From practical geometry to the laboratory method. The search for an alternative to Euclid in the history of teaching geometry

This paper wants to show how practical geometry, created to give a concrete help to people involved in trade, in land-surveying and even in astronomy, underwent a transformation that underlined its didactical value and turned it first into a way of teaching via problem solving, and then into an experimental-intuitive teaching that could be an alternative to the deductive-rational teaching of geometry. This evolution will be highlighted using textbooks that proposed alternative presentations of geometry

Guido Castelnuovo e l'insegnamento della matematica

At the beginning of the 900s Guido Castelnuovo turned his attention toward methodological, didactical, historical and applicative issues. He was an active member of the ICMI (International Commission on Mathematical Instruction) and of the Mathesis, an Italian association of mathematics teachers. He also was the author of the mathematics curricula for the new Modern Lycee and he taught the first University courses devoted to preservice training of mathematics teachers. His course on Precision and Application Mathematics, inspired by Felix Klein, shows Castelnuovo's point of view on mathematics and presents a higher point of view on the programmes of the Modern Lycee.Comment: in Italia

Luigi Cremona and Wilhelm Fiedler: the link between descriptive and projective geometry in technical instruction

This paper considers Luigi Cremona’s and Wilhelm Fiedler’s outlook on technical instruction at school and university level, their vision about the educational role of descriptive geometry and its relation to Monge’s original conception. Like Cremona, Fiedler sees a symbiosis between descriptive and projective geometry via the fundamental idea of central projection. The link between projective and descriptive geometry plays a double role: an educational one due to the graphical aspects of the two disciplines and a conceptual one due to the connection of theory to practice. Thus, projective and descriptive geometry contribute to form a class of scientifically educated people, and the link between them epitomizes – in the opinion of Cremona – the link between pure mathematics and its applications. According to Fiedler, the main scope of the teaching of descriptive geometry is the scientific construction and development of “Raumanschauung”, as stated in a paper published in the Italian journal Giornale di Matematiche. The textbooks by Fiedler (1871) and Cremona (1873) were used in Italy to develop the geometry programs for the sezione fisico matematica (physics and mathematics section) within technical secondary instruction. While the relation between projective and descriptive geometry – and, thus, between pure and applied mathematics – had a short life at secondary school level in Italy, at the turn of the century there was a new expansion at university level due to the important role that then mathematicians had in the creation of the Faculty of Architecture

Editorial

Parte I- Monográfico: Formación, trabado docente y desigualdades. Contribuciones y debates a partir del III Coloquio de Investigación Educativa 2019Los entramados vínculos entre la formación, el trabajo docente, los procesos de escolarización y las desigualdades sociales han constituido, posiblemente, una de las mayores preocupaciones del campo de la investigación educativa en Argentina en las últimas décadas (Vasilliades, 2018). No es casual, por tanto, que la comunidad de investigadores en educación se preocupe por abordarla y actualizar no solo desde su indagación sino también desde las posibles líneas de intervención con el objetivo de contribuir a saldar, al menos en parte, la desigualdad socioeducativa contemporánea. El cierre de este año tan particular que transitamos nos encuentra, curiosamente, entusiasmados. Será que el campo de la educación se sostiene en las promesas, en esos horizontes utópicos que nos inspiran para andar y, entonces, las condiciones de inestabilidad, incertidumbre e incluso intermitente desesperanza han logrado traducirse en preguntas interesantes. Parece ya cierto que la desigualdad se ha hecho obscena, y esta pornografía nos exige aprovechar la interrupción y decidir. Como dice Sara Ahmed (2019: 437), “Cuando hay una crisis, tenemos que hacernos la pregunta “¿hacia dónde vamos?”. Cuando el camino se convierte en una pregunta, nos volvemos conscientes de la posibilidad. Nos volvemos conscientes de hasta qué punto no es necesario que vivamos la vida que vivimos”

Movimento, percezione e dimostrazione

Summary. Geometry can be treated from a logical point of view, following the precise sequence of its statements, or from an intuitive or perceptive point of view, which is linked to a global understanding of geometrical objects. The balance between these two aspects is the core of geometrical education. In this paper we will show and discuss examples of proofs linked to diagrams or models, in which the argument is based on intuition. We will then see how the introduction of motion can give a major role to perception, seen as the skill to develop an argument based only on images and diagrams, almost without any linguistic support. But sometimes perception needs an "external control"

C-peptide: a predictor of cardiovascular mortality in subjects with established atherosclerotic disease

Aim: Insulin resistance and type 2 diabetes are independent risk factors for cardiovascular diseases. Levels of C-peptide are increased in these patients and its role in the atherosclerosis progression was studied in vitro and in vivo over the past years. To evaluate the possible use of C-peptide as cardiovascular biomarkers, we designed an observational study in which we enrolled patients with mono- or poly-vascular atherosclerotic disease. Methods: We recruited 431 patients with stable atherosclerosis and performed a yearly follow-up to estimate the cardiovascular and total mortality and cardiovascular events. Results: We performed a mean follow-up of 56months on 268 patients. A multivariate Cox analysis showed that C-peptide significantly increased the risk of cardiovascular mortality [Hazard Ratio: 1.29 (95% confidence interval: 1.02-1.65, p<0.03513)] after adjustment for age, sex, diabetes treatment, estimated glomerular filtration rate and known diabetes status. Furthermore, levels of C-peptide were significantly correlated with metabolic parameters and atherogenic factors. Conclusion: C-peptide was associated with cardiovascular mortality independently of known diabetes status in a cohort of patients with chronic atherosclerotic disease. Future studies using C-peptide into a reclassification approach might be undertaken to consider its potential as a cardiovascular disease biomarker

Plastics in biogenic matrices intended for reuse in agriculture and the potential contribution to soil accumulation

The spread of biogenic matrices for agricultural purposes can lead to plastic input into soils, raising a question on possible consequences for the environment. Nonetheless, the current knowledge concerning the presence of plastics in biogenic matrices is very poor. Therefore, the objective of the present study was a quali-quantitative characterization of plastics in different matrices reused in agriculture as manures, digestate, compost and sewage sludges. Plastics were quantified and characterized using a Fourier Transform Infrared Spectroscopy coupled with an optical microscope (μFT-IR) in Attenuated Total Reflectance mode. Our study showed the presence of plastics in all the investigated samples, albeit with differences in the content among the matrices. We measured a lower presence in animal matrices (0.06–0.08 plastics/g wet weight w.w.), while 3.14–5.07 plastics/g w.w. were measured in sewage sludges. Fibres were the prevalent shape and plastic debris were mostly in the micrometric size. The most abundant polymers were polyester (PEST), polypropylene (PP) and polyethylene (PE). The worst case was observed in the compost sample, where 986 plastics/g w.w. were detected. The majority of these plastics were compostable and biodegradable, with only 8% consisting of fragments of PEST and PE. Our results highlighted the need to thoroughly evaluate the contribution of reused matrices in agriculture to the plastic accumulation in the soil system