Los futuros maestros aprenden cuando preparan sus clases de matemáticas

La asignatura Didáctica de las Matemáticas tiene por objetivo que los alumnos, que de aquí en adelante llamaremos futuros maestros, sean capaces de planificar y llevar a la práctica actividades que permitan a sus futuros alumnos lograr en el área de matemática aprendizajes significativos. Esto implica que deban poner en juego conocimientos de matemáticas, de didáctica en general, y en particular las que responden al paradigma constructivista y su puesta en práctica en el desarrollo de una clase, pudiendo elegir otros modelos didácticos, según lo requiera el proceso de aprendizaje del alumno y en relación con los contenidos a aprender

Examples of signature (2,2) manifolds with commuting curvature operators

We exhibit Walker manifolds of signature (2,2) with various commutativity properties for the Ricci operator, the skew-symmetric curvature operator, and the Jacobi operator. If the Walker metric is a Riemannian extension of an underlying affine structure A, these properties are related to the Ricci tensor of A

Density and reproductive characteristics of female brown bears in the Cantabrian Mountains, NW Spain

Here we present annual nearest-neighbour distances (as a proxy of density) between females with cubs-of-the-year (hereafter FCOY) and reproductive characteristics of brown bears Ursus arctos in the Cantabrian Mountains (NW Spain), from 1989 to 2017. FCOY nearest-neighbour distances and reproduction parameters of 19 focal females followed over several consecutive years (from 2004 to 2017) were obtained from bears inhabiting the western sector of the Cantabrian Mountains, where most of the bear population resides. In contrast, general reproductive characteristics were studied in the whole Cantabrian Mountains (western and eastern sectors together) on a sample of 362 litter sizes and 695 cubs. Mean nearest-neighbour distance between FCOY was 2559 ± 1222 m (range = 1305–4757 m). Mean litter size was significantly larger in the west (1.8 ± 0.2 cubs) than in the east (1.3 ± 0.6 cubs). Mean litter size for the whole of the Cantabrian Mountains was 1.6 ± 0.3 cubs. Litter sizes of one, two and three cubs represented 33.4, 56.1 and 10.5% of observed family groups, respectively. Interannual variations in litter size were not significant for both the western and the eastern areas. Mean cub mortality was 0.2 ± 0.5 cubs and did not vary among years. Cub mortality per litter size was 3.9% for one cub, 69.2% for two cubs and 26.9% for three cubs. Mean reproductive rate of the 19 focal females was 1.5 ± 0.6 cubs (n = 58 litters). Litter size of focal FCOY did not differ from the litter size obtained from systematic observations in the whole Cantabrian Mountains. During this period, cub mortality occurred in 24.1% of the 58 litters. Females usually bred every second year (average litter interval = 2.2 years). The estimated reproductive rate for the bear population was 0.7 young born/year/reproductive adult female

Coulomb explosion sputtering of selectively oxidized Si

We have studied multiply charged Arq+ ion induced potential sputtering of a unique system comprising of coexisting Silicon and Silicon oxide surfaces. Such surfaces are produced by oblique angle oxygen ion bombardment on Si(100), where ripple structures are formed and one side of each ripple gets more oxidized. It is observed that higher the potential energy of Arq+ ion, higher the sputtering yield of the non conducting (oxide) side of the ripple as compared to the semiconducting side. The results are explained in terms of Coulomb explosion model where potential sputtering depends on the conductivity of the ion impact sites.Comment: 9 pages and 3 figure

Effectiveness of dry needling for headache: A systematic review.

Introducción El uso de tratamientos no farmacológicos en pacientes con cefalea, como la punción seca (PS), está asociado a una baja morbimortalidad y a un bajo coste sanitario. Algunos han demostrado utilidad en la práctica clínica. El objetivo de esta revisión fue analizar el grado de evidencia de la efectividad de la PS en la cefalea. Métodos Revisión sistemática de ensayos clínicos aleatorizados sobre cefalea y PS en las bases de datos biomédicas PubMed, Web of Science, Scopus y PEDro. Se evaluó la calidad de los estudios incluidos mediante la escala PEDro por 2 evaluadores de forma independiente. Resultados De un total de 136 estudios, se seleccionaron 8 ensayos clínicos publicados entre 1994 y 2019, incluyendo en total 577 pacientes. Dos estudios evaluaron pacientes con cefalea cervicogénica, otros 2, pacientes con cefalea tensional, y otro, pacientes con migraña. Los otros 3 estudios evaluaron pacientes con cefalea de características mixtas (tensional/migraña). La calidad de los estudios incluidos osciló entre «baja» (3/10) y «alta» (8/10). La eficacia de la PS sobre los episodios de cefalea fue similar a la de los tratamientos con los que se comparó. No obstante, obtuvo mejoras significativas respecto a variables funcionales y de sensibilidad. Conclusiones La punción seca es una técnica a considerar para el tratamiento de las cefaleas en la consulta, pudiendo utilizarse de forma rutinaria, bien de forma aislada, bien en combinación con terapias farmacológicas. Introduction Non-pharmacological treatment of patients with headache, such as dry needling (DN), is associated with less morbidity and mortality and lower costs than pharmacological treatment. Some of these techniques are useful in clinical practice. The aim of this study was to review the level of evidence for DN in patients with headache. Methods We performed a systematic review of randomised clinical trials on headache and DN on the PubMed, Web of Science, Scopus, and PEDro databases. Methodological quality was evaluated with the Spanish version of the PEDro scale by 2 independent reviewers. Results Of a total of 136 studies, we selected 8 randomised clinical trials published between 1994 and 2019, including a total of 577 patients. Two studies evaluated patients with cervicogenic headache, 2 evaluated patients with tension-type headache, one study assessed patients with migraine, and the remaining 3 evaluated patients with mixed-type headache (tension-type headache/migraine). Quality ratings ranged from low (3/10) to high (7/10). The effectiveness of DN was similar to that of the other interventions. DN was associated with significant improvements in functional and sensory outcomes. Conclusions Dry needling should be considered for the treatment of headache, and may be applied either alone or in combination with pharmacological treatments

An Alternative Interpretation for the Moduli Fields of the Cosmology Associated to Type IIB Supergravity with Fluxes

We start with a particular cosmological model derived from type IIB supergravity theory with fluxes, where usually the dilaton is interpreted as a Quintessence field. Instead of that, in this letter we interpret the dilaton as the dark matter of the universe. With this alternative interpretation we find that in this supergravity model gives a similar evolution and structure formation of the universe compared with the $\Lambda$CDM model in the linear regime of fluctuations of the structure formation. Some free parameters of the theory are fixed using the present cosmological observations. In the non-linear regimen there are some differences between the type IIB supergravity theory with the traditional CDM paradigm. The supergravity theory predicts the formation of galaxies earlier than the CDM and there is no density cusp in the center of galaxies. These differences can distinguish both models and can give a distinctive feature to the phenomenology of the cosmology coming from superstring theory with fluxes.Comment: 7 pages, 5 figures, references added, minor modifications, typos corrected. Version accepted for publication in IJMP

An easy phylogenetically informative method to trace the globally invasive potamopyrgus mud snail from river's eDNA

Potamopyrgus antipodarum (New Zealand mud snail) is a prosobranch mollusk native to New Zealand with a wide invasive distribution range. Its non-indigenous populations are reported from Australia, Asia, Europe and North America. Being an extremely tolerant species, Potamopyrgus is capable to survive in a great range of salinity and temperature conditions, which explains its high invasiveness and successful spread outside the native range. Here we report the first finding of Potamopyrgus antipodarum in a basin of the Cantabrian corridor in North Iberia (Bay of Biscay, Spain). Two haplotypes already described in Europe were found in different sectors of River Nora (Nalon basin), suggesting the secondary introductions from earlier established invasive populations. To enhance the surveillance of the species and tracking its further spread in the region, we developed a specific set of primers for the genus Potamopyrgus that amplify a fragment of 16S rDNA. The sequences obtained from PCR on DNA extracted from tissue and water samples (environmental DNA, eDNA) were identical in each location, suggesting clonal reproduction of the introduced individuals. Multiple introduction events from different source populations were inferred from our sequence data. The eDNA tool developed here can serve for tracing New Zealand mud snail populations outside its native range, and for inventorying mud snail population assemblages in the native settings if high throughput sequencing methodologies are employed