Reinventing learning: a design-research odyssey

Design research is a broad, practice-based approach to investigating problems of education. This approach can catalyze the development of learning theory by fostering opportunities for transformational change in scholars’ interpretation of instructional interactions. Surveying a succession of design-research projects, I explain how challenges in understanding students’ behaviors promoted my own recapitulation of a historical evolution in educators’ conceptualizations of learning—Romantic, Progressivist, and Synthetic (Schön, Intuitive thinking? A metaphor underlying some ideas of educational reform (working paper 8). Division for Study and Research in Education, MIT, Cambridge, 1981)—and beyond to a proposed Systemic view. In reflection, I consider methodological adaptations to design-research practice that may enhance its contributions in accord with its objectives

Guilt By Genetic Association: The Fourth Amendment and the Search of Private Genetic Databases by Law Enforcement

Over the course of 2018, a number of suspects in unsolved crimes have been identified through the use of GEDMatch, a public online genetic database. Law enforcement’s use of GEDMatch to identify suspects in cold cases likely does not constitute a search under the Fourth Amendment because the genetic information hosted on the website is publicly available. Transparency reports from direct-to-consumer (DTC) genetic testing providers like 23andMe and Ancestry suggest that federal and state officials may now be requesting access to private genetic databases as well. Whether law enforcement’s use of private DTC genetic databases to search for familial relatives of a suspect’s genetic profile constitutes a search within the meaning of the Fourth Amendment is far less clear. A strict application of the third-party doctrine suggests that individuals have no expectation of privacy in genetic information that they voluntarily disclose to third parties, including DTC providers. This Note, however, contends that the U.S. Supreme Court’s recent decision in Carpenter v. United States overwhelmingly supports the proposition that genetic information disclosed to third-party DTC providers is subject to Fourth Amendment protection. Approximately fifteen million individuals in the United States have already submitted their genetic information to DTC providers. The genetic information held by these providers can reveal a host of highly intimate details about consumers’ medical conditions, behavioral traits, genetic health risks, ethnic background, and familial relationships. Allowing law enforcement warrantless access to investigate third-party DTC genetic databases circumvents their consumers’ reasonable expectations of privacy by exposing this sensitive genetic information to law enforcement without any meaningful oversight. Furthermore, individuals likely reasonably expect that they retain ownership over their uniquely personal genetic information despite their disclosure of that information to a thirdparty provider. This Note therefore asserts that the third-party doctrine does not permit law enforcement to conduct warrantless searches for suspects on private DTC genetics databases under the Fourth Amendment

A Note on Constructing 50-50 Step Probability Binomial Lattices to Replicate Wiener Diffusion

Binomial lattices are sequences of discrete distributions commonly used to approximate the future value states of a financial claim, such as a stock price, when the instantaneous rate of return is assumed to be governed by a Wiener diffusion process. In that case, both pedagogical and professional conventions generally follow the lattice construction methodology used by Cox, Ross, and Rubinstein ("CRR") in their classical article. In some applications, it is more convenient to replace the "implied" branching probabilities of that construction with a more natural and tractable alternative: that is, with the probability of "up" and "down" branching being exactly one-half, or, vernacularly, with a "50-50 step" probability. This elementary note reviews such an alternative formulation for constructing a binomial lattice, which can be viewed as simply entailing multiplicative shifts of every state value on a CRR-constructed binomial lattice. This transformation maintains (in fact, improves) the equivalence of the lattice values' moments to those arising from the replicated diffusion. The expression of that transform is derived, and the effect on the lattice values' moments and orders of convergence to the limit imposed by the continuous process are given. To show the absence of numerical effect, the values of some simple European options obtained from the two alternative binomial lattice constructions are compared against the limiting Black Scholes values.Binomial Lattices, Wiener Processes, Option Valuation Methods

A "One-line" Simulator for Maxima or Minima on Drifting Brownian Paths

A simple transform of a standard uniform variate is given for simulation of the maximum attained by a Wiener process with drift, conditioned upon the level attained by the process over an arbitrary time interval. The transform arises directly from inversion of the joint distribution function of the maximum and the final Wiener process level.Brownian Motion, Extreme Values, Simulation, Monte Carlo Methods, Algorithms and Computer Methods

All Moments of Discrete and Continuous Arithmetic Averages on Brownian Paths: A Closed Form

This note derives new expressions for the moments of the average of values taken by Wiener paths at an arbitrary number, N, of discrete times. The expressions are closed summations, which entail only the N-th powers of, and the successive differences between, the moments of the lognormal finite dimensional distribution of the process' values at the time of the first averaging. By passing to the limit of the average when the averaging frequency becomes continuous, known forms for the continuous average are generalized by a single expression.Brownian Motion, Wiener Processes, Moments, Asian Options, Sample Path Properties, Computation