach. An assessment of the accuracy of the derived atomic data is performed.

Energy levels and radiative rates for Li-like Ar XVI and Fe XXIV

Energy levels for transitions among the lowest 24 fine- structure levels belonging to the 1s(2)nl(n greater than or equal to 5) configurations of Li-like Ar XVI and Fe XXIV have been calculated using the fully relativistic GRASP code. Oscillator strengths, radiative rates and line strengths have also been generated among these levels for the four types of transitions: electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2) and magnetic quadrupole (M2). Comparisons are made for the electric dipole transitions with other available results, and the accuracy of the present data is assessed.

Electron impact excitation of Fe XVI: radiative and excitation rates

Aims. In this paper we report calculations for energy levels, radiative rates, collision strengths, and effective collision strengths for transitions in Fe XVI. Methods. For energy levels and radiative rates we have used the General purpose Relativistic Atomic Structure Package ( grasp), and for the compuations of collision strengths the Dirac Atomic R-matrix Code (darc) has been adopted. Results. Energies for the lowest 39 levels among the n

Citizens’ attitudes toward public services. Satisfaction in 2009-2011

The aim of this paper is to study the recent changes on citizens’ satisfaction with the performance ofpublic services, in the period 2009-2011 in Spain. Using data from the surveys on Quality of PublicServices, developed by the Sociological Research Center jointly with the National Agency for theEvaluation of Public Services and Quality of Services, our results show that the level of satisfactionhas slightly increased, which seems to display a greater tendency to positively value public servicesduring economic retrenchment. A major determinant of high satisfaction is self-reported ideology.Besides, immigrants display higher levels of satisfaction than Spaniards.