Geometry of Policy Improvement

We investigate the geometry of optimal memoryless time independent decision making in relation to the amount of information that the acting agent has about the state of the system. We show that the expected long term reward, discounted or per time step, is maximized by policies that randomize among at most $k$ actions whenever at most $k$ world states are consistent with the agent's observation. Moreover, we show that the expected reward per time step can be studied in terms of the expected discounted reward. Our main tool is a geometric version of the policy improvement lemma, which identifies a polyhedral cone of policy changes in which the state value function increases for all states.Comment: 8 page

Stakes Increase for End of Course Exams in 2009-10

As of the 2009-10 academic year, high school students in Arkansas will be required to pass socalled “End of Course” (or “EOC”) examinations in Algebra I, Biology, Geometry, and English. Students who fail to meet the requisite passing standard will be required to retake the class or to pass “an appropriate alternative exit course in order to receive credit for the course on his or her transcript and in order to graduate.” In other words, these four EOC tests will become high school exit exams. Thus, as of 2009-10, Arkansas will join some 23 other states that have high school exit exams

Limits on the Capacity of In-Band Full Duplex Communication in Uplink Cellular Networks

Simultaneous co-channel transmission and reception, denoted as in-band full duplex (FD) communication, has been promoted as an attractive solution to improve the spectral efficiency of cellular networks. However, in addition to the self-interference problem, cross-mode interference (i.e., between uplink and downlink) imposes a major obstacle for the deployment of FD communication in cellular networks. More specifically, the downlink to uplink interference represents the performance bottleneck for FD operation due to the uplink limited transmission power and venerable operation when compared to the downlink counterpart. While the positive impact of FD communication to the downlink performance has been proved in the literature, its effect on the uplink transmission has been neglected. This paper focuses on the effect of downlink interference on the uplink transmission in FD cellular networks in order to see whether FD communication is beneficial for the uplink transmission or not, and if yes for which type of network. To quantify the expected performance gains, we derive a closed form expression of the maximum achievable uplink capacity in FD cellular networks. In contrast to the downlink capacity which always improves with FD communication, our results show that the uplink performance may improve or degrade depending on the associated network parameters. Particularly, we show that the intensity of base stations (BSs) has a more prominent effect on the uplink performance than their transmission power

What Do International Tests Really Show About U.S. Student Performance?

Evidence-based policy has been a goal of American education policymakers for at least two decades. School reformers seek data about student knowledge and skills, hoping to use this information to improve schools. One category of such evidence, international test results, has seemingly permitted comparisons of student performance in the United States with that in other countries. Such comparisons have frequently been interpreted to show that American students perform poorly when compared to students internationally. From this, reformers conclude that U.S. public education is failing and that its failure imperils America's ability to compete with other nations economically.This report, however, shows that such inferences are too glib. Comparative student performance on international tests should be interpreted with much greater care than policymakers typically give it

High School End-of-Course Exams Show Proficiency Gains for 2010

In July, the ADE released results for the 2009-10 end-ofcourse (EOC) exams given in Algebra I, Geometry, and Biology administered in April 2010. These results followed the Grade 11 Literacy results released in June. First, we present statewide 2010 results compared to last year. Second, test scores are examined across the state by districts\u27 region, poverty level, and size. Third, we consider the performance of Arkansas students on other assessments to see if these results are consistent with EOC results

Alternative High School Math Pathways in Massachusetts: Developing an On-Ramp to Minimize College Remediation in Mathematics

Of the Massachusetts graduates from the Class of 2005 who enrolled in public colleges, an appalling 29 percent enrolled in a developmental (remedial) math course during the fall semester. Nationally, 63 percent of college students who remediate in mathematics do not earn a 2- or 4-year degree. At a time when a college degree is one of the critical components of one's ability to afford a home and support a family, that such high rates of Massachusetts' high school graduates require remediation in math is cause for alarm - and action. The Rennie Center for Education Research and Policy has produced a policy brief that proposes a new pathway in high school mathematics aimed at eliminating the need for college remediation in math.The policy brief, entitled Alternative High School Math Pathways in Massachusetts: Developing an On-Ramp to Minimize College Remediation in Mathematics, proposes a plan designed to significantly reduce, and ultimately, eliminate the number of students who require college remediation in mathematics.Rather than the traditional progression of math courses (Algebra I, Geometry, Algebra II, Calculus), we propose three new math courses at the middle and high school levels - including a new fourth year math course titled: Topics in Applied Mathematics for College Preparation that would provide an alternative to Pre-calculus/Calculus for students pursuing non-math related majors. We recommend that Massachusetts policymakers and school and district leaders should take the following steps toward establishing to a well-aligned, effective system that ensures all students are ready for college-level mathematics:Ensure mastery of arithmetic by the end of seventh grade;Focus on mastery and application of algebraic concepts;Offer the ACCUPLACER(R) test to high school juniors;Provide guidance based on the Elementary Algebra ACCUPLACER(R) score; andEncourage all students to take mathematics during their first college semester