Do High School Exit Exams Influence Educational Attainment or Labor Market Performance?

State requirements that high school graduates pass exit exams were the leading edge of the movement towards standards-based reform and continue to be adopted and refined by states today. In this study, we present new empirical evidence on how exit exams influenced educational attainment and labor market experiences using data from the 2000 Census and the National Center for Education Statistics' Common Core of Data (CCD). Our results suggest that the effects of these reforms have been heterogeneous. For example, our analysis of the Census data suggests that exit exams significantly reduced the probability of completing high school, particularly for black students. Similarly, our analysis of grade-level dropout data from the CCD indicates that Minnesota's recent exit exam increased the dropout rate in urban and high-poverty school districts as well as in those with a relatively large concentration of minority students. This increased risk of dropping out was concentrated among 12th grade students. However, we also found that Minnesota's exit exam lowered the dropout rate in low-poverty and suburban school districts, particularly among students in the 10th and 11th grades. These results suggest that exit exams have the capacity to improve student and school performance but also appear to have exacerbated the inequality in educational attainment.

Rational Ignorance in Education: A Field Experiment in Student Plagiarism

Despite the concern that student plagiarism has become increasingly common, there is relatively little objective data on the prevalence or determinants of this illicit behavior. This study presents the results of a natural field experiment designed to address these questions. Over 1,200 papers were collected from the students in undergraduate courses at a selective post-secondary institution. Students in half of the participating courses were randomly assigned to a requirement that they complete an anti-plagiarism tutorial before submitting their papers. We found that assignment to the treatment group substantially reduced the likelihood of plagiarism, particularly among student with lower SAT scores who had the highest rates of plagiarism. A follow-up survey of participating students suggests that the intervention reduced plagiarism by increasing student knowledge rather than by increasing the perceived probabilities of detection and punishment. These results are consistent with a model of student behavior in which the decision to plagiarize reflects both a poor understanding of academic integrity and the perception that the probabilities of detection and severe punishment are low.

Selection, Stability and Renormalization

We illustrate how to extend the concept of structural stability through applying it to the front propagation speed selection problem. This consideration leads us to a renormalization group study of the problem. The study illustrates two very general conclusions: (1) singular perturbations in applied mathematics are best understood as renormalized perturbation methods, and (2) amplitude equations are renormalization group equations.Comment: 38 pages, LaTeX, two PostScript figures available by anonymous ftp to gijoe.mrl.uiuc.edu (128.174.119.153) files /pub/front_kkfest_fig

Structural Stability and Renormalization Group for Propagating Fronts

A solution to a given equation is structurally stable if it suffers only an infinitesimal change when the equation (not the solution) is perturbed infinitesimally. We have found that structural stability can be used as a velocity selection principle for propagating fronts. We give examples, using numerical and renormalization group methods.Comment: 14 pages, uiucmac.tex, no figure

On the validity of the linear speed selection mechanism for fronts of the nonlinear diffusion equation

We consider the problem of the speed selection mechanism for the one dimensional nonlinear diffusion equation $u_t = u_{xx} + f(u)$. It has been rigorously shown by Aronson and Weinberger that for a wide class of functions $f$, sufficiently localized initial conditions evolve in time into a monotonic front which propagates with speed $c^*$ such that $2 \sqrt{f'(0)} \leq c^* < 2 \sqrt{\sup(f(u)/u)}$. The lower value $c_L = 2 \sqrt{f'(0)}$ is that predicted by the linear marginal stability speed selection mechanism. We derive a new lower bound on the the speed of the selected front, this bound depends on $f$ and thus enables us to assess the extent to which the linear marginal selection mechanism is valid.Comment: 9 pages, REVTE

Multiple Front Propagation Into Unstable States

The dynamics of transient patterns formed by front propagation in extended nonequilibrium systems is considered. Under certain circumstances, the state left behind a front propagating into an unstable homogeneous state can be an unstable periodic pattern. It is found by a numerical solution of a model of the Fr\'eedericksz transition in nematic liquid crystals that the mechanism of decay of such periodic unstable states is the propagation of a second front which replaces the unstable pattern by a another unstable periodic state with larger wavelength. The speed of this second front and the periodicity of the new state are analytically calculated with a generalization of the marginal stability formalism suited to the study of front propagation into periodic unstable states. PACS: 47.20.Ky, 03.40.Kf, 47.54.+rComment: 12 page

The Weakly Pushed Nature of "Pulled" Fronts with a Cutoff

The concept of pulled fronts with a cutoff $\epsilon$ has been introduced to model the effects of discrete nature of the constituent particles on the asymptotic front speed in models with continuum variables (Pulled fronts are the fronts which propagate into an unstable state, and have an asymptotic front speed equal to the linear spreading speed $v^*$ of small linear perturbations around the unstable state). In this paper, we demonstrate that the introduction of a cutoff actually makes such pulled fronts weakly pushed. For the nonlinear diffusion equation with a cutoff, we show that the longest relaxation times $\tau_m$ that govern the convergence to the asymptotic front speed and profile, are given by $\tau_m^{-1} \simeq [(m+1)^2-1] \pi^2 / \ln^2 \epsilon$, for $m=1,2,...$.Comment: 4 pages, 2 figures, submitted to Brief Reports, Phys. Rev.

Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts

Fronts that start from a local perturbation and propagate into a linearly unstable state come in two classes: pulled and pushed. ``Pulled'' fronts are ``pulled along'' by the spreading of linear perturbations about the unstable state, so their asymptotic speed $v^*$ equals the spreading speed of linear perturbations of the unstable state. The central result of this paper is that the velocity of pulled fronts converges universally for time $t\to\infty$ like $v(t)=v^*-3/(2\lambda^*t) + (3\sqrt{\pi}/2) D\lambda^*/(D{\lambda^*}^2t)^{3/2}+O(1/t^2)$. The parameters $v^*$, $\lambda^*$, and $D$ are determined through a saddle point analysis from the equation of motion linearized about the unstable invaded state. The interior of the front is essentially slaved to the leading edge, and we derive a simple, explicit and universal expression for its relaxation towards $\phi(x,t)=\Phi^*(x-v^*t)$. Our result, which can be viewed as a general center manifold result for pulled front propagation, is derived in detail for the well known nonlinear F-KPP diffusion equation, and extended to much more general (sets of) equations (p.d.e.'s, difference equations, integro-differential equations etc.). Our universal result for pulled fronts thus implies independence (i) of the level curve which is used to track the front position, (ii) of the precise nonlinearities, (iii) of the precise form of the linear operators, and (iv) of the precise initial conditions. Our simulations confirm all our analytical predictions in every detail. A consequence of the slow algebraic relaxation is the breakdown of various perturbative schemes due to the absence of adiabatic decoupling.Comment: 76 pages Latex, 15 figures, submitted to Physica D on March 31, 1999 -- revised version from February 25, 200

New exact fronts for the nonlinear diffusion equation with quintic nonlinearities

We consider travelling wave solutions of the reaction diffusion equation with quintic nonlinearities $u_t = u_{xx} + \mu u (1 -u ) ( 1 +\alpha u + \beta u^2 +\gamma u^3)$. If the parameters $\alpha , \beta$ and $\gamma$ obey a special relation, then the criterion for the existence of a strong heteroclinic connection can be expressed in terms of two of these parameters. If an additional restriction is imposed, explicit front solutions can be obtained. The approach used can be extended to polynomials whose highest degree is odd.Comment: Revtex, 5 page

Universal Algebraic Relaxation of Velocity and Phase in Pulled Fronts generating Periodic or Chaotic States

We investigate the asymptotic relaxation of so-called pulled fronts propagating into an unstable state. The ``leading edge representation'' of the equation of motion reveals the universal nature of their propagation mechanism and allows us to generalize the universal algebraic velocity relaxation of uniformly translating fronts to fronts, that generate periodic or even chaotic states. Such fronts in addition exhibit a universal algebraic phase relaxation. We numerically verify our analytical predictions for the Swift-Hohenberg and the Complex Ginzburg Landau equation.Comment: 4 pages Revtex, 2 figures, submitted to Phys. Rev. Let