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‣ Demographics, Persistence, and Academic Performance: A Logistic Regression Analysis of who Chooses to Enter the Mathematics and Science Teaching Pipeline

Joseph, Esther
Fonte: FIU Digital Commons Publicador: FIU Digital Commons
Tipo: Artigo de Revista Científica Formato: application/pdf
Português
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As of 1999, high school teachers without majors in their subject areas number 37% of biology teachers, 59% of physical science teachers, and 60% of mathematics teachers. These discouraging statistics grow more extreme in middle schools and high poverty public high schools, especially regarding mathematics and physical sciences instruction. The statistics are especially worrisome given the strong correlation between thorough teacher subject matter preparation and higher student performance. Unfortunately, the literature is limited in terms of a direct comparison between mathematics and science majors and individuals who become mathematics and science teachers. This study was undertaken to add to the body of literature in hopes of informing universities and school districts of the characteristics of individuals who enter the mathematics and science teacher pipeline. The purpose of this study was to determine whether predictive relationships exist among the independent variables and the dependent variable, and whether certain attributes account for significant differences between mathematics and science degree earners who choose to enter the mathematics and science teacher pipeline and those who show no interest in mathematics and science teaching. This study provided a snapshot of the characteristics of both groups of individuals. The sample for this investigation came from the Baccalaureate and Beyond Longitudinal Study (B&B: 08/09) cohort of approximately 19...

‣ Rendimiento matemático en contextos bilingües: Análisis de la incidencia de algunas variables del contexto socio-educativo; Rendimiento matemático en contextos bilingües: Análisis de la incidencia de algunas variables del contexto socio-educativo

Pifarré Turmo, Manoli; Sanuy Burgués, Jaume; Huguet Canalis, Angel; Vendrell Serés, Contxita
Tipo: Artigo de Revista Científica Formato: application/pdf
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This work is situated in the bilingual context of the Lleida province. In this province two languages are in contact, the catalan and the Spanish, but in the family and in the school context the Catalan language is used more frequently than the Spanish language.In this context, our study analyses the influence of the variables of the social and educative context as such linguistic familiar condition and the social and professional condition of the family, and the individual variables as such: intellectual coefficient and self perception of mathematics achievement.The results of our work show, on one hand, the relevance of the language as a mediator for the teaching and learning of mathematics contents. The achievement of the students in mathematics is related with the knowledge and the use of the teaching language —the Catalan—.On the other hand, our work shows a significant correlation between the achievement in mathematics and the individual variables as the intellectual coefficient and the self-perception of the own achievement.; El trabajo que se presenta en este artículo se sitúa en el contexto bilingüe de la provincia de Lleida en la que coexisten dos lenguas en contacto, el catalán y el castellano, si bien existe un predominio de uso familiar y escolar de la primera de ellas.En este contexto...

‣ Dimensión afectiva hacia la matemática: resultados de un análisis en Educación Primaria; Affective dimension towards mathematics: results of a study in Primary Education

Mato Vázquez, María Dorinda; Espiñeira Bellón, Eva; Chao Fernández, Rocío
Tipo: Artigo de Revista Científica Formato: application/pdf
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Este artículo evalúa la dimensión afectiva de 1180 alumnos de Educación Primaria respecto a las matemáticas durante el curso 2012.Para ello se describe, en primer lugar, la percepción que tienen los estudiantes sobre las actitudes de su profesor de matemáticas, así como la satisfacción que siente hacia la materia y el valor que le otorga de cara a su futuro profesional. Posteriormente se analizan las asociaciones e influencias respecto a las variables centro (público y concertado) y curso (3º, 4º, 5º y 6º) mediante la prueba no paramétrica de Kruskal-Wallis. Finalmente, para conocer los efectos generales y específicos de la variable actitud sobre el rendimiento académico recurrimos a la correlación de Pearson.Finaliza el artículo con los resultados y la presentación de las conclusiones obtenidas.Podemos decir que los procesos afectivos influyen en las experiencias de los alumnos cuándo se enfrentan al aprendizaje matemático y repercuten en su calificación.; This article analyzed the affective dimension towards mathematics of 1,180 primary education undergraduate students during the 2011-2012 academic year. We described students´ perception of their mathematics teacher's attitude, students´ satisfaction with the subject matter...

‣ The effectiveness of an intelligent tutoring system on the attitude and achievement of developmental mathematics students in a community college

Burton, Linda Kramer
Fonte: FIU Digital Commons Publicador: FIU Digital Commons
Tipo: Artigo de Revista Científica
Português
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This study examined the effectiveness of intelligent tutoring system instruction, grounded in John Anderson's ACT theory of cognition, on the achievement and attitude of developmental mathematics students in the community college setting. The quasi-experimental research used a pretest-posttest control group design. The dependent variables were problem solving achievement, overall achievement, and attitude towards mathematics. The independent variable was instructional method.^ Four intact classes and two instructors participated in the study for one semester. Two classes (n = 35) served as experimental groups; they received six lessons with real-world problems using intelligent tutoring system instruction. The other two classes (n = 24) served as control groups; they received six lessons with real-world problems using traditional instruction including graphing calculator support. It was hypothesized that students taught problem solving using the intelligent tutoring system would achieve more on the dependent variables than students taught without the intelligent tutoring system.^ Posttest mean scores for one teacher produced a significant difference in overall achievement for the experimental group. The same teacher had higher means...

‣ Variables separated equations: Strikingly different roles for the Branch Cycle Lemma and the Finite Simple Group Classification

Fried, Michael d.
Tipo: Artigo de Revista Científica
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H. Davenport's Problem asks: What can we expect of two polynomials, over the integers, with the same ranges on almost all residue class fields? This stood out among many separated variable problems posed by Davenport, D.J. Lewis and A. Schinzel. By bounding the degrees, but expanding the maps and variables in Davenport's Problem, Galois stratification enhanced the separated variable theme, solving an Ax and Kochen problem from their Artin Conjecture work. J. Denef and F. Loeser applied this to add Chow motive coefficients to previously introduced zeta functions on a diophantine statement. By restricting the variables, but leaving the degrees unbounded, we found the striking distinction between Davenport's problem over the rationals, solved by applying the Branch Cycle Lemma, and its generalization over any number field, solved using the simple group classification. This encouraged J. Thompson to formulate the genus 0 problem on rational function monodromy groups. R. Guralnick and Thompson led its solution in stages. We look at at two developments since the solution of Davenport's problem. * Stemming from C. MacCluer's 1967 thesis, identifying a general class of problems, including Davenport's, as monodromy precise. * R(iemann) E(xistence) T(heorem)'s role as a converse to problems generalizing Davenport's...

‣ Surface Operators and Separation of Variables

Frenkel, Edward; Gukov, Sergei; Teschner, Joerg
Tipo: Artigo de Revista Científica
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Alday, Gaiotto, and Tachikawa conjectured relations between certain 4d N=2 supersymmetric field theories and 2d Liouville conformal field theory. We study generalizations of these relations to 4d theories with surface operators. For one type of surface operators the corresponding 2d theory is the WZW model, and for another type - the Liouville theory with insertions of extra degenerate fields. We show that these two 4d theories with surface operators exhibit an IR duality, which reflects the known relation (the so-called separation of variables) between the conformal blocks of the WZW model and the Liouville theory. Furthermore, we trace this IR duality to a brane creation construction relating systems of M5 and M2 branes in M-theory. Finally, we show that this duality may be expressed as an explicit relation between the generating functions for the changes of variables between natural sets of Darboux coordinates on the Hitchin moduli space.; Comment: 56 pages

‣ On the multiplication of free $n$-tuples of non-commutative random variables

Nica, Alexandru; Speicher, Roland
Tipo: Artigo de Revista Científica
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Let $a_{1},...,a_{n}, b_{1},...,b_{n}$ be random variables in some (non-commutative) probability space, such that $\{a_{1}, ..., a_{n} \}$ is free from $\{b_{1}, ..., b_{n} \}$. We show how the joint distribution of the $n$-tuple $(a_{1} b_{1}, ..., a_{n} b_{n})$ can be described in terms of the joint distributions of $(a_{1}, ..., a_{n})$ and $(b_{1}, >..., b_{n})$, by using the combinatorics of the $n$-dimensional $R$-transform. We point out a few applications that can be easily derived from our result, concerning the left-and-right translation with a semicircular element (see Sections 1.6-1.10) and the compression with a projection (see Sections 1.11-1.14) of an $n$-tuple of non-commutative random variables. A different approach to two of these applications is presented by Dan Voiculescu in an Appendix to the paper.; Comment: LaTeX2e, Appendix upon request, to appear in Amer. J. Math

‣ Control Problem on Space of Random Variables and Master Equation

Bensoussan, Alain; Yam, Phillip
Tipo: Artigo de Revista Científica
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We study in this paper a control problem in a space of random variables. We show that its Hamilton Jacobi Bellman equation is related to the Master equation in Mean field theory. P.L. Lions in [14,15] introduced the Hilbert space of square integrable random variables as a natural space for writing the Master equation which appears in the mean field theory. W. Gangbo and A. \'Swi\k{e}ch [10] considered this type of equation in the space of probability measures equipped with the Wasserstein metric and use the concept of Wasserstein gradient. We compare the two approaches and provide some extension of the results of Gangbo and \'Swi\k{e}ch.

‣ A change of variables theorem for the multidimensional Riemann integral

Molnár, Zoltán; Nagy, Ilona; Szilágyi, Tivadar
Tipo: Artigo de Revista Científica
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The most general change of variables theorem for the Riemann integral of functions of a single variable has been published in 1961 (by Kestelman). In this theorem, the substitution is made by an indefinite integral', that is, by a function of the form (t\mapsto c+\int_a^tg=:G(t)) where (g) is Riemann integrable on ([a,b]) and (c) is any constant. We prove a multidimensional generalization of this theorem for the case where (G) is injective -- using the fact that the Riemann primitives are the same as those Lipschitz functions which are almost everywhere strongly differentiable in ((a,b)). We prove a generalization of Sard's lemma for Lipschitz functions of several variables that are almost everywhere strongly differentiable, which enables us to keep all our proofs within the framework of the Riemannian theory which was our aim.; Comment: 17 pages

‣ Polynomial Hamiltonian system in two variables with $W({A}^{(1)}_1)$-symmetry and the second Painlev\'e hierarchy

Sasano, Yusuke
Tipo: Artigo de Revista Científica
Português
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We find a one-parameter family of polynomial Hamiltonian system in two variables with $W({A}^{(1)}_1)$-symmetry. We also show that this system can be obtained by the compatibility conditions for the linear differential equations in three variables. We give a relation between it and the second member of the second Painlev\'e hierarchy. Moreover, we give some relations between an autonomous version of its polynomial Hamiltonian system in two variables and the mKdV hierarchies.; Comment: 29 pages, 2 figures

‣ Free Probability for Pairs of Faces III: 2-Variables Bi-free Partial S- and T-Transforms

Voiculescu, Dan-Virgil
Tipo: Artigo de Revista Científica
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We introduce two 2-variables transforms: the partial bi-free S-transform and the partial bi-free T-transform. These transforms are the analogues for the bi-multiplicative and respectively for the additive-multiplicative bi-free convolution of the 2-variables partial bi-free R-transform in our previous paper in this series.; Comment: 16 pages, corrected typos and added a note at the end after the references

‣ Generic Variables in Acyclic Cluster Algebras and Bases in Affine Cluster Algebras

Dupont, G.
Tipo: Artigo de Revista Científica
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Let $Q$ be a finite quiver without oriented cycles and $\mathcal A(Q)$ be the coefficient-free cluster algebra with initial seed $(Q,\textbf u)$. Using the Caldero-Chapoton map, we introduce and investigate a family of generic variables in $\Z[\textbf u^{\pm 1}]$ containing the cluster monomials of $\mathcal A(Q)$. The aim of these generic variables is to give an explicit new method for constructing $\Z$-bases in the cluster algebra $\mathcal A(Q)$. If $Q$ is an affine quiver with minimal imaginary root $\delta$, we investigate differences between cluster characters associated to indecomposable representations of dimension vector $\delta$. We define the notion of \emph{difference property} which gives an explicit description of these differences. We prove in particular that this property holds for quivers of affine type $\tilde A$. When $Q$ satisfies the difference property, we prove that generic variables span the cluster algebra $\mathcal A(Q)$. If $\mathcal A(Q)$ satisfies some gradability condition, we prove that generic variables are linearly independent over $\mathbb Z$ in $\mathcal A(Q)$. In particular, this implies that generic variables form a $\Z$-basis in a cluster algebra associated to an affine quiver of type $\tilde A$.; Comment: 63 pages. v2: Title changed since the first part of this article can now be found as an independent article under the initial title

‣ On the Damping-Induced Self-Recovery Phenomenon in Mechanical Systems with Several Unactuated Cyclic Variables

Chang, Dong Eui; Jeon, Soo
Tipo: Artigo de Revista Científica
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The damping-induced self-recovery phenomenon refers to the fundamental property of underactuated mechanical systems: if an unactuated cyclic variable is under a viscous damping-like force and the system starts from rest, then the cyclic variable will always move back to its initial condition as the actuated variables come to stop. The regular momentum conservation phenomenon can be viewed as the limit of the damping-induced self-recovery phenomenon in the sense that the self-recovery phenomenon disappears as the damping goes to zero. This paper generalizes the past result on damping-induced self-recovery for the case of a single unactuated cyclic variable to the case of multiple unactuated cyclic variables. We characterize a class of external forces that induce new conserved quantities, which we call the damping-induced momenta. The damping-induced momenta yield first-order asymptotically stable dynamics for the unactuated cyclic variables under some conditions, thereby inducing the self-recovery phenomenon. It is also shown that the viscous damping-like forces impose bounds on the range of trajectories of the unactuated cyclic variables. Two examples are presented to demonstrate the analytical discoveries: the planar pendulum with gimbal actuators and the three-link planar manipulator on a horizontal plane.

‣ Generic Variables in Acyclic Cluster Algebras

Dupont, Gregoire
Tipo: Artigo de Revista Científica
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Let $Q$ be an acyclic quiver. We introduce the notion of generic variables for the coefficient-free acyclic cluster algebra $\mathcal A(Q)$. We prove that the set $\mathcal G(Q)$ of generic variables contains naturally the set $\mathcal M(Q)$ of cluster monomials in $\mathcal A(Q)$ and that these two sets coincide if and only if $Q$ is a Dynkin quiver. We establish multiplicative properties of these generic variables analogous to multiplicative properties of Lusztig's dual semicanonical basis. This allows to compute explicitly the generic variables when $Q$ is a quiver of affine type. When $Q$ is the Kronecker quiver, the set $\mathcal G(Q)$ is a $\mathbb Z$-basis of $\mathcal A(Q)$ and this basis is compared to Sherman-Zelevinsky and Caldero-Zelevinsky bases.; Comment: 20 pages. This is an adaptation of the first part of the preprint arXiv:0811.2909. To appear in the Journal of Pure and Applied Algebra

‣ Reducing the number of variables of a polynomial

Carlini, Enrico
Tipo: Artigo de Revista Científica
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In this paper, we consider two basic questions about presenting a homogeneous polynomial f: how many variables are needed for presenting f? How can one find a presentation of f involving as few variables as possible? We give a complete answer to both questions, determining the minimal number of variables needed, NEssVar(f), and describing these variables through their linear span, EssVar(f). Our results give rise to effective algorithms which we implemented in the computer algebra system CoCoA.

‣ Concentration and Moment Inequalities for Polynomials of Independent Random Variables

Schudy, Warren; Sviridenko, Maxim
Tipo: Artigo de Revista Científica
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In this work we design a general method for proving moment inequalities for polynomials of independent random variables. Our method works for a wide range of random variables including Gaussian, Boolean, exponential, Poisson and many others. We apply our method to derive general concentration inequalities for polynomials of independent random variables. We show that our method implies concentration inequalities for some previously open problems, e.g. permanent of a random symmetric matrices. We show that our concentration inequality is stronger than the well-known concentration inequality due to Kim and Vu. The main advantage of our method in comparison with the existing ones is a wide range of random variables we can handle and bounds for previously intractable regimes of high degree polynomials and small expectations. On the negative side we show that even for boolean random variables each term in our concentration inequality is tight.; Comment: 46 pages

‣ On axiomatic aspects of N=2 vertex superalgebras with odd formal variables, and deformations of N=1 vertex superalgebras

Barron, Katrina
Tipo: Artigo de Revista Científica
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The notion of "N = 2 vertex superalgebra with two odd formal variables" is presented, the main axiom being a Jacobi identity with odd formal variables in which an N=2 superconformal shift is incorporated into the usual Jacobi identity for a vertex superalgebra. It is shown that as a consequence of these axioms, the N=2 vertex superalgebra is naturally a representation of the Lie algebra isomorphic to the three-dimensional algebra of superderivations with basis consisting of the usual conformal operator and the two N=2 superconformal operators. The notion of N=2 Neveu-Schwarz vertex operator superalgebra with two odd formal variables is introduced, and consequences of this notion are derived. Various other formulations of the notion of N=2 (Neveu-Schwarz) vertex (operator) superalgebra appearing in the mathematics and physics literature are discussed, and several mistakes in the literature are noted and corrected. The notion of `N=2 (Neveu-Schwarz) vertex (operator) superalgebra with one odd formal variable" is formulated. It is shown that this formulation naturally arises from alternate notions of N=1 superconformality and the continuous deformation of an N=1 (Neveu-Schwarz) vertex (operator) superalgebra with one odd formal variable. This notion is formulated to reflect the underlying N=1 superanalytic geometry...

‣ N=1 Neveu-Schwarz vertex operator superalgebras over Grassmann algebras and with odd formal variables

Barron, Katrina Deane
Tipo: Artigo de Revista Científica
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The notions of N=1 Neveu-Schwarz vertex operator superalgebra over a Grassmann algebra and with odd formal variables and of N=1 Neveu-Schwarz vertex operator superalgebra over a Grassmann algebra and without odd formal variables are introduced, and we show that the respective categories of such objects are isomorphic. The weak supercommutativity and weak associativity properties for an N=1 Neveu-Schwarz vertex operator superalgebra with odd formal variables are established, and we show that in the presence of the other axioms, weak supercommutativity and weak associativity are equivalent to the Jacobi identity. In addition, we prove the supercommutativity and associativity properties for an N=1 Neveu-Schwarz vertex operator superalgebra with odd formal variables and show that in the presence of the other axioms, supercommutativity and associativity are equivalent to the Jacobi identity.; Comment: 34 pages, LaTeX

‣ Preprojective cluster variables of acyclic cluster algebras

Zhu, Bin
Tipo: Artigo de Revista Científica
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For any valued quiver, by using BGP-reflection functors, an injection from the set of preprojective objects in the cluster category to the set of cluster variables of the corresponding cluster algebra is given, the images are called preprojective cluster variables. It is proved that all preprojective cluster variables have denominators $u^{\underline{dim}M}$ in their irreducible fractions of integral polynomials, where $M$ is the corresponding preprojective module or preinjective module. If the quiver is of Dynkin type, we generalize the denominator theorem in [FZ2] to any seed, and also generalize the corresponding results in [CCS1] [CCS2] [CK1] to non-simply-laced case. Given a finite quiver (with trivial valuations) without oriented cycles, fixed a tilting seed $(V, B_V)$, it is proved that the existence and uniqueness of a bijection (abstractly, not in explicit form, compare [CK2]) from the set of exceptional indecomposable objects in the cluster categories to the set of cluster variables associated to $B_V$ which sends $V_i[1]$ to $u_i$ and sends cluster tilting objects to clusters.; Comment: second version

‣ Dual Lukacs regressions for non-commutative variables

Szpojankowski, Kamil; Wesolowski, Jacek
Dual Lukacs type characterizations of random variables in free probability are studied here. First, we develop a freeness property satisfied by Lukacs type transformations of free-Poisson and free-Binomial non-commutative variables which are free. Second, we give a characterization of non-commutative free-Poisson and free-Binomial variables by properties of first two conditional moments, which mimic Lukacs type assumptions known from classical probability. More precisely, our result is a non-commutative version of the following result known in classical probability: if $U$, $V$ are independent real random variables, such that $E(V(1-U)|UV)$ and $E(V^2(1-U)^2|UV)$ are non-random then $V$ has a gamma distribution and $U$ has a beta distribution.