Conceptions of basic education teachers about math proof: influence of professional experience

A prova é uma atividade que desempenha um papel fundamental na construção do conhecimento matemático, razão pela qual adquire relevância nos programas escolares de Matemática. Admitindo que as conceções dos professores sobre a prova afetam a forma como ela é tratada em sala de aula, procuramos averiguar as conceções de professores portugueses de Matemática do 3.º ciclo do Ensino Básico (do 7.º ao 9.º ano) sobre diferentes aspetos da prova matemática e a influência que a experiência profissional tem nessas conceções. Adotando uma abordagem metodológica mista, recolhemos os dados através de um questionário, respondido por 72 professores, e de uma entrevista a duas professoras com experiências profissionais diferentes. Os resultados revelam que os professores, sobretudo os que têm menos tempo de docência, consideram que a prova matemática tem uma natureza distinta da de outras disciplinas, é uma atividade essencial para a construção do conhecimento matemático, tem como função verificar e explicar a veracidade de uma afirmação e permite desenvolver o raciocínio e a comunicação matemática. No que respeita à participação dos alunos na atividade de provar, são os professores com mais tempo de docência que mais o destacam, o que permite aos alunos perceberem a natureza desta atividade. Em termos curriculares, são os professores com menos experiência docente que mais concordam com a presença da prova logo nos primeiros anos, embora salientem que esta atividade só faz sentido em alguns tópicos programáticos.Proof is an activity that plays a key role in the construction of mathematical knowledge, which is why it acquires relevance in mathematics programs. Admitting that teachers' conceptions about proof influence how it is handled in the classroom, we tried to investigate the conceptions of Portuguese mathematics teachers from the 3rd cycle of basic education (grade 7 to 9) on different aspects of mathematical proof and the relationship that the teachers’ experience has in these conceptions. Adopting a mixed methodological approach, we collected data through a questionnaire answered by 72 teachers, and an interview with two teachers with different professional experience. The results show that teachers, especially those with less experience, consider that mathematical proof has a distinct nature from other disciplines, it is an essential activity for the construction of mathematical knowledge and its function is to verify and explain the truth of a statement by developing reasoning and mathematical communication. With respect to student participation in the activity of proving, teachers with more teaching experience are the ones that most highlight it, which allows students to realize the nature of this activity. In curriculum terms, teachers with less experience are the ones that most agree with the presence of proof in early grades, while emphasizing that this activity only makes sense in some program topics.Este trabalho contou com o apoio de Fundos Nacionais através da FCT – Fundação para a Ciência e a Tecnologia no âmbito do projeto PEst-OE/CED/UI1661/2014, do CIEdUM e do projeto UID/Multi/04016/2016info:eu-repo/semantics/publishedVersio

Search for anomalous t t-bar production in the highly-boosted all-hadronic final state

A search is presented for a massive particle, generically referred to as a Z', decaying into a t t-bar pair. The search focuses on Z' resonances that are sufficiently massive to produce highly Lorentz-boosted top quarks, which yield collimated decay products that are partially or fully merged into single jets. The analysis uses new methods to analyze jet substructure, providing suppression of the non-top multijet backgrounds. The analysis is based on a data sample of proton-proton collisions at a center-of-mass energy of 7 TeV, corresponding to an integrated luminosity of 5 inverse femtobarns. Upper limits in the range of 1 pb are set on the product of the production cross section and branching fraction for a topcolor Z' modeled for several widths, as well as for a Randall--Sundrum Kaluza--Klein gluon. In addition, the results constrain any enhancement in t t-bar production beyond expectations of the standard model for t t-bar invariant masses larger than 1 TeV.Comment: Submitted to the Journal of High Energy Physics; this version includes a minor typo correction that will be submitted as an erratu

Combined search for the quarks of a sequential fourth generation

Results are presented from a search for a fourth generation of quarks produced singly or in pairs in a data set corresponding to an integrated luminosity of 5 inverse femtobarns recorded by the CMS experiment at the LHC in 2011. A novel strategy has been developed for a combined search for quarks of the up and down type in decay channels with at least one isolated muon or electron. Limits on the mass of the fourth-generation quarks and the relevant Cabibbo-Kobayashi-Maskawa matrix elements are derived in the context of a simple extension of the standard model with a sequential fourth generation of fermions. The existence of mass-degenerate fourth-generation quarks with masses below 685 GeV is excluded at 95% confidence level for minimal off-diagonal mixing between the third- and the fourth-generation quarks. With a mass difference of 25 GeV between the quark masses, the obtained limit on the masses of the fourth-generation quarks shifts by about +/- 20 GeV. These results significantly reduce the allowed parameter space for a fourth generation of fermions.Comment: Replaced with published version. Added journal reference and DO

Measurement of the Z/gamma* + b-jet cross section in pp collisions at 7 TeV

The production of b jets in association with a Z/gamma* boson is studied using proton-proton collisions delivered by the LHC at a centre-of-mass energy of 7 TeV and recorded by the CMS detector. The inclusive cross section for Z/gamma* + b-jet production is measured in a sample corresponding to an integrated luminosity of 2.2 inverse femtobarns. The Z/gamma* + b-jet cross section with Z/gamma* to ll (where ll = ee or mu mu) for events with the invariant mass 60 < M(ll) < 120 GeV, at least one b jet at the hadron level with pT > 25 GeV and abs(eta) < 2.1, and a separation between the leptons and the jets of Delta R > 0.5 is found to be 5.84 +/- 0.08 (stat.) +/- 0.72 (syst.) +(0.25)/-(0.55) (theory) pb. The kinematic properties of the events are also studied and found to be in agreement with the predictions made by the MadGraph event generator with the parton shower and the hadronisation performed by PYTHIA.Comment: Submitted to the Journal of High Energy Physic

Search for new physics with same-sign isolated dilepton events with jets and missing transverse energy

A search for new physics is performed in events with two same-sign isolated leptons, hadronic jets, and missing transverse energy in the final state. The analysis is based on a data sample corresponding to an integrated luminosity of 4.98 inverse femtobarns produced in pp collisions at a center-of-mass energy of 7 TeV collected by the CMS experiment at the LHC. This constitutes a factor of 140 increase in integrated luminosity over previously published results. The observed yields agree with the standard model predictions and thus no evidence for new physics is found. The observations are used to set upper limits on possible new physics contributions and to constrain supersymmetric models. To facilitate the interpretation of the data in a broader range of new physics scenarios, information on the event selection, detector response, and efficiencies is provided.Comment: Published in Physical Review Letter

Azimuthal anisotropy of charged particles at high transverse momenta in PbPb collisions at sqrt(s[NN]) = 2.76 TeV

The azimuthal anisotropy of charged particles in PbPb collisions at nucleon-nucleon center-of-mass energy of 2.76 TeV is measured with the CMS detector at the LHC over an extended transverse momentum (pt) range up to approximately 60 GeV. The data cover both the low-pt region associated with hydrodynamic flow phenomena and the high-pt region where the anisotropies may reflect the path-length dependence of parton energy loss in the created medium. The anisotropy parameter (v2) of the particles is extracted by correlating charged tracks with respect to the event-plane reconstructed by using the energy deposited in forward-angle calorimeters. For the six bins of collision centrality studied, spanning the range of 0-60% most-central events, the observed v2 values are found to first increase with pt, reaching a maximum around pt = 3 GeV, and then to gradually decrease to almost zero, with the decline persisting up to at least pt = 40 GeV over the full centrality range measured.Comment: Replaced with published version. Added journal reference and DO

Compressed representation of a partially defined integer function over multiple arguments

In OLAP (OnLine Analitical Processing) data are analysed in an n-dimensional cube. The cube may be represented as a partially defined function over n arguments. Considering that often the function is not defined everywhere, we ask: is there a known way of representing the function or the points in which it is defined, in a more compact manner than the trivial one

Search for a W' boson decaying to a bottom quark and a top quark in pp collisions at sqrt(s) = 7 TeV

Results are presented from a search for a W' boson using a dataset corresponding to 5.0 inverse femtobarns of integrated luminosity collected during 2011 by the CMS experiment at the LHC in pp collisions at sqrt(s)=7 TeV. The W' boson is modeled as a heavy W boson, but different scenarios for the couplings to fermions are considered, involving both left-handed and right-handed chiral projections of the fermions, as well as an arbitrary mixture of the two. The search is performed in the decay channel W' to t b, leading to a final state signature with a single lepton (e, mu), missing transverse energy, and jets, at least one of which is tagged as a b-jet. A W' boson that couples to fermions with the same coupling constant as the W, but to the right-handed rather than left-handed chiral projections, is excluded for masses below 1.85 TeV at the 95% confidence level. For the first time using LHC data, constraints on the W' gauge coupling for a set of left- and right-handed coupling combinations have been placed. These results represent a significant improvement over previously published limits.Comment: Submitted to Physics Letters B. Replaced with version publishe