Lo que el constructivismo puede ser para la educación de la matemática

Analizadas las conceptualizaciones sobre constructivismo, se estudian sus implicaciones desde la educación de la matemática. A partir de ejemplos y experiencias se abordan tópicos y expresiones en un intento de responder a preguntas cómo: ¿qué parece ser el constructivismo? ¿qué no parece ser? y ¿qué necesita ser?Once the conceptualizations on constructivism have been analised, their implicacions are studied from the point of view of the education of mathematics. Starting with examples and experiences, we approach issues and expressions in an attempt to answer questions such as: what does constructivism seem to be like?, what does it not seem to be? and what does it need to be

The mathematics teacher and curriculum change

One of the most compelling lessons of the new math reform era --from the mid 1950s to the mid 1970s-- concerned the pivotal role of the mathematics teacher in effecting curriculum change. Recent efforts to change the school mathematics curriculum are rediscovering that old lesson: The teacher is the key to change. Consequently, when teachers are confronted with arguments against the direction that proposals for curriculum change are taking, it is important for them to analyze and discuss the proposed changes. Recent experiences in the United States, which does not have the same centralized curriculum organization as Portugal but which is experiencing some of the same proposals and arguments against them, may be helpful in understanding the role that teachers can play in the social process of creating a curriculum

Cambio local y global del currículo

La colaboración que se requiere en el currículo de las matemáticas escolares implica reconocer que el cambio del currículo comienza y termina en el salón de clase. El consenso que han asumido las propuestas de reforma curricular tanto locales como regionales y nacionales ha sido con frecuencia ilusorio y las realidades de la práctica diaria no se han tenido en cuenta. Los esfuerzos para obligar a los profesores a que cambien sus currículos son poco promisorios en el nivel regional y aun en el nacional. Superar la estabilidad de los currículos puede requerir un enfoque diferente del que pueden realizar las comunidades de práctica reflexiva. La tecnología puede jugar un papel clave en este proceso aunque el problema básico no es tecnológico

Review of U.S. Math Performance in Global Perspective: How Well Does Each State Do at Producing High-Achieving Students

A report from Harvard's Program on Education Policy and Governance and the journal Education Next finds that only 6% of U.S. students in the high school graduating class of 2009 achieved at an advanced level in mathematics compared with 28% of Taiwanese students and more than 20% of students in Hong Kong, Korea, and Finland. Overall, the United States ranked behind most of its industrialized competitors. The report compares the mathematics performance of high achievers not only across countries but also across the 50 U.S. states and 10 urban districts. Most states and cities ranked closer to developing countries than to developed countries. However, the study has three noteworthy limitations: (a) internationally, students were sampled by age and not by grade, and countries varied greatly on the proportion of the student cohort included in the compared grades; in fact, only about 70% of the U.S. sample would have been in the graduating class of 2009, which makes the comparisons unreliable; (b) the misleading practice of reporting rankings of groups of high-achieving students hides the clustering of scores, inaccurately exaggerates small differences, and increases the possibility of error in measuring differences; and (c) the different tests used in the study measured different domains of mathematics proficiency, and the international measure was limited because of relatively few test items. The study's deceptive comparison of high achievers on one test with high achievers on another says nothing useful about the class of 2009 and offers essentially no assistance to U.S. educators seeking to improve students' performance in mathematics.This brief is published by the National Education Policy Center (NEPC), and is one of a series of briefs made possible in part by funding from The Great Lakes Center for Education Research and Practice

Educación Matemática. Errores y dificultades de los estudiantes. Resolución de problemas. Evaluación. Historia

En este libro, el lector encontrará textos de dos de los investigadores más importantes a nivel mundial en el área de la educación matemática: el profesor Jeremy Kilpatrick, de la Universidad de Georgia y el catedrático Luis Rico, de la Universidad de Granada. El lector podrá tener una visión global de esta disciplina y de algunos de los temas que preocupan en la actualidad a su comunidad internacional. En la primera parte, el profesor Kilpatrick hace una reflexión acerca de la historia de la investigación en educación matemática y de algunos de sus temas de actualidad. Por su parte, el catedrático Rico hace una presentación de la evolución que la educación matemática ha tenido en España hasta el momento actual. Finalmente el doctor Carlos Vasco, hace una relación de algunas de las líneas de investigación en educación matemática que se han trabajado en Colombia. La segunda parte del libro presenta las opiniones de los investigadores alrededor de dos temas de gran actualidad en la educación matemática: la resolución de problemas y la evaluación. Estos textos son producto de las discusiones que estos dos profesores tuvieron con un grupo de investigadores colombianos. En la tercera y última parte del libro, el lector encontrará dos textos de educación matemática con gran valor práctico. El catedrático Rico hace una reflexión sobre los errores y dificultades en el aprendizaje de las matemáticas. El profesor Kilpatrick presenta algunas técnicas de evaluación para profesores de matemáticas. Este es un libro de gran interés para el profesor de matemáticas y el investigador en educación matemática. En él, ellos encontrarán tanto una visión general de la disciplina, como reflexiones lógicas y metodológicas de la investigación y resultados y sugerencias prácticas para la actividad docente en matemáticas

Evidence for fracture-hosted fluid-rock reactions within geothermal reservoirs of the eastern trans-Mexico volcanic belt

Fractures within hydrothermal systems represent major pathways for fluid flow, and it is therefore vital that we understand processes occurring along them as these may have an impact on productivity of hot fluids during geothermal exploitation. This is especially important where hydrothermal activity crosses contrasting rock types, as fluid movement can result in a range of fluid�rock reactions, mineral dissolution and precipitation, and possible changes in fracture permeability. Here we report evidence of fluid-rock reactions within basement carbonates and overlying volcanic rocks within hydrothermally altered rocks of the eastern trans-Mexico volcanic belt, as part of the Europe-Mexico collaborative ‘GEMex’ project (EU-H2020, GA No. 727550). Identified reactions within basement carbonates include initial high temperature Si-metasomatism linked to igneous intrusions to form minerals such as olivine, wollastonite, garnet and diopside, followed by subsequent lower temperature hydration (back reaction) at lower temperatures, where olivine and diopside hydrate to form serpentine and talc. Reactions of overlying andesitic units include Ca-metasomatism and bleaching through interaction of rising acidic, carbonate-equilibrated fluids. Secondary minerals produced during these reactions appear to seal fractures, implying tectonic reactivation of fractures to maintain long-term fluid flow through fracture zones

Misperception: No evidence to dismiss RPE as regulator of moderate-intensity exercise

This document is the Accepted Manuscript version of a published work that appeared in final form in Medicine and Science in Sport and Exercise. To access the final edited and published work see https://doi.org/10.1249/MSS.0000000000000748.Dear Editor-in-Chief, Shaykevich et al. (7) demonstrate the efficacy of auditory feedback anchored at 75% of age-predicted HRmax to regulate intensity (claimed as ‘‘moderate’’) during several 20-min bouts of cycling. Their technical approach is novel, but 76% HRmax is the upper limit of moderate intensity, so given the large error in age-predicted HRmax, it is unlikely that their exercise bandwidth was ‘‘moderate’’ for all participants. This is not our major concern, but it reveals one among other inaccuracies: the most serious include training, interpretation, and inferences relating to the RPE

Genetic risk and a primary role for cell-mediated immune mechanisms in multiple sclerosis.

Multiple sclerosis is a common disease of the central nervous system in which the interplay between inflammatory and neurodegenerative processes typically results in intermittent neurological disturbance followed by progressive accumulation of disability. Epidemiological studies have shown that genetic factors are primarily responsible for the substantially increased frequency of the disease seen in the relatives of affected individuals, and systematic attempts to identify linkage in multiplex families have confirmed that variation within the major histocompatibility complex (MHC) exerts the greatest individual effect on risk. Modestly powered genome-wide association studies (GWAS) have enabled more than 20 additional risk loci to be identified and have shown that multiple variants exerting modest individual effects have a key role in disease susceptibility. Most of the genetic architecture underlying susceptibility to the disease remains to be defined and is anticipated to require the analysis of sample sizes that are beyond the numbers currently available to individual research groups. In a collaborative GWAS involving 9,772 cases of European descent collected by 23 research groups working in 15 different countries, we have replicated almost all of the previously suggested associations and identified at least a further 29 novel susceptibility loci. Within the MHC we have refined the identity of the HLA-DRB1 risk alleles and confirmed that variation in the HLA-A gene underlies the independent protective effect attributable to the class I region. Immunologically relevant genes are significantly overrepresented among those mapping close to the identified loci and particularly implicate T-helper-cell differentiation in the pathogenesis of multiple sclerosis