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It is well known that there is an integral theorem for quaternion-valued functions analogous to Cauchys Theorem for complex-valued functions, namely Fueters Theorem. The class of quaternionic functions for which this applies are generally referred to as regular functions, and these provide the most productive means of generalising the class of holomorphic complex functions. This paper derives a second integral theorem, also analogous to Cauchys Theorem, and which is believed to be quite distinct from that of Fueter, despite appearances. The paper takes the opportunity to present the basis of the derivation of both theorems, and also their extension to the associated classes of right-regular and conjugate regular functions. Both theorems can also be extended into the biquaternionic domain in which the four quaternion coordinates may be complex valued. This is of interest in physics as the Hermitian biquaternions have a natural norm which is Minkowskian and provide an elegant formalism for Lorentz transformations., Comment: 20 pages, 1 Figure

This abstract seeks to introduce the ISSAC community to the DEWCAD project, which is based at Coventry University and the University of Bath, in the United Kingdom. The project seeks to push back the Doubly Exponential Wall of Cylindrical Algebraic Decomposition, through the integration of SAT/SMT technology, the extension of Lazard projection theory, and the development of new algorithms based on CAD technology but without producing CADs themselves. The project also seeks to develop applications of CAD and will focus on applications in the domains of economics and bio-network analysis., Comment: 5 pages. Accepted as short communication at ISSAC 2021

Sensors fabricated from high resistivity, float zone, silicon material have been the basis of vertex detectors and trackers for the last 30 years. The areas of these devices have increased from a few square cm to $\> 200\ m^2$ for the existing CMS tracker. High Luminosity Large Hadron Collider (HL-LHC), CMS and ATLAS tracker upgrades will each require more than $200\ m^2$ of silicon and the CMS High Granularity Calorimeter (HGCAL) will require more than $600\ m^2$. The cost and complexity of assembly of these devices is related to the area of each module, which in turn is set by the size of the silicon sensors. In addition to large area, the devices must be radiation hard, which requires the use of sensors thinned to 200 microns or less. The combination of wafer thinning and large wafer diameter is a significant technical challenge, and is the subject of this work. We describe work on development of thin sensors on $200 mm$ wafers using wafer bonding technology. Results of development runs with float zone, Silicon-on-Insulator and Silicon-Silicon bonded wafer technologies are reported., Comment: 11 pages

We consider a problem from biological network analysis of determining regions in a parameter space over which there are multiple steady states for positive real values of variables and parameters. We describe multiple approaches to address the problem using tools from Symbolic Computation. We describe how progress was made to achieve semi-algebraic descriptions of the multistationarity regions of parameter space, and compare symbolic results to numerical methods. The biological networks studied are models of the mitogen-activated protein kinases (MAPK) network which has already consumed considerable effort using special insights into its structure of corresponding models. Our main example is a model with 11 equations in 11 variables and 19 parameters, 3 of which are of interest for symbolic treatment. The model also imposes positivity conditions on all variables and parameters. We apply combinations of symbolic computation methods designed for mixed equality/inequality systems, specifically virtual substitution, lazy real triangularization and cylindrical algebraic decomposition, as well as a simplification technique adapted from Gaussian elimination and graph theory. We are able to determine multistationarity of our main example over a 2-dimensional parameter space. We also study a second MAPK model and a symbolic grid sampling technique which can locate such regions in 3-dimensional parameter space., Comment: 60 pages - author preprint. Accepted in the Journal of Symbolic Computation

In 2016, a higher education task force of St. Louis Graduates (STLG), a collaborative network whose mission is to increase degree completion for low income students, first-generation students, and students of color from St. Louis, commissioned this study from the Illinois Education Research Council (IERC). Through discussion, the following goals were established for this project: (1) identify those higher education institutions that are more successful in supporting and graduating underrepresented students from the St. Louis region: and (2) determine the strategies that institutions are using to graduate underrepresented students with less debt. This study was undertaken to determine successful college completion strategies for low-income students, first-generation students, and students of color. The ultimate goal is to identify promising practices for graduating underrepresented students with less debt and to share those strategies and practices with other institutions so they can be adopted and adapted. This would ultimately create a broad network of colleges and universities that are using evidence based strategies for affordable college completion for underrepresented students. Starting with a list of 20 four-year institutions in Missouri and Illinois where St. Louis students most often attend college, a Success metric was developed to determine which institutions were best supporting underrepresented students. From this study, a group of five institutions rose to the top. In the second phase of this project, administrators in the areas of academic and student affairs, enrollment management, and financial aid as well as a group of students, from each of these five institutions were interviewed to find the key ingredients of their "secret sauce" in supporting underrepresented students to graduation with less debt. [This study was funded from a grant from St. Louis Graduates through support from the Missouri Higher Education Loan Authority, MOHELA. For the executive summary, "Degrees with Less Debt: Effective Higher Education Strategies for Underrepresented Student Populations. Executive Summary. IERC 2017-2," see ED574361. For the research highlights, "Degrees with Less Debt: Effective Higher Education Strategies for Underrepresented Student Populations. Research Highlights. IERC 2017-2," see ED574360.]

In 2016, a higher education task force of St. Louis Graduates (STLG), a collaborative network whose mission is to increase degree completion for low income students, first-generation students, and students of color from St. Louis, commissioned this study from the Illinois Education Research Council (IERC). Through discussion, the following goals were established for this project: (1) identify those higher education institutions that are more successful in supporting and graduating underrepresented students from the St. Louis region; and (2) determine the strategies that institutions are using to graduate underrepresented students with less debt. The higher education landscape is becoming increasingly more adverse for students of color, first-generation students, and low-income students. College affordability, or lack thereof, is cited as the primary reason students are not able to complete their degrees. Given this context this study was undertaken to determine successful college completion strategies for low-income students, first-generation students, and students of color. The ultimate goal was to identify practices for graduating underrepresented students with less debt and to share those strategies and practices with other institutions. This could ultimately create a network of colleges and universities using evidence-based strategies for affordable college completion for underrepresented students. With feedback from the STLG Task Force, a success metric based on the median student debt at graduation and 6-year actual versus predicted graduation rates for institutions with similar contexts was developed. The five highest ranking institutions based on the Success Formula (see Appendix in full report) identified as graduating underrepresented students with less debt in alphabetical order were: Maryville University, Missouri State University--Springfield (MSU), Southeast Missouri State University (SEMO), University of Central Missouri (UCM), and Webster University. Five themes emerged from the qualitative interview data that describe the practices or strategies that supported underrepresented minority students to graduation with less debt. Two of the five themes reflected the overall organizational culture of the university. One of these themes was University Leadership. Two of the five themes reflected the overall organizational culture of the university. One of these themes was University Leadership. The other three themes that emerged from the data were Early College Experiences, Flexible and Sufficient Financial Aid, and Just-in-Time Academic Supports. Implications are highlighted that the researchers believe are applicable in a broad array of institutional settings and if adopted, would further the persistence and completion of underrepresented students. [This study was funded from a grant from St. Louis Graduates through support from the Missouri Higher Education Loan Authority, MOHELA. For the full report, "Degrees with Less Debt: Effective Higher Education Strategies for Underrepresented Student Populations. Policy Research. IERC 2017-2," see ED574359. For the research highlights, "Degrees with Less Debt: Effective Higher Education Strategies for Underrepresented Student Populations. Research Highlights. IERC 2017-2," see ED574360.]

This report is an evaluation of efforts made by Illinois Action for Children (IAFC), with oversight from the Illinois Governor's Office for Early Childhood Development (OECD), to test, support, and facilitate innovations in the early childhood system in 11 communities across the state. The Early Childhood Innovation Zones (IZ) initiative, funded by Illinois' Race to the Top--Early Learning Challenge (RttT-ELC) grant, was designed to spur experimentation with new systemic strategies for increasing the number of children from priority populations enrolled in high quality early learning programs. This mixed methods study is designed to help further the state's understanding of the functioning of the project's logic model and describe the relationships between stages in the theory of action. The analyses focus on identifying and describing the supports, capacities, strategies, and outcomes observed within each collaborative, as well as across collaboratives. The analyses utilized the following: (1) qualitative data, including interviews with zone partners and state level program staff; (2) project documentation, along with quantitative data on enrollment and quality collected by each zone; and (3) surveys distributed to all program participants. The first section addresses innovations in capacity-building, technical assistance and other supports facilitated by IAFC, and describes the problem-solving and decision-making strategies introduced to the zones, as well as the obstacles to implementing the project framework. The second section provides information about barriers to enrollment in early learning programs, and an in-depth exploration of the strategies zones used to overcome these barriers and increase enrollment of priority populations. The third section of this report describes innovations for improving quality implemented by the four zones that chose this path. The report concludes with a discussion of key lessons learned and questions arising from this study, along with implications for future policymaking efforts. The following are appended: (1) Innovation Zone Interview Protocol; (2) IAFC Interview Protocol; (3) Innovation Zones Interview Coding Schema; (4) Innovation Zones End-of-Grant Survey; and (5) Appendix Tables 1 and 2. [For the executive summary, "Illinois' Early Childhood Innovation Zones: A New Model for State Policy? IERC 2017-1. Executive Summary," see ED574336. For the research highlights, "Illinois' Early Childhood Innovation Zones: A New Model for State Policy? IERC 2017-1. Research Highlights," see ED574339.]

We present extractions of the nucleon non-singlet moments utilizing new precision data on the deuteron $F_2$ structure function at large Bjorken-$x$ determined via the Rosenbluth separation technique at Jefferson Lab Experimental Hall C. These new data are combined with a complementary set of data on the proton previously measured in Hall C at similar kinematics and world data sets on the proton and deuteron at lower $x$ measured at SLAC and CERN. The new Jefferson Lab data provide coverage of the upper third of the $x$ range, crucial for precision determination of the higher moments. In contrast to previous extractions, these moments have been corrected for nuclear effects in the deuteron using a new global fit to the deuteron and proton data. The obtained experimental moments represent an order of magnitude improvement in precision over previous extractions using high $x$ data. Moreover, recent exciting developments in Lattice QCD calculations provide a first ever comparison of these new experimental results with calculations of moments carried out at the physical pion mass, as well as a new approach which first calculates the quark distributions directly before determining moments.

We consider problems originating in economics that may be solved automatically using mathematical software. We present and make freely available a new benchmark set of such problems. The problems have been shown to fall within the framework of non-linear real arithmetic, and so are in theory soluble via Quantifier Elimination (QE) technology as usually implemented in computer algebra systems. Further, they all can be phrased in prenex normal form with only existential quantifiers and so are also admissible to those Satisfiability Module Theory (SMT) solvers that support the QF_NRA. There is a great body of work considering QE and SMT application in science and engineering, but we demonstrate here that there is potential for this technology also in the social sciences., Comment: To appear in Proc. SC-Square 2018. Dataset described is hosted by Zenodo at: https://doi.org/10.5281/zenodo.1226892 . arXiv admin note: substantial text overlap with arXiv:1804.10037

In 2010, Illinois became one of the first states to legislatively require a complete redesign of all its principal preparation programs, with the goal of advancing statewide school improvement through strengthening school leadership. This effort was ambitious and sweeping, calling for radical shifts in previous practice, including: (1) A targeted principal endorsement, instead of a general administrative certificate; (2) Formal partnerships with school districts in preparation program design and delivery; (3) More selective admissions criteria and processes; (4) Focus on leading all students, including students with disabilities, English Language Learners, and early childhood education; (5) Collaborative support for candidates from highly qualified faculty supervisors and mentor principals; and (6) A competency-based internship, with an emphasis on demonstrated leadership skills. For many decades prior to the redesign, principal preparation had typically consisted of administrative courses such as school law, finance, and educational theory, followed by an internship consisting of a set number of hours that were mainly spent shadowing a principal. Programs varied greatly in the quality of both course content and mentoring and generally had few, if any, selection criteria beyond what was required by the college or university. Meanwhile, a growing body of research evidence indicated that principals play a critical role in improving student performance and leading effective schools. This research identified the importance of principals as effective instructional leaders rather than simply efficient building managers, and identified key components of effective principal preparation programs, including: targeted recruitment and selection, a rigorous curriculum focused on instruction and school improvement; integration of coursework and fieldwork; and robust, sustained internships that allow candidates to gain leadership experience working with an expert mentor. As a result, traditional principal preparation began to be perceived as providing inadequate training, and principal preparation programs became the target of intense scrutiny. For the past two years, the authors have studied the implementation of Illinois' new principal preparation programs and the changes that have occurred as a result of the new policy. In this policy brief, they highlight key findings and implications from the second phase of the study. The full findings and analysis are presented in the final report. [For the final report, "Navigating the Shift to Intensive Principal Preparation in Illinois: An In-Depth Look at Stakeholder Perspectives. Policy Research: IERC 2016-2," see ED567016.]

In 2010, Illinois policymakers sought to advance statewide school improvement by strengthening school leadership. Illinois became one of the first states to legislatively require a complete redesign of all its principal preparation programs with the goal of ensuring future principals would be "highly effective in leadership roles" and prepared "to improve teaching and learning and increase academic achievement and the development of all students" (Programs for the Preparation of Principals in Illinois, 2016). The new requirements, which went into effect in 2014, called for the reauthorization of all programs and several radical shifts from the status quo. First, all programs had to establish formal partnerships with school districts so that they would be more aware of and responsive to district needs. Second, principal internships required candidates to illustrate the mastery of critical competencies rather than complete observations and log hours. Third, principal training was required to emphasize creating instructional leaders able to catalyze school change rather than developing managers. Fourth, programs also needed to prepare all principals to work with all students from pre-K to twelfth grade, including students with disabilities and English language learners (ELLs). Finally, programs were expected to collect and utilize data for continuous improvement. The current study provides the first statewide, in-depth examination of how Illinois programs and their district partners have interpreted this policy and redesigned their training. Overall, the authors find that Illinois' principal preparation has undergone extensive change. While programs vary, many have made significant alterations to courses, staffing, and district partnerships, and the internship experience has undergone a fundamental change. In this report, the authors will describe these shifts and provide stakeholders' perspectives on their successes and the challenges. The following are appended: (1) Project Advisory Board; (2) Methodology; and (3) Supplementary Data Tables.

The Illinois Board of Higher Education (IBHE) provided Early Childhood Educator Preparation Program Innovation (EPPI) grants to 20 partnerships comprised of two- and four-year institutions to further develop models for early childhood educator preparation and build capacity in key areas of need. Recipients used grant funds to design and implement a wide range of seamless pathways for degree and credential attainment through innovative articulation initiatives, systems for aligning assessments to demonstrate candidate attainment of key competencies, and strategies for advising and supporting transfer students. Promising practices to improve early math learning, bilingual/English language learning, infant/toddler development, and quality field experience placements were also developed. This qualitative implementation study provides a systematic review of the innovations and strategies EPPI grant recipients utilized in addressing common barriers and practice-oriented issues experienced in early childhood educator preparation. The study is summarized in this report. [For the full report, "Innovations for High Quality, Aligned Early Childhood Educator Preparation. IERC 2016-3," see ED574328. For the research highlights, "Innovations for High Quality, Aligned Early Childhood Educator Preparation. IERC 2016-3. Research Highlights," see ED574330.]

Charter schools are publicly-funded educational entities that operate independently from local school districts and are exempt from certain state and local requirements, particularly with regard to teacher personnel policy. In exchange for this flexibility, charter schools are held more accountable for results and may be shut down if they fail to meet the expectations described in their performance contract (or charter). The degree to which charter schools have leveraged both flexibility and competition for successful innovation has been the subject of much debate. The aim of this study is to investigate the human resource (HR) management policies and practices in Illinois charter schools. Many recent education policy initiatives at the federal-, state-, district-, and school-levels have zeroed in on human resource management reforms as a route to strengthen the learning climate by bolstering teacher effectiveness, and, in turn, improve student achievement. The theory of action undergirding these reforms is that by implementing more research-based, efficient, and strategic HR policies, schools will be able to recruit more talented teachers, support and improve the performance of the teachers in their buildings, and retain and reward their most effective educators. Because charter schools are granted additional flexibility in many areas of HR management, and because evidence suggests that many charter schools are exercising this flexibility, the charter school sector presents a promising venue to test this theory of action. To do this, the author begins by reviewing existing research on charter school teachers and human resource management in education. Next, he conducted surveys and interviews with Illinois charter school leaders to document the strategies they use to attract, develop, and retain high quality teachers, and use descriptive statistics and examples from practice to present these findings and highlight trends across differently-situated charter schools. He then analyzed these responses to discern overarching themes in these practices across schools and HR functions. Finally, the author examines the relationships between distinct sets of HR management practices and school outcomes which the theory suggests ought to be affected--teacher retention, school climate, and student achievement. It is the hope that these analyses will demonstrate the degree to which Illinois charter schools are leveraging the flexibility allowed by the state's charter law to drive more strategic management of their human resources and yield findings about the effects of HR practices that can help guide personnel policies in both the charter and non-charter school sectors, where appropriate. The following are appended: (1) Phone Interview Protocols; (2) Online Survey; and (3) HR Practices by School Characteristics.

In June 2010, the Illinois General Assembly passed Public Act 96-0903, a sweeping restructuring of the preparation of school principals and assistant principals that represented 10 years of effort from a broad coalition of stakeholders. The restructuring in Illinois was part of a movement nationwide to provide stronger training for principals in order to better equip them to direct instructional change and lead schools that produce high levels of student achievement. This study, examining the initial implementation of the new policy lays the groundwork for the subsequent evaluation studies which will examine the impact of the new policy. Results of phase one of a implementation review study of Illinois' new policy for principal preparation indicate that a majority of those interviewed support the policy goals and have a positive outlook on its future impact. Concerns about a constricted pipeline and strained resources were also expressed. Future policy implications are suggested. Appended are: (1) I-PREP Advisory Board; (2) Study Methodology; and (3) Statewide Scan Interview Protocol.

The goals of the current mixed methods study--the Illinois Principal Preparation Implementation Review Project (I-PREP)--are to describe how the new policy is being implemented, learning which aspects of the implementation have been challenging and why they present challenges, and how programs are addressing challenges and realizing improvements in the preparation of their candidates. This report presents findings from the first phase of the study. Results of interviews with program representatives and key Illinois education stakeholders showed the majority of those interviewed support the goals of the new policy and have a positive outlook on its future impact of principal preparation in Illinois. Although some concerns about the implementation were expressed, most believe the redesigned principal preparation programs will ultimately create better prepared school administrators, improved student achievement, and more successful schools. The final report, due in summer 2016, will integrate the findings from this interim report, site visits with selected programs, and a survey with all programs to provide research-based insights in how to improve the policy and its implementation. The following are appended: (1) I-PREP Advisory Board; (2) Study Methodology; and (3) Statewide Scan Interview Protocol. [For the executive summary, see ED560523.]

The goals of the current mixed methods study--the Illinois Principal Preparation Implementation Review Project (I-PREP)--are to describe how the new policy is being implemented, learning which aspects of the implementation have been challenging and why they present challenges, and how programs are addressing challenges and realizing improvements in the preparation of their candidates. This report presents findings from the first phase of the study. Results of interviews with program representatives and key Illinois education stakeholders showed the majority of those interviewed support the goals of the new policy and have a positive outlook on its future impact of principal preparation in Illinois. Although some concerns about the implementation were expressed, most believe the redesigned principal preparation programs will ultimately create better prepared school administrators, improved student achievement, and more successful schools. The final report, due in summer 2016, will integrate the findings from this interim report, site visits with selected programs, and a survey with all programs to provide research-based insights in how to improve the policy and its implementation. The following are appended: (1) I-PREP Advisory Board; (2) Study Methodology; and (3) Statewide Scan Interview Protocol. [For the full report, see ED560522.]

The purpose of this study was to demonstrate how data on the geography of Illinois' new teacher pipeline can be used to inform the design of policies and practices to improve the supply of academically skilled, diverse individuals into teaching in the state's public schools. This study builds on a prior IERC study which connects data for two cohorts of Illinois students, the public high school classes of 2002 and 2003. To address the research questions regarding the role that geography plays in where new teachers obtain their first teaching employment, we focus our analyses on the 7,209 new teachers who emerged from these two Illinois high school cohorts. The study establishes that labor markets for new teachers overall tend to be quite small geographically and that the geographic size of new teacher labor markets was more closely linked to characteristics of a teacher's high school than to his or her academic qualifications. Other findings suggests that all new teachers, not just those in urban environments, will need to be prepared for the possibility of working in substantially different educational settings from what they experienced as students. Contains supplemental materials and tables. The following are appended: (1) Average Differences in Characteristics of Students in their Former High School; and (2) Average Differences in Characteristics of Students in their First School of Employment. [For the previous study referenced in this report, "A Longitudinal Study of the Illinois High School Class of 2002: A Six-Year Analysis of Postsecondary Enrollment and Completion. Policy Research: IERC 2010-3," see ED511808.]

The purpose of this study is to examine how Illinois school districts are utilizing the Illinois 5Essentials Survey results, particularly for school improvement, to determine challenges to successful implementation, and to make recommendations for improvements to the 5E Survey and implementation process for statewide use. We also summarize district/school stakeholders' familiarity with the 5E Survey, perceived value of the survey, preferences for training, levels of supports, and reasons for not using the 5E Survey data. Examples of district's promising practices for utilizing the 5E data are also highlighted. Three appendices are included: (1) Interview Protocol; (2) Additional Suggestions Improving the 5Essentials Survey; and (3) Survey Tables for ISBE Implementation Feedback Survey.

The MINERvA collaboration operated a scaled-down replica of the solid scintillator tracking and sampling calorimeter regions of the MINERvA detector in a hadron test beam at the Fermilab Test Beam Facility. This article reports measurements with samples of protons, pions, and electrons from 0.35 to 2.0 GeV/c momentum. The calorimetric response to protons, pions, and electrons are obtained from these data. A measurement of the parameter in Birks' law and an estimate of the tracking efficiency are extracted from the proton sample. Overall the data are well described by a Geant4-based Monte Carlo simulation of the detector and particle interactions with agreements better than 4%, though some features of the data are not precisely modeled. These measurements are used to tune the MINERvA detector simulation and evaluate systematic uncertainties in support of the MINERvA neutrino cross section measurement program., Comment: as accepted by NIM A

A new algorithm to compute cylindrical algebraic decompositions (CADs) is presented, building on two recent advances. Firstly, the output is truth table invariant (a TTICAD) meaning given formulae have constant truth value on each cell of the decomposition. Secondly, the computation uses regular chains theory to first build a cylindrical decomposition of complex space (CCD) incrementally by polynomial. Significant modification of the regular chains technology was used to achieve the more sophisticated invariance criteria. Experimental results on an implementation in the RegularChains Library for Maple verify that combining these advances gives an algorithm superior to its individual components and competitive with the state of the art.

Cylindrical algebraic decompositions (CADs) are a key tool in real algebraic geometry, used primarily for eliminating quantifiers over the reals and studying semi-algebraic sets. In this paper we introduce cylindrical algebraic sub-decompositions (sub-CADs), which are subsets of CADs containing all the information needed to specify a solution for a given problem. We define two new types of sub-CAD: variety sub-CADs which are those cells in a CAD lying on a designated variety; and layered sub-CADs which have only those cells of dimension higher than a specified value. We present algorithms to produce these and describe how the two approaches may be combined with each other and the recent theory of truth-table invariant CAD. We give a complexity analysis showing that these techniques can offer substantial theoretical savings, which is supported by experimentation using an implementation in Maple., Comment: 26 pages

This study uses a unique, longitudinal statewide database to track students through the new teacher supply pipeline from high school through college and initial teacher certification. The report examines how each stage influences the characteristics of those who enter the teaching profession, with particular attention to academic skills and racial/ethnic diversity, characteristics that are of national and local concern because of their impact on teacher effectiveness.

In a very short period during the spring and summer of 2012, researchers at the University of Chicago Consortium on Chicago School Research (CCSR) and the Illinois Education Research Council (IERC) collected data from respondents in five districts across Illinois to examine how school districts in the state approach designing and implementing new teacher evaluation systems. Drawing on research in these districts, which are located in north, central, and southern Illinois, this report describes the challenges experienced across the districts. In addition, the authors present strategies the districts used to address these challenges as they occurred and their reflections on lessons learned: (1) Cultivating Buy-In and Understanding; (2) Using Evaluations for Instructional Improvement; (3) Reducing the Burden on Principals; and (4) Incorporating Student Growth into Teacher Evaluation Systems. For all that has been accomplished by these case study districts, teacher evaluation, in all cases, remains a work in progress. Many in their interview sample described ongoing issues and some complicated problems. The report synthesizes these issues and raises some key questions for districts to consider around three common themes: teacher and principal support, communication, and buy-in; ensuring that ratings are accurate and consistent; and developing high-quality student assessments. Appended are: (1) Matrix of Teacher Evaluation Program Characteristics; and (2) Methodological Notes and Protocols. (Contains 2 tables and 3 endnotes.) [Funding for this paper was provided by the Grand Victoria Foundation.]

This report, the fourth in an IERC series on public school principals in Illinois, summarizes recent research on the characteristics associated with principal effectiveness and examines Illinois data on the relationship between principal characteristics, student proficiency, and teacher qualifications. In order to investigate the relationships between principal characteristics, teacher qualifications, and student achievements using Illinois data, we use two-level hierarchical linear growth models to measure the impact of principal characteristics on growth in student proficiency and teacher qualifications over time. In these models, the first level measures within school change over time and the second level measures differences between schools in initial school achievement or teacher qualifications status. Appended are: (1) Statistical Models; (2) Descriptive Statistics for Variables Included in Statistical Models; (3) Results from Model of Student Proficiency; and (4) Results from Model of Teacher Academic Qualifications. (Contains 3 tables and 3 footnotes.)

Although principals play a vital role as school leaders, exactly how principal leadership affects student learning is only beginning to be understood. In fact, only a few states have analyzed basic profile data on their principals--their demographics, education, and prior experience before leading a school. Most states also have yet to examine how principals change jobs over time or why they leave the profession. The research presented here marks the most comprehensive profile undertaken to date of Illinois principals. With support from The Joyce Foundation, the Illinois Education Research Council (IERC) at Southern Illinois University Edwardsville integrated its research on principal demographics and turnover with research on principal effectiveness and a survey of current Illinois principals' job-related beliefs and practices. The IERC analyzed demographic and employment trends among over 7100 individuals serving as Illinois public school principals between 2001 and 2008, statistically modeled principal impact on student achievement and teacher qualifications in over 3500 Illinois public schools, and surveyed more than one in five active public school principals in the 2010-2011 school year. Only charter schools were excluded from the analyses because their personnel are not consistently included in state records of educator employment. This report highlights emerging trends among Illinois principals, synthesizes key findings from the research, and offers recommendations for policy, practice, and preparation to enhance principals' ability to increase student achievement. (Contains 10 figures, 1 table and 6 footnotes.)

This report is the second in an Illinois Education Research Council series on public school principals in Illinois. This study focuses on principals' movements during the 2001 to 2008 time period, thereby providing recent information on principal retention and turnover during a time marked by increasing school accountability and public scrutiny of principal effectiveness. For our analyses, we focus on principal- and school-level data from state administrative records and other state and national sources for the eight years from 2001 to 2008. By piecing together annual data files across those years, we are able to track each Illinois principal from one year to the next throughout the period. We use descriptive, inferential, and multivariate analyses to determine the extent of principals' movements, as well as the personal and school-based factors that are associated with those movements. (Contains 6 tables, 6 figures and 9 footnotes.)

Accurate and comprehensible knowledge about the position of branch cuts is essential for correctly working with multi-valued functions, such as the square root and logarithm. We discuss the new tools in Maple 17 for calculating and visualising the branch cuts of such functions, and others built up from them. The cuts are described in an intuitive and accurate form, offering substantial improvement on the descriptions previously available.