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

Fonte: FIU Digital Commons
Publicador: FIU Digital Commons

Tipo: Artigo de Revista Científica
Formato: application/pdf

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#math education#science education#recruitment#teacher pipeline#Curriculum and Instruction#Science and Mathematics Education

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...

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## ‣ 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

Fonte: Universidade de Múrcia
Publicador: Universidade de Múrcia

Tipo: Artigo de Revista Científica
Formato: application/pdf

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#Bilinguism#Mathematics achievement#Language knowledge#Social and educative#Bilingüismo#Rendimiento matemático#Conocimiento lingüístico#Contexto socio educativo#Autoconcepto#Cociente intelectual

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...

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

Fonte: Universidade de Múrcia
Publicador: Universidade de Múrcia

Tipo: Artigo de Revista Científica
Formato: application/pdf

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#Actitudes#Matemáticas#Variables#Rendimiento#Attitudes towards the mathematics#Evaluation#Reliability#Academic performance

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...

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

Fonte: FIU Digital Commons
Publicador: FIU Digital Commons

Tipo: Artigo de Revista Científica

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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...

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#Mathematics - Number Theory#Mathematics - Algebraic Geometry#Mathematics - Group Theory#Primary 11G18, 141130, 14H25, 14M41, 20B15, 20C15, 30F10, Secondary
11R58, 12D05, 12E30, 12F10, 20E22

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...

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## ‣ Surface Operators and Separation of Variables

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 24/06/2015
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#High Energy Physics - Theory#Mathematical Physics#Mathematics - Algebraic Geometry#Mathematics - Quantum Algebra#Mathematics - Representation Theory

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

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/04/1996
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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

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## ‣ Control Problem on Space of Random Variables and Master Equation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 04/08/2015
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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.

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## ‣ A change of variables theorem for the multidimensional Riemann integral

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 15/04/2008
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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

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#Mathematics - Algebraic Geometry#Mathematical Physics#Mathematics - Classical Analysis and ODEs#Mathematics - Dynamical Systems#34M55, 34M45, 58F05, 32S65

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

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#Mathematics - Operator Algebras#Mathematics - Functional Analysis#Mathematics - Probability#Primary: 46L54, Secondary: 44Axx

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

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

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

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 08/02/2013
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#Mathematics - Dynamical Systems#Mathematical Physics#Mathematics - Optimization and Control#Physics - Classical Physics#70H33, 70Q05, 93D99, 37J15

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.

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## ‣ Generic Variables in Acyclic Cluster Algebras

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 01/06/2010
Português

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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

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## ‣ Reducing the number of variables of a polynomial

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 26/07/2005
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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.

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## ‣ Concentration and Moment Inequalities for Polynomials of Independent Random Variables

Fonte: Universidade Cornell
Publicador: Universidade Cornell

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

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/10/2007
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#Mathematics - Quantum Algebra#High Energy Physics - Theory#Mathematical Physics#17B69#17B81#81R10#81T40

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...

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 02/10/1999
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#Mathematics - Quantum Algebra#High Energy Physics - Theory#Mathematics - Representation Theory#17B69

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

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## ‣ Preprojective cluster variables of acyclic cluster algebras

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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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

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## ‣ Dual Lukacs regressions for non-commutative variables

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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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.

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