Représentations dynamiques et tangibles dans l'enseignement mathématique

International audienceDynamic geometry environments offer a new kind of representation of mathematical objects that are variable and behave "mathematically" when one of the elements of the construction is dragged. The chapter addresses three dimensions about the transformations brought by this new kind of representation in mathematics and mathematics education: an epistemological dimension, a cognitive dimension and a didactic dimension. As so often stated since the time of ancient Greece, the nature of mathematical objects is by essence abstract. Mathematical objects are only indirectly accessible through representations (D'Amore 2003, pp. 39-43) and this contributes to the paradoxical character of mathematical knowledge: "The only way of gaining access to them is using signs, words or symbols, expressions or drawings. But at the same time, mathematical objects must not be confused with the used semiotic representations" (Duval 2000, p. 60). Other researchers have stressed the importance of these semiotic systems under various names. Duval calls them registers. Bosch and Chevallard (1999) introduce the distinction between ostensive and non ostensive objects and argue that mathematicians have always considered their work as dealing with non-ostensive objects and that the treatment of ostensive objects (expressions, diagrams, formulas, graphical representations) plays just an auxiliary role for them. Moreno Armella (1999) claims that every cognitive activity is an action mediated by material or symbolic tools. Through digital technologies, new representational systems were introduced with increased capabilities in manipulation and processing. The dragging facility in dynamic geometry environments (DGE) illustrates very well the transformation technology can bring in the kind of representations offered for mathematical activity and consequently for the meaning of mathematical objects. A diagram in a DGE is no longer a static diagram, representing an instance of a geometricalLes environnements de géométrie dynamique offrent un nouveau type d'objets mathématiques variables qui se modifient quand l'un des éléments de la construction est déplacé.Le chapitre aborde trois dimensions relatives aux transformations apportées par ce nouveau type de représentations en mathématiques et dans l'enseignement des mathématiques : une dimension épistémologique, une dimension cognitive et une dimension didactique

Effect of Planting Date, Clipping Height, and Cultivar on Forage and Grain Yield of Winter Wheat in Argentinean Pampas

In Argentinean Pampas, new wheat (Triticum aestivum L.) cultivars are routinely introduced to farmers for dual-purpose production. The objective of this study was to evaluate the effect of planting date, clipping height on forage, and grain yield for wheat cultivars. Treatments were arranged as a 3 × 3 × 3 factorial distributed in a split-split plot within a randomized complete block design. Main plots were planting date (March, April, and May); split-plots were clipping height (3 cm, 7 cm, and no clipping); and split-split plots were a facultative cultivar Pincen, and two nonfacultative cultivars Charrua and Bordenave 223 (Bve223). In 1995 and 1996 forage yield decreased in response to a delayed planting date from March to May, whereas in 1997 it was not affected by planting date. The 3-cm clipping height yielded 21% more forage than plots clipped at 7 cm. Bve223 and Charrua produced significantly more forage than Pincen each year. Grain yield increased as planting date progressed from March to May. Clipping at 3 cm reduced grain yield compared with no clipping, while during 2 to 3 yr, 7 cm produced no significant change in grain yield compared with no clipping. In all years Bve223 produced more grain than Charrua or Pincen. Forage yield lost in response to later planting date ranged between 0 and 81% during the 3 yr; whereas grain yield increased from 40 to 190% for wheat planted in May compared with March. In conclusion, dual-purpose wheat planted during April had both good forage and grain production, and its success was influenced by cultivars.Fil: Arzadún, M. J.. Provincia de Buenos Aires. Ministerio de Asuntos Agrarios; ArgentinaFil: Arroquy, Jose Ignacio. Instituto Nacional de Tecnología Agropecuaria; ArgentinaFil: Laborde, Hugo Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Centro de Recursos Naturales Renovables de la Zona Semiárida. Universidad Nacional del Sur. Centro de Recursos Naturales Renovables de la Zona Semiárida; ArgentinaFil: Brevedan, Roberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Centro de Recursos Naturales Renovables de la Zona Semiárida. Universidad Nacional del Sur. Centro de Recursos Naturales Renovables de la Zona Semiárida; Argentin

Welfare Impacts of Agricultural and Non-Agricultural Trade Reforms

The variability of protection rates within sectors is frequently particularly high in agriculture relative to non-agriculture. Standard aggregation procedures ignore the variability within sectors, and underweight the importance of highly protected sectors. It therefore seems likely that they underestimate the potential benefits of agricultural trade reform relative to non-agricultural reform. This study examines this question using a new procedure for aggregating trade distortions. It finds that the key impact of using better aggregators is to increase the benefits of both agricultural and non-agricultural reform. It finds that using optimal aggregation procedures increases the measured importance of agricultural trade reform relative to non-agricultural reform from a very high initial level, but only by around two percentage points.agricultural trade, nonagricultural trade, trade distortions, tariffs, aggregation, World Trade Organization, WTO, trade reform, Food Security and Poverty, International Relations/Trade, F13, F14, Q13, Q17, Q18,

Influencia de la calidad del heno suplementario y la localización de la pastura sobre el rendimiento de bovinos de carne a pastoreo sobre avena

Heifers grazing oat pasture (OP) at two locations in Argentina, Argerich (ARG) and Pasman (PAS), were subjected to one of three different dietary supplement treatments: (1) control (CON, no supplement), (2) sorghum hay (SH), or (3) alfalfa-grass hay (AGH), all provided ad libitum in individual pens. The variables measured were: dry matter (DM) yield and composition of OP, hay intake, average daily weight gain (ADG), rumen pH and NH3-N, and blood mineral levels. DM availability did not limit OP intake. OP crude protein (CP) content ranged from 11.3 to 13% at ARG, and 10.7 to 13.3% at PAS. OP-minerals varied with location; the mean K/(Ca + Mg) ratios were 5.68 meq (ARG) and 4.82 meq (PAS). Heifers ate more AGH (785 g) than SH (684 g; P = 0.08). Hay consumption was 2.88 times greater at PAS than at ARG (P < 0.05). ADG was larger with SH (558 g) and AGH 594 g than with CON treatment (454 g); the average for ARG animals was 571 g compared to 500 g for PAS animals (P <0.05). Rumen pH was lower at 14:30 h (pH 6.7) than at 10:00 h (pH 7.5; P < 0.05). NH3-N values were higher at 14:30 h (19.59 mg dl-1) than at 10:00 h (4.69 mg dl-1; P < 0.05). Plasma Ca (15.50 mg dl–1) and Mg (2.84 mg dl–1) levels were higher in PAS cattle (P < 0.05). Animal performance improved with hay supplementation, but location affected response intensity.Se realizaron tres tratamientos con novillas pastoreando verdeos de avena (VA) en dos localidades de Argentina, Argerich (ARG) y Pasman (PAS): (1) Control (CON, sin suplemento), (2) heno de sorgo (HS), y (3) heno de alfalfa y gramíneas (HAG), suplementados ad libitum en corrales individuales. Evaluamos rendimiento de materia seca (MS) y composición en VA; y en los animales consumo del heno, ganancia diaria de peso (GDP), pH y N-NH3 en rumen, y minerales en sangre. La disponibilidad de MS no limitó el consumo de VA; su proteína bruta (PB) osciló entre 11,3 y 13% (ARG), 10,7 y 13.3% (PAS). Los minerales en VA variaron entre localidades, la relación K/(Ca + Mg) promedió 5,68 meq (ARG) y 4,82 meq (PAS). Las novillas consumieron diariamente más HAG (785 g) que HS (684 g; P = 0.08), y 2,88 veces más heno en PAS que en ARG (P < 0,05). En GDP, HS (558 g) y HAG (594 g) superaron al CON (454 g), y la media de ARG (571 g) a PAS (500 g; P < 0,05). En el rumen el pH decreció a las 14:30 h (6,7) vs. 10:00 h (7,5; P < 0,05), y el N-NH3 (mg dl-1) aumentó a las 14:30 h (19,59) vs. 10:00 h (4,69; P < 0,05). Ca (15.50 mg dl–1) y Mg (2.84 mg dl–1) en plasma fue mayor en PAS (P < 0,05). El rendimiento animal mejoró con la suplementación, pero la magnitud de respuesta estuvo afectada por la localidad.Fil: Arelovich, Hugo Mario. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Centro de Recursos Naturales Renovables de la Zona Semiárida. Universidad Nacional del Sur. Centro de Recursos Naturales Renovables de la Zona Semiárida; ArgentinaFil: Laborde, Hugo Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Centro de Recursos Naturales Renovables de la Zona Semiárida. Universidad Nacional del Sur. Centro de Recursos Naturales Renovables de la Zona Semiárida; ArgentinaFil: Arzadún, M. J.. Provincia de Buenos Aires. Ministerio de la Producción. Chacra Experimental Coronel Suarez; ArgentinaFil: Vasquez, Maria Gabriela. Universidad Nacional del Sur. Departamento de Agronomía; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Centro de Recursos Naturales Renovables de la Zona Semiárida. Universidad Nacional del Sur. Centro de Recursos Naturales Renovables de la Zona Semiárida; Argentin

Modélisation pluie-débit à l’échelle annuelle en Algérie du nord

La modélisation du comportement hydrologique des bassins versants est incontournable dès lors que l'on s'intéresse à des problématiques relatives à l’évaluation et la gestion optimale des ressources en eau. Ceci s’illustre par un aspect quantitatif, dans les pays comme l’Algérie où l’alimentation en eau est un facteur limitant. L’objectif principal de cet article est d’expliciter les relations entre les conditions hydrologiques et la disponibilité en eau de surface. A cet effet, un modèle pluie-débit à l’échelle annuelle qui prend en compte les paramètres physiques et climatiques a été mis au point. L’application porte sur l’Algérie du Nord dont la superficie est de 325 000 km2.La mise au point de ce modèle nécessite au préalable une base de données qui a été acquise lors des travaux antérieurs incluant la carte des pluies médianes, la carte des perméabilités et le modèle numérique de terrain. Afin de compléter cette base de données, la cartographie des pluies des différentes années pour lesquelles on dispose des débits a été réalisée en utilisant une méthodologie intitulée "cartographie de la pluie centrée réduite". Ainsi, les données de 467 postes pluviométriques ont été traitées et ont permis de tracer les cartes des isohyètes annuelles.L’étude de la relation pluie-débit à l’échelle annuelle est basée sur les données de débits de 50 stations hydrométriques réparties à travers la zone d’étude. La démarche utilisée s’est inspirée de la fonction de production du S.C.S (Soil Conservation Service). Les résultats du modèle après calage ont permis d’obtenir un coefficient d’explication de 0,75, ce qui signifie que 75 % de la variance est expliquée par la pluie moyenne, la surface et un coefficient (a) qui correspond à la pente moyenne des bassins versants.Modelling the hydrological behaviour of drainage basins is very important for solving problems related to the evaluation and optimal management of water resources. This is illustrated quantitatively in countries such as Algeria where water supply is a limiting factor. The principal aim of this paper was to explain the relationship between hydrological conditions and the availability of surface water. A model of rainfall-discharge was developed on a yearly scale, taking into account physical and climatic parameters. The application was carried out in northern Algeria where the total land surface is about 325 000 km2.The development of this model required a database, which was acquired during previous studies where maps of median rainfall and permeability as well as the digital elevation model were developed. In order to complete this database, the cartography of rainfall for the years for which we have discharge data was carried out using a methodology entitled "mapping standardized rainfall". To estimate and map annual rainfall, the kriging method was used. Two problems were encountered:- The presence of a drift highly altered the variogram and made it very difficult to infer a sub- structure function;- The variogram is significant only if the hypothesis of ergodicity is valid, which was not easy to assume for any given year.In order to resolve these difficulties, a homogeneous random and secondary stationary order function (same mean at all points and same covariance function) must be calculated. A previous study by ANRH (1993) allowed us to know the statistical parameters of the distribution at each point. These parameters were mapped, taking into consideration the topographical relief and distance to the sea. For every year and at each rainfall measure point, the standardized rainfall could be deduced. The correlogram gave information about the spatial variability of the phenomenon and its range, and subsequently the standardized rainfall was then interpolated. Annual rainfall was calculated by combining the grids of the means, the variances and the centered reduced rainfall (TOUAZI and LABORDE, 2000). Thus, the data of 467 rainfall gauges were used in order to create maps of the yearly isohyets.The rainfall-discharge relationship on an annual scale was based on 50 hydrometric stations distributed throughout the study area. The methodology used was derived from the production function of the S.C.S (Soil Conservation Service). This production function was part of modelling, which transformed total rainfall to net rainfall. This method was very representative of the natural hydrological processes. Indeed, it takes into account rainfall and the maximum infiltration capacity (S), which depends on the nature of the soil (lithology), vegetation and soil moisture content. In the current study, the basin surface and a regional parameter (a) were introduced in order to calibrate the model. This production function was implemented by supplying different values for the parameter (S). The values (n+1) were obtained by increasing the previous value (n) by 10 %. We evaluated the different values of (S) in the same way to obtain the last value (i). We calculated for these different values of the parameter (S) the square of the difference between the measured and estimated discharges for each year by measuring the discharge at different stations. For each station, we calculated the sum of these values for all the years and we retained the value of (S) that gave the minimal value. The results demonstrated that the values of (S) obtained were not significant because they tend to the infinite. For this reason, (S) was considered as a constant. In order to improve the model, we repeated the same operation, but instead of (S), we used the parameter (a) and performed the same calculation. After calibration of the model the results gave a coefficient of determination of 0.75, which means that 75 % of the variance was explained by the mean rainfall, the surface and the parameter (a).To explain the parameter (a), we calculated the correlation between its value at each station with the corresponding geology. This latter variable was characterized by the average storage capacity, which corresponds to the weighted average of the surfaces of the basin assigned to each permeability category (TOUAZI, 2001). The results demonstrated a coefficient of determination of 0.1. The correlation with the topographical relief was not necessary because it was taken into account in the cartography of the rainfall. We then proceeded to the cartography of the parameter (a). The results demonstrated an east-west gradient that was constant and a north-south gradient that decreased from north to south. With the digital elevation model, we used a geographical information system to deduce the slopes. For each basin, the average slope was calculated by taking the average of the values of the slopes of all the pixels that constituted the individual basin. The correlation between slopes and corresponding values of the parameter (a) gave a coefficient of correlation of 0.6.The results obtained by this model after calibration gave a coefficient of determination of 0.75, which means that 75% of the variance was explained by the mean rainfall, the surface and a coefficient (a), which corresponds to the average slope of the drainage basins

Une méthode stochastique pour la prédétermination des fluctuations probables des durées de service des réservoirs collinaires en Tunisie

Un modèle de génération stochastique de pluies est couplé ˆ un modèle de calcul de l'index de leurs érosivités, dérivé de l'Equation Universelle de l'Erosion des Sols (USLE). Le premier fonctionne au pas de temps de 30mn, il est calé sur une série pluviographique de 15 ans de la Tunisie centrale. Le second modèle fonctionne par calcul automatique des cumuls et moyennes de l'érosivité des pluies générées.En mode opérationnel, ces deux modèles sont exploités pour simuler les aléas de l'envasement annuel des réservoirs collinaires de la zone aride et semi-aride de la Tunisie : le bassin versant est considéré comme une "boite noire" où l'agressivité climatique est la principale variable (quelques pluies extrêmes font l'essentiel de l'érosion), les autres facteurs sont considérés constants durant la durée de service du réservoir. Nous observons sur trois bassins versants répartis du nord au sud de la frange comprise entre 500mm et 250mm (de pluie moyenne annuelle), que la distribution annuelle des index d'érosivité des pluies peut être assimilée ˆ la distribution des transports solides.Sur l'un de ces bassins versants (OUED EL HISSIANE : 15,9 ) nous observons également que les valeurs extrêmes de l'érosion sont proportionnelles aux valeurs extrêmes de l'index d'érosivité des pluies. Seulement l'automne et le printemps sont des saisons érosives.Dans le cas de petits bassins versants non-jaugés, comme ceux pour l'aménagement de réservoirs collinaires, le générateur nous permet de constituer des chroniques d'érosivité de pluie. Si on considère que les autres paramètres sont constants, ce modèle nous aide à déterminer les intervalles de confiance de durées de service probables.Une analyse de sensibilité par la modification des paramètres du générateur (nombre d'épisodes, hauteur de pluie, maximum et durée d'averse etc ...) valide la méthodologie. De même une analyse régionale montre les faibles fluctuations des résultats sur l'étendue aride et semi-aride de la Tunisie.Ces deux résultats nous ont conduit à proposer un abaque régional de prédétermination des fluctuations probables des durées de service des réservoirs collinaires, compte tenu de la connaissance préalable de la durée de service moyenne probable.Cette méthode directement opérationnelle peut être utilisée pour l'aménagement, la planification, et la gestion des réservoirs collinaires. Elle améliore les études de faisabilité, notamment lorsqu'on la couple aux calculs économiques.A stochastic rainfall generator and a model for calculating the erosivity index of the Universal Soil Loss Equation (USLE) are coupled. The first one operates on a 30 min time step and it is calibrated on a 15 year historical pluviographic database for central Tunisia. The second model works like an automatic calculator, where the rain erosivity index can be averaged or summed. These two models are applied to simulate the annual siltation of hill reservoirs in arid and semi-arid areas of Tunisia. The catchment is considered as a "black-box" where mostly climatic aggressivity is varying (some extreme rainfall events cause most of the erosion) and the other erosion parameters are considered to remain constant over the lifetime of the reservoir. We know that the WISCHMEIER rain erosion index has no upper limit. When all the other factors are maintained constant, erosion is proportional to it. This climatic index is calculated for each rain event, but we can also calculate the annual average or sum it over many years. Soil losses (or solid transport) during a period are proportional to the value of this index summed over the same period.We demonstrate on three representative catchments lying from north to south (from 500 mm to 250 mm annual average rainfall) that the annual rain erosion index distribution can be considered comparable to the solid transport distribution (Galton distributions with equal statistical parameters).For the OUED EL HISSIANE catchment (15.9 km2), the annual extreme value of erosion is proportional to the annual extreme value of the rain erosion index. Only spring and autumn storms need be considered to calculate the annual sediment loss.On gauged small catchments like those of hill reservoirs, the rainfall generator can provide an erosivity rainfall record. Considering that the other erosion parameters are constant, this model allows one to calculate the confidence intervals of a reservoir's predicted durations. We equate the annual erosivity index distribution to the annual solid supplies distribution, and we generate and sum over several consecutive years many series of "solid supplies" to simulate the progressive silting up of the reservoirs (represented by the chosen period : sum over T=5 years, 10 years, 15 years ...). In the context of setting up hill reservoirs, this study concerns the potential duration and possible services of hydraulic structures (including the risk of rapid silting up of the reservoirs). This generator can be computed over many years and avoids the limitation due to the short observed time series.The methodological benefit of such an approach is therefore to avoid the difficulty of limited observed samples. It enlarges the data analysis of the series dispersal and residuals. This approach, based on observations and a statistical method, supports experimental analysis. It gives a clear idea of the rate of siltation, according to climatic hazards. A sensitivity analysis, where we modify the rainfall generator parameters (number of episodes and quantity of rain, peak and duration of storm...), is used to validate the methodology. A regional analysis shows a very low fluctuation considering the whole arid and semi-arid area of Tunisia. These two results led us to set up a regional abacus. This abacus reports the forecasts of the fluctuations of the time length service for hilly and small dams, including the probable average of their service duration. It allow a predetermination of the small dams' life time together with a confidence interval, and it can be used for small dam construction, planning and management. It improves the first feasibility study and can be included in economic calculations

Coping related variables, cardiac vagal activity and working memory performance under pressure

The aim of this study was to assess the predictive role of coping related variables (trait emotional intelligence and reinvestment, challenge and threat appraisals and cardiac vagal activity) on cardiac vagal activity and working memory under low pressure (LP) and high pressure (HP) conditions. Participants (n = 49) completed trait questionnaires, the Decision Specific Reinvestment Scale, the Movement Specific Reinvestment Scale and Trait Emotional Intelligence Questionnaire. They realized the automated span task, which tests working memory, under counterbalanced LP and HP conditions. Cardiac vagal activity measurements were taken at rest, task and post task for 5 min, along with self-reported ratings of stress. Upon completion of the task, self-report measures of motivation, stress appraisal, attention and perceived pressure were completed. Current findings suggest cardiac vagal activity at rest can predict cardiac vagal activity under pressure, decision reinvestment influences cardiac vagal activity in cognitive tasks under LP and working memory performance is predicted by task cardiac vagal activity in HP only. These results show the importance of combining both subjective and objective psychophysiological variables in performance prediction and strengthen the need for this approach to be adopted across samples

Effective density of Aquadag and fullerene soot black carbon reference materials used for SP2 calibration

The mass and effective density of black carbon (BC) particles generated from aqueous suspensions of Aquadag and fullerene soot was measured and parametrized as a function of their mobility diameter. The measurements were made by two independent research groups by operating a differential mobility analyser (DMA) in series with an aerosol particle mass analyser (APM) or a Couette centrifugal particle mass analyser (CPMA). Consistent and reproducible results were found in this study for different production lots of Aquadag, indicating that the effective density of these particles is a stable quantity and largely unaffected by differences in aerosol generation procedures and suspension treatments. The effective density of fullerene soot particles from one production lot was also found to be stable and independent of suspension treatments. Some differences to previous literature data were observed for both Aquadag and fullerene soot at larger particle diameters. Knowledge of the exact relationship between mobility diameter and particle mass is of great importance, as DMAs are commonly used to size-select particles from BC reference materials for calibration of single particle soot photometers (SP2), which quantitatively detect the BC mass in single particles

Transcutaneous vagus nerve stimulation via tragus or cymba conchae: Are its psychophysiological effects dependent on the stimulation area?

Efforts in optimizing transcutaneous vagus nerve stimulation (tVNS) are crucial to further develop its potential in improving cognitive and autonomic regulation. The present study focused on this topic. The aim was to compare for the first time the main stimulation areas of the ear currently used in studies with tVNS, taking cognitive as well as neurophysiological effects into account. The main areas to be compared with one another were tragus, cymba conchae, and earlobe (sham) stimulation. Post-error slowing, which has already been shown to be influenced by tVNS, was used to investigate the cognitive effects of tVNS when applied on the different auricular areas. On the neurophysiological level, we measured pupillary responses as an index of norepinephrine activity during post-error slowing, and cardiac vagal activity to investigate the activation of neural pathways involved in post-error slowing. Stimulation of different auricular areas led to no differences in post-error slowing and in pupillary responses. However, the neurological processes involved in post-error slowing could be observed, since norepinephrine activity increased after committing an error. Further, there was an increase in cardiac vagal activity over the test period that was independent of the stimulation areas. The results suggest that tVNS targeting the ear might have a non-specific effect on the processing of error commission, on pupillary responses, and on cardiac vagal activity. We conclude that it is necessary to consider alternatives for sham conditions other than electrical earlobe stimulation. [Abstract copyright: Copyright © 2021 Elsevier B.V. All rights reserved.