Analysis of a task aimed to introduce sampling and sampling distributions in high school

II Congreso Internacional Virtual sobre el Enfoque Ontosemiótico del Conocimiento y la Instrucción Matemáticos (CIVEOS-2), 23-26 de marzo de 2017. [http://enfoqueontosemiotico.ugr.es/]Se describe la tarea inicial de una Trayectoria Hipotética de Aprendizaje sobre muestreo y distribución muestral dirigida a estudiantes mexicanos de bachillerato (17-19 años). Se utilizan elementos teóricos del Enfoque Ontosemiótico para identificar los objetos matemáticos implícitos en la tarea, así como para analizar algunas respuestas de los estudiantes.We describe the initial task of a Hypothetical Learning Trajectory about sampling and sampling distributions directed to Mexican high school students (17-19 years-old). Some theoretical tools from the Onto-Semiotic Approach are used to identify the mathematical objects embedded in the task, and to analyse some students’ responses.Trabajo realizado parcialmente en el marco del Proyecto EDU2016-74848-P (MEC)

Patterns of reasoning on signification tests of high school students

III Congreso Internacional Virtual de Educación Estadística (CIVEEST), 21-24 febrero de 2019. [www.ugr.es/local/fqm126/civeest.html]La presente investigación tiene el objetivo de explorar los patrones de razonamiento que exhiben estudiantes de bachillerato cuando enfrentan problemas de pruebas de significación con el método de simulación de muestreo repetido por computadora. Dieciocho parejas de estudiantes de 10º grado (16-17 años de edad) que no habían llevado el curso de probabilidad y estadística participaron en un taller de 6 sesiones, en la que abordaron 4 problemas de prueba de significación, generando en cada caso la distribución muestral correspondiente mediante una técnica de simulación. Como resultado, los estudiantes aprendieron la técnica y utilizaron la distribución muestral para tomar una decisión correcta acerca de rechazar o no la hipótesis. No obstante, varias parejas de estudiantes muestran, en sus respuestas, evidencia de concepciones erróneas acerca de la prueba mediante el método de muestreo repetido.This research has the objective of exploring the reasoning patterns exhibited by high school students when they face problems of significance tests with the repeated sampling simulation method by computer. Eighteen pairs of 10th grade students (16-17 years-old) who had not taken the probability and statistics course, participated in a 6-session workshop, in which they addressed 4 significance test problems, generating in each case the corresponding sample distribution by means of a simulation technique. As a result, the students learned the technique and used the sample distribution to make a correct decision about whether or not to reject the hypothesis. However, several pairs of students show, in their answers, evidence of misconceptions about the significance test using the repeated sampling method

Forward-central two-particle correlations in p-Pb collisions at root s(NN)=5.02 TeV

Two-particle angular correlations between trigger particles in the forward pseudorapidity range (2.5 2GeV/c. (C) 2015 CERN for the benefit of the ALICE Collaboration. Published by Elsevier B. V.Peer reviewe

Event-shape engineering for inclusive spectra and elliptic flow in Pb-Pb collisions at root(NN)-N-S=2.76 TeV

Peer reviewe

Azimuthal anisotropy of charged jet production in root s(NN)=2.76 TeV Pb-Pb collisions

We present measurements of the azimuthal dependence of charged jet production in central and semi-central root s(NN) = 2.76 TeV Pb-Pb collisions with respect to the second harmonic event plane, quantified as nu(ch)(2) (jet). Jet finding is performed employing the anti-k(T) algorithm with a resolution parameter R = 0.2 using charged tracks from the ALICE tracking system. The contribution of the azimuthal anisotropy of the underlying event is taken into account event-by-event. The remaining (statistical) region-to-region fluctuations are removed on an ensemble basis by unfolding the jet spectra for different event plane orientations independently. Significant non-zero nu(ch)(2) (jet) is observed in semi-central collisions (30-50% centrality) for 20 <p(T)(ch) (jet) <90 GeV/c. The azimuthal dependence of the charged jet production is similar to the dependence observed for jets comprising both charged and neutral fragments, and compatible with measurements of the nu(2) of single charged particles at high p(T). Good agreement between the data and predictions from JEWEL, an event generator simulating parton shower evolution in the presence of a dense QCD medium, is found in semi-central collisions. (C) 2015 CERN for the benefit of the ALICE Collaboration. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).Peer reviewe

Pseudorapidity and transverse-momentum distributions of charged particles in proton-proton collisions at root s=13 TeV

The pseudorapidity (eta) and transverse-momentum (p(T)) distributions of charged particles produced in proton-proton collisions are measured at the centre-of-mass energy root s = 13 TeV. The pseudorapidity distribution in vertical bar eta vertical bar <1.8 is reported for inelastic events and for events with at least one charged particle in vertical bar eta vertical bar <1. The pseudorapidity density of charged particles produced in the pseudorapidity region vertical bar eta vertical bar <0.5 is 5.31 +/- 0.18 and 6.46 +/- 0.19 for the two event classes, respectively. The transverse-momentum distribution of charged particles is measured in the range 0.15 <p(T) <20 GeV/c and vertical bar eta vertical bar <0.8 for events with at least one charged particle in vertical bar eta vertical bar <1. The evolution of the transverse momentum spectra of charged particles is also investigated as a function of event multiplicity. The results are compared with calculations from PYTHIA and EPOS Monte Carlo generators. (C) 2015 CERN for the benefit of the ALICE Collaboration. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).Peer reviewe

Elliptic flow of muons from heavy-flavour hadron decays at forward rapidity in Pb-Pb collisions at root s(NN)=2.76TeV

The elliptic flow, v(2), of muons from heavy-flavour hadron decays at forward rapidity (2.5 <y <4) is measured in Pb-Pb collisions at root s(NN)= 2.76TeVwith the ALICE detector at the LHC. The scalar product, two- and four-particle Q cumulants and Lee-Yang zeros methods are used. The dependence of the v(2) of muons from heavy-flavour hadron decays on the collision centrality, in the range 0-40%, and on transverse momentum, p(T), is studied in the interval 3 <p(T)<10 GeV/c. A positive v(2) is observed with the scalar product and two-particle Q cumulants in semi-central collisions (10-20% and 20-40% centrality classes) for the p(T) interval from 3 to about 5GeV/c with a significance larger than 3 sigma, based on the combination of statistical and systematic uncertainties. The v(2) magnitude tends to decrease towards more central collisions and with increasing pT. It becomes compatible with zero in the interval 6 <p(T)<10 GeV/c. The results are compared to models describing the interaction of heavy quarks and open heavy-flavour hadrons with the high-density medium formed in high-energy heavy-ion collisions. (C) 2015 CERN for the benefit of the ALICE Collaboration. Published by Elsevier B.V.Peer reviewe

Centrality evolution of the charged-particle pseudorapidity density over a broad pseudorapidity range in Pb-Pb collisions at root s(NN)=2.76TeV

Peer reviewe

Where Brain, Body and World Collide

The production cross section of electrons from semileptonic decays of beauty hadrons was measured at mid-rapidity (|y| &lt; 0.8) in the transverse momentum range 1 &lt; pt &lt; 8 Gev/c with the ALICE experiment at the CERN LHC in pp collisions at a center of mass energy sqrt{s} = 7 TeV using an integrated luminosity of 2.2 nb^{-1}. Electrons from beauty hadron decays were selected based on the displacement of the decay vertex from the collision vertex. A perturbative QCD calculation agrees with the measurement within uncertainties. The data were extrapolated to the full phase space to determine the total cross section for the production of beauty quark-antiquark pairs