My calculator does not work

Pretendemos que mediante una serie de actividades con calculadora a las que denominamos "actividades con teclas estropeadas", el alumno conozca diferentes algoritmos para las operaciones, los cuales pueden ser los clásicos, de todos conocidos, o creados por el mismo alumno. Estas actividades, suponemos, le ayudarán para el estudio de las propiedades de los números y operaciones, así como en la práctica del cálculo aproximado.We are trying through a series of activities with the calculator, called "activities with broken key" to make the pupil understand different algorisms for the mathematic operations, those which could be traditional, which everyone knows or created by the pupil himself. We presume these activities will help with the study of numbers and operations, as well as the practice of estimating calculus.peerReviewe

Cartesian Certainty, Realism and Scientific Inference

In the Principles, Descartes explains several observable phenomena showing that they are caused by special arrangements of unobservable microparticles. Despite these microparticles being unobservable, many passages suggest that he was very confident that these explanations were correct. In other passages, however, Descartes points out that these explanations merely hold the status of ‘suppositions’ or ‘conjectures’ that could be wrong. The aim of this chapter is to clarify this apparent conflict. I argue that the possibility of natural explanations being wrong should be understood as these explanations not being absolutely certain, but as being morally certain. Cartesian explanations rely on what Ernan McMullin calls retroduction, which is a mode of inference that justifies beliefs in concrete unobservable entities and processes. I use as a foil the debate in contemporary philosophy of science between scientific realism and instrumentalism, and argue that for Descartes we could indeed have knowledge of the unobservable world. In that sense, he was closer to being a scientific realist

Lab-grown futures: Design exploration for the development of fungi as a leather-like material

Living organisms such as fungi – mycelium – are opening a new paradigm for the manufacturing industry through the technology of biofabrication. To engage in this phenomena, designers and scientists are starting to collaborate in transdisciplinary contexts. However, little is known as to how this collaboration with experts takes place and even less how designers develop their interaction with living organisms in laboratories. Fungi possess a biological machinery of their own, which is often unknown to designers. The research for this master’s thesis took place primarily at the laboratories of VTT Technical Research Centre of Finland. This work explores how design processes using fungi can lead to sustainable alternatives to animal leather through the practice of biofabrication. I define this practice as a process that integrates living matter for the manufacturing of biological materials or products. The aim is to open the spectrum of physical materialities for fungi and through this practice understand the interaction between the designer and the living material as it grows and speaks to the designer. These materials are alive and possess an agency of their own. Through the interaction with fungi and the collaboration with scientists, this practice of design offers new possibilities to extend beyond the traditional forms of doing design. One is by engaging users in the process to explore material experiences and another one is by applying speculative design when exploring future applications for these materials. The focus of this research lies on the practical design work in the laboratory. The methodology includes constructive design research, material design driven method and user involvements through two workshops and ten interviews. The contextual research includes the practices of speculative design and biodesign. Further research includes more centralized research on a single species of fungi, conducting a life cycle assessment, and internal research on the use of design practices in the context of laboratories

Contact forces distribution for a granular material from a Monte Carlo study on a single grain

The force network ensemble is one of the most promising statistical descriptions of granular media, with an entropy accounting for all force configurations at mechanical equilibrium consistent with some external stress. It is possible to define a temperature-like parameter, the angoricity {\alpha}^{-1}, which under isotropic compression is a scalar variable. This ensemble is frequently studied on whole packings of grains; however, previous works have shown that spatial correlations can be neglected in many cases, opening the door to studies on a single grain. Our work develops a Monte Carlo method to sample the force ensemble on a single grain at constant angoricity on two and three-dimensional mono-disperse granular systems, both with or without static friction. The results show that, despite the steric exclusions and the constrictions of Coulomb's limit and repulsive normal forces, the pressure per grain always show a gamma distribution with scale parameter {\nu} = {\alpha}^{-1} and shape parameter k close to k', the number of degrees of freedom in the system. Moreover, the average pressure per grain fulfills an equipartition theorem =k'{\alpha}^{-1} in all cases (in close parallelism with the one for an ideal gas). These results suggest the existence of k' independent random variables (i.e. elementary forces) with identical exponential distributions as the basic elements for describing the force network ensemble at low angoricities under isotropic compression, in analogy with the volume ensemble of granular materials

Análisis de las representaciones geométricas en los libros de texto

La investigación analiza y clasifica las imágenes gráficas relacionadas con la enseñanza-aprendizaje de la geometría en libros de textos. Se estudian varios aspectos de las representaciones geométricas a lo largo de las unidades de geometría de los libros. Algunos de estos aspectos son la variedad de representaciones al introducir conceptos geométricos, los elementos de las imágenes que puedan derivar en dificultades en el proceso de enseñanza-aprendizaje de la geometría, la representación plana de figuras tridimensionales y las imágenes reales que se utilizan para aludir a elementos geométricos abstractos. Se realiza una categorización que sirve como instrumento de análisis de los textos

Recuerdos, expectativas y concepciones de los estudiantes para maestro sobre la geometría escolar

Numerosos trabajos de investigación han puesto de manifiesto la importancia de analizar las concepciones de los estudiantes para profesores sobre las matemáticas y sobre su enseñanza-aprendizaje durante su proceso de formación. Éstas aparecen y se desarrollan durante su etapa escolar y son estables y resistentes a los cambios. Como consecuencia de ello, asumimos que, para aprender a enseñar matemáticas, debemos considerar las exigencias que proceden de las propias concepciones y conocimientos sobre la matemática escolar. Partiendo de esta premisa hemos desarrollado una investigación con el objetivo de describir y analizar las concepciones sobre la geometría escolar y su enseñanza-aprendizaje de los estudiantes para maestro. Para ello hemos considerado la hipótesis de que los recuerdos y las expectativas de los estudiantes nos dan información para caracterizar sus concepciones en el campo de la geometría y su enseñanza-aprendizaje en primaria.Several studies have shown the importance of prospective teachers' conceptions about mathematics and its teaching-learning during their educational process. They indicate that to learn to teach mathematics we must take into account the demands that originate from our own conceptions of school-level mathematics, since these are stable and resistant to change. On the basis of this idea, we have developed a study aimed at describing and analysing prospective primary teachers' conceptions about school-level geometry and its teaching-learning. To this end, we considered the hypothesis that the students' memories and expectations provide information with which to characterize prospective primary teachers' conceptions in the field of geometry and its teaching-learning at primary school level

Análisis de las concepciones de los profesores en formación sobre la enseñanza y aprendizaje de la geometría

En nuestro trabajo asumimos que las concepciones aparecen y se desarrollan durante la etapa escolar, y constituyen una lente que los estudiantes para profesores de Primaria utilizan, consciente o inconscientemente, para filtrar los contenidos de Didáctica de la Matemática, en general, y en particular los de Didáctica de la Geometría. Por ello, consideramos importante analizarlas para tenerlas en cuenta en el proceso de aprender a enseñar geometría dentro de la formación inicial de los maestros

Main referents about geometry teaching in secondary education

A partir de un trabajo más amplio relativo a una revisión bibliográfica sobre la enseñanza y el aprendizaje de la geometría en la última década, hemos extraído los principales referentes respecto a la enseñanza de esta materia en Secundaria. Éstos pueden servir como referencia de base teórica para tesis, proyectos y otros trabajos académicos o como un material nuevo al alcance del docente que le garanticen mejores resultados en su actividad docente y de desempeño en el aula.From a broader analysis where we conducted a bibliographical review on the teaching and learning of geometry during the last decade, we have scrutinized the main references concerning the teaching of this academic subject in Secondary Education. These can serve as a reference for theoretical theses, projects and further academic research or as a new material available for the teachers in order to achieve better results in teaching and classroom practice.peerReviewe

Un extractor de jugo teórico. El papel de las matemáticas en la explicación científica

"A theoretical juice extractor: The role of mathematics in scientific explanation". There have recently been proposed cases where, supposedly, mathematics would play a genuinely explanatory role in science. These have been divided into those situations where the explanatory role would be played by mathematical operations, and those where it would be played by mathematical entities. In this article, I analyze some of these purported cases and argue that claims that mathematics can be genuinely explanatory are unfounded. Throughout my discussion, I emphasize the representational role of mathematics, as opposed to its supposed explanatory role: the role of mathematics, even in the cases that I discuss, is to represent physical facts and help draw inferences about those fact