NAEP STATE ANALYSIS PROJECT



-915447-924449Florida Value-Added ModelTechnical ReportWorking draft for review and comment. Please do not cite or distribute.American Institutes for ResearchTable of Contents TOC \o "3-3" \h \z \t "Heading 1,1,Heading 2,2,UH2,3,UH1,2,TTl,1" Florida Value-added Model PAGEREF _Toc299718724 \h 1Introduction PAGEREF _Toc299718725 \h 1Value-Added Modeling PAGEREF _Toc299718726 \h 2Two Common Value-Added Designs PAGEREF _Toc299718727 \h 2The Florida Value-Added Model PAGEREF _Toc299718728 \h 3Attribution of School Component to Teacher Effect PAGEREF _Toc299718729 \h 4Methods PAGEREF _Toc299718730 \h 6Covariate Adjustment Model PAGEREF _Toc299718731 \h 6Defining Teacher and School Effects in the Covariate Adjustment Model PAGEREF _Toc299718732 \h 6Accounting for Measurement Error in the Predictor Variables PAGEREF _Toc299718733 \h 9Replacing U'Ω-1U with Its Expectations PAGEREF _Toc299718734 \h 10Empirical Bayes versus Fixed Effects PAGEREF _Toc299718735 \h 11Standard Errors of Fixed and Random Effects PAGEREF _Toc299718736 \h 12Computing the Value-Added Model PAGEREF _Toc299718737 \h 14Final Estimates of the Teacher Effect PAGEREF _Toc299718738 \h 14Classification Probabilities PAGEREF _Toc299718739 \h 15Simulations PAGEREF _Toc299718740 \h 16Configurations PAGEREF _Toc299718741 \h 17Quality of model parameters PAGEREF _Toc299718742 \h 17Quality of unit (teacher or school) effects PAGEREF _Toc299718743 \h 18Results PAGEREF _Toc299718744 \h 19Teacher and School Variance Components PAGEREF _Toc299718745 \h 19Teacher and School Standard Errors PAGEREF _Toc299718746 \h 21Impact of VAM on Different Student Groups PAGEREF _Toc299718747 \h 22Differences in Student Growth Expectations by Gifted Status PAGEREF _Toc299718748 \h 22Differences in Conditional Student Growth Expectations by ELL Status PAGEREF _Toc299718749 \h 24Effects of Teacher Characteristics on Teacher Value-Added Estimates PAGEREF _Toc299718750 \h 25Conclusion PAGEREF _Toc299718751 \h 29References PAGEREF _Toc299718752 \h 31Appendix A. Student growth implementation committee (SGIC) Member RosterAppendix B. florida course codes USed in the value-added modelAppendix C. Fixed Effect EstimatesAppendix D. Teacher Value-added scores by DistrictAppendix E. School component by DistrictAppendix F. Expected Student Growth by Student Characteristics APPENDIX G. TEACHER VALUE-ADDED ESTIMATES BY TEACHER AND CLASSROOM CHARACTERISTICSFlorida Value-added ModelIntroductionThe State of Florida has committed to using value-added methods as a component of its teacher evaluation system as required by the Student Success Act (Senate Bill 736) as well as its Race to the Top proposal (RTTT). The value-added model (VAM) described in this technical report is applied to the Florida Comprehensive Assessment Test (FCAT) in reading and mathematics across grades 3 through 10. Other models using data from different sources, such as End-of-Course assessments, will be developed in subsequent work. In 2011, the Florida Legislature passed Senate Bill 736, which was also closely aligned with the objectives for teacher evaluation as proposed in the state’s RTTT application. The Act and the RTTT application both require the use of student achievement test score data as one element of a teacher evaluation system. The role of the VAM is to differentiate teacher performance by using statistical models to measure student learning growth and attribute this growth to specific teachers. It accomplishes this by making use of Florida’s longitudinal test score data from the FCAT. The State enlisted a diverse group of stakeholders, referred to as the Student Growth Implementation Committee (SGIC), to serve as an evaluation committee and to make final recommendations as to the specific value added model that is best suited to the needs of teachers and students across the state. The members of the SGIC include teachers, principals, parents, union representatives, superintendents, school board members, district administrators, and postsecondary faculty who contribute expertise in various teaching subjects and grades, educational administration at all levels, and in the areas of measurement and assessment. The names and affiliations of the SGIC members are provided in Appendix A. This committee convened twice in Orlando, Florida and held approximately four phone conferences with the Florida Department of Education and the contracted vendor, the American Institutes for Research (AIR), to consider advantages and disadvantages of different modeling approaches that have been proposed in the value-added literature. Based on SGIC recommendations, AIR implemented over 120 different VAMs, which were subsequently reviewed and compared by the SGIC. Based on the SGIC’s review of the results across the array of models, a specific model was recommended to the State Commissioner of Education. The committee’s recommended model was selected by the Commissioner and will become the model used operationally for the FCAT reading and math tests to support SB 736 and all RTTT activities. This technical report describes the value-added model selected by the SGIC and the Commissioner and provides summaries of its results. The complete technical and computational details of the model are provided as well as a summary of its results. The report is organized to provide some context on different modeling approaches that were presented to the SGIC. A more comprehensive description of different value-added modeling techniques and how these different approaches relate to each other can be found in McCaffrey, Lockwood, Koretz, Louis, and Hamilton et al (2004). Value-Added ModelingValue-added modeling with educational test score data is the process of statistically analyzing student level test scores collected over a period of time with the intent of separating factors unique to students and schools from factors unique to a classroom teacher to attribute growth in student achievement to teachers and schools. The factor unique to a teacher is typically referred to as a teacher effect and is thought to be the causal impact of the teacher’s instructional efficacy on the student’s achievement as reflected via the test scores. All VAMs have similar aims, but use different assumptions and principles. McCaffrey et al. (2004) have demonstrated the relationship across commonly used VAM approaches, showing how different models can be viewed as special cases of a more general longitudinal model. Nonetheless, it is fair to characterize VAMs as falling into two modeling categories: those which we refer to as learning path models (typically referred to as variable persistence in the literature) and covariate adjustment models. These are described briefly below.Two Common Value-Added DesignsAll value-added models use longitudinal, student-level data. However, various models make use of the data in different ways. For instance, the variable persistence model (McCaffrey et al, 2004) uses the student level data as the vector of outcomes in a mixed linear regression and makes assumptions about how prior year teachers contribute to current year learning gains. Such an approach implicitly assumes all students have a predetermined learning trajectory relative to the mean outcomes in the state and that current year teachers can alter that trajectory upwards with good instruction or downwards with less effective instruction. Covariate adjustment models use the longitudinal data somewhat differently. In these models, the current year test score alone serves as the outcome in a linear regression and the prior year scores are used as conditioning variables. The models assume that students with a teacher of average effectiveness will score similar to other students with similar prior test scores and other characteristics. A teacher with a positive impact will alter the student’s current year outcome in a way such that the student performs better than is predicted, and a teacher with negative impact will affect the outcome such that the student does not perform as well as predicted. In either case, the outcomes across different subject areas (e.g., reading and math) can be modeled marginally—a separate regression for math and another for reading or jointly—where reading and math scores are simultaneously used as outcomes in a regression. Accommodating the latter approach presents additional computational challenge, requiring a slight difference in the parameterization of the within-student covariance matrix to account for correlation across error terms across the different tests. However, Lockwood, McCaffrey, Mariano, and Setodji (2007) have shown that modeling the outcomes jointly has only very modest effects on estimates of value added. They show that the estimated teacher effects from a joint and marginal model were correlated greater than .99. The conditional variances of the teacher effects were also shown to differ only by nominal amounts. There is one additional characteristic of the variable persistence model that does not appear in the covariate adjustment design—the impact of prior year teachers on current year outcomes. There are essentially two competing approaches on how to treat prior year teachers. One assumes complete persistence, meaning that the impact of a prior teacher on current outcomes does not dissipate at all (Ballou, Sanders, Wright, 2004). In other words, the impact that prior teachers had on the students learning path perpetually remains with that student. This implies that prior teachers have permanently impacted student learning paths.A separate approach assumes that the impact of the prior teacher is an additional parameter of the model and it should be estimated from the data (McCaffrey et al, 2004). In most cases, the impact of the prior teacher diminishes in some fashion, meaning that the impact of prior year teachers most likely declines with students over time. Under these assumptions, the fact that last year’s teacher had a large impact on the student’s learning path does not mean that the student’s learning path is forever altered by that teacher as is assumed with complete persistence. One additional issue that affects covariate adjustment models that has a significant impact on the model results is the impact of measurement error in the predictor variables. It is well established that conditioning on variables measured with error yields bias in the model parameters (Greene, 2000). Some approaches use an instrumental variables (IV) approach (Meyer, 1992). The use of IV is typically used when one of the predictor variables is correlated with the error term in the regression model—a situation which occurs when predictor variables are measured with error. However, there are challenges in identifying what to use as useful instruments. Ignoring this error in high stakes accountability systems yields results that are subject to much criticism and should be accounted for.The Florida Value-Added ModelThe model implemented for the State of Florida is a covariate adjustment model that includes two prior test scores as predictor variables (except in grade 4 where only one predictor is available), a set of measured characteristics for students, with teachers and schools treated as coming from a distribution of random effects. The model is an error-in-variables regression to account for the measurement error in the predictor variables used. A complete technical description of the model is found in the Methods section of this report. The predictor variables used in the model are the same across all grades in both reading and math, and they are:The number of subject-relevant courses in which the student is enrolled: Some students are enrolled in multiple courses that, according to the Florida course code directory, are linked to an FCAT test. This variable counts, for each student, the number of courses they are enrolled in that is linked to the FCAT test via the course code directory (see Appendix B).Two prior years of achievement scores: These are always the scores for the subject from the two prior years. For example, grade 8 math uses grades 6 and 7 FCAT math scores as predictors.Disabilities (SWD) status: This is a dichotomous variable denoting whether a student receives special education services for a specific disability.English language learner (ELL) status: This is a dichotomous variable denoting whether students are currently enrolled in an English language learner program or not for less than two years.Gifted status: This is a dichotomous variable denoting if the student is enrolled in a gifted program or not.Attendance: This is a continuous variable counting the number of days the student was present during the school year. Mobility (number of transitions). This is a continuous variable counting the number of transitions across schools within the same school year.Difference from modal age in grade (as an indicator of retention): This is a continuous variable computed as xi-x where xi is the age in months for student i and x is the modal age for students enrolled in the same grade across the state.Class size: A continuous measure counting the number of students linked to teacher j.Homogeneity of entering test scores in the class: A continuous variable computed as the interquartile range of student entering scores in the class. Certain properties of the FCAT scale caused for some concern over its proposed interval nature. The FCAT reports what is referred to as a developmental scaled score (DSS), which is a vertical scale measuring achievement across all grades. However, disparate patterns of growth in different grades suggest gain scores may not be comparable in different grades. For instance, we observe much larger growth estimates for grade 4 students than other grades, especially in reading.One possible consequence of this disparate pattern is that teachers in lower grades could appear to have larger value-added estimates relative to teachers in higher grades if all teachers were included in the same analysis. There are many possible ways to address this concern, some of which can be model-based (i.e., parameterize the model to account for these differences) or run separate models for each grade. We chose the latter to address this concern. Attribution of School Component to Teacher EffectThe VAM applied to the FCAT data decomposes total variation in achievement into three orthogonal components: variation between schools, variation between teachers within a school, and variance between students within a classroom. The parameterization of the model forms what is commonly referred to as a hierarchical linear model (HLM). While all parameters are estimated simultaneously, it is useful to consider the levels separately. First, student-level prior test scores (i.e., the lags) and the covariates are used to establish a statewide conditional expectation. This expectation is the score a student is expected to have, given his or her prior test score history and measured characteristics. However, schools exhibit differential amounts of growth. The model cannot differentiate whether these differences are due to independent factors at the school (e.g., particularly effective leadership) or simply due to the sorting of high-growth teachers into some schools rather than others. We refer to this as the common school component of student growth. The common school component therefore describes the amount of learning that is typical for students in each school that differs from the statewide conditional expectation.Whether or not to estimate the common school component and teacher effects was a source of significant discussion for the SGIC, and it is a source of significant discussion in the value-added literature. If school effects are ignored and the model includes only teacher effects, then legitimate differences between teachers could be exaggerated as some of the teacher effect includes the common school component. In other words, some teachers could appear to have higher (or lower) value-added than is true in reality as their effect includes things that may be reasonably viewed as out of their immediate control, such as principal leadership. In contrast, if school effects are included, then some of the legitimate differences between teachers could be minimized. In other words, the school effect now captures some of the teacher effect. As a result, when estimating a value-added model, we needed to determine whether the model should:1.estimate the common school component, thus potentially removing some legitimate differences between teachers; or2.ignore the common school component and assume that any difference in learning across classes is entirely a function of classroom instruction; or 3.find some middle ground where teacher value-added scores include some but not all of the common school component.If we subscribe to the notion that some of the school component reflects the sorting of more effective teachers into some schools, then we may wish to apportion some of the school effect back to teachers. However, how much of the school effect gets attributed back to teachers cannot be determined via the value-added model though these decisions have important implications for interpreting teacher value-added scores, particularly across schools. Specifically, if the committee voted to add none of the school component (0%) to teachers’ value-added scores there would be one model, but different standards for student outcomes for different schools. Teachers with high-growth in high-growth schools may earn lower value-added scores than teachers with lower growth at a low growth schools. In contrast, if the committee voted to add all of the school component (100%) to teachers’ value-added scores, there would be one model with the same standard for student outcomes, regardless of school. Teachers with high student growth in high growth schools will earn higher value-added scores than teachers with lower growth at low growth schools, regardless of how the teachers’ performances compare to their respective schools. After significant discussion, as well as with a second follow-up meeting, the SGIC determined that some of the school effect should be attributed back to teachers. The proportion allocated back was put to vote and agreed upon by the SGIC as 50 percent. Hence, teacher effects are then subject to the following calculation:Teacher Value-Added Score = Unique Teacher Component + .50 * Common School ComponentThis formula simply recognizes that some of the school component is a result of teacher actions within their schools and that they should receive some credit in their overall value-added effects. MethodsCovariate Adjustment ModelThe statistical value-added model implemented for the State of Florida is typically referred to as a covariate adjustment model (McCaffrey et al, 2004) as the current year observed score is conditioned on prior levels of student achievement as well as other possible covariates that may be related to the selection of students into classrooms.In its most general form, the model can be represented as:yti=Xiβ+r=1Lyt-r,iγt-r+q=1QZqiθq+eiwhere yti is the observed score at time t for student i, Xi is the model matrix for the student and school level demographic variables, β is a vector of coefficients capturing the effect of any demographics included in the model, yt-r,i is the observed lag score at time t-r (r∈1,2,…,L), γ is the coefficient vector capturing the effects of lagged scores, Zqi is a design matrix with one column for each unit in q (q∈1,2,…,Q) and one row for each student record in the database. The entries in the matrix indicate the association between the test represented in the row and the unit (e.g., school, teacher) represented in the column. We often concatenate the sub-matrices such that Z={Z1,…,ZQ}. θq is the vector of effects for the units within a level. For example, it might be the vector of school or teacher effects which may be estimated as random or fixed effects. When the vector of effects is treated as random, then we assume θq~N(0, σθq2) for each level of q.Corresponding to Z={Z1,…,ZQ}, we define θ'=(θ1',…,θQ'). In the subsequent sections, we use the notation δ'={β', γ'}, and W={X,yt-1, yt-2,…, yt-L} to simplify computation and explanation.Note that all test scores are measured with error, and that the magnitude of the error varies over the range of test scores. Treating the observed scores as if they were the true scores introduces a bias in the regression and this bias cannot be ignored within the context of a high stakes accountability system. Our approach to incorporating measurement error in the model is described in a later section.Defining Teacher and School Effects in the Covariate Adjustment ModelThe terms teacher and school “effect” imply something causal about the role of teachers and students in the model. While the VAM clearly aims to disentangle factors idiosyncratic to a student and school from a teacher, we truly only have some residual variation at the teacher level that is then attributed to the classroom teacher as their instructional influence. We retain the use of the term teacher effect because the VAM intends to identify this effect directly. However, the term school effect is not the most appropriate term. Accounting for other factors that are unique to students attending the school does not imply the school itself caused the effect. Instead, including a school component is capturing the latent effect of all potential impacts of the school community, including principal leadership, neighborhood effects, etc. Hence, we prefer the term unique school component for this level.Because the model is a covariate adjustment model, predictions for students are set for students conditioned on their observed characteristics and prior test scores. That is, the conditional expectation for a student is formally defined as:EytiW=Wδ=yti=WδTherefore, the basic idea is to find a conditional expectation for student i based on how other students with similar measured characteristics and prior test score have performed. Given the predicted value we then have rti=yti-yti, which denotes the observed difference between their observed test performance and their predicted performance. When teachers and schools are treated as random effects, as the SGIC decided to do in Florida value-added model, these residuals are then aggregated for teacher j to form the empirical Bayes estimate as:Θj=Njσt2Njσs2+σt2+σe2i=1Njr(j)iNj(1)where σt2 is the teacher level variance, σs2 is the school level variance, σe2 is the residual variance, Nj denotes the number of students in class j and the notation (j)i is used to mean that student i in class j. Equation 1 above is nothing more than the scalar representation of the commonly used matrix notation: Θ=DZ'V-1y-Wδwhere V=ZDZ'+Ω. and V is block-diagonal. However, in Equation 1 we can see that student level residuals form the basis for the quantity referred to as a teacher effect. Hence, given estimates of the model parameters, including the fixed effects and variances of the random effects, we can formally define the teacher effect as the weighted mean of the student level residuals. Because the estimated teacher effect is a weighted mean of the student level residuals, it is easy to see that a teacher with a positive value-added effect is one whose students, on average, perform better than conditionally expected and a teacher with a negative value added effect is one whose students perform lower than conditionally expected.Measurement Error in Educational Achievement Tests and How its Effect Propagates into the VAMClassical test theory posits that the observed test score is the sum of a true score plus a disturbance, x=t+e and also posits that the observed score variance is the sum of two orthogonal variances, var(x)=var(t)+var(e). From these basic principles, we can define reliability as the ratio of true score variance to the observed score variance, ρ2=var(t)/var(x) and also write the classical standard error of measurement as σe=σx(1-ρ). This classical standard error assumes homoscedasticity of the error term across the score range and almost all error-in-variable models are constructed around the classical true score model (Kmenta, 1971). Item response theory (IRT) extends these basic principles and introduces the concept of the test information function (TIF) (Lord, 1980). Rather than a single index characterizing the precision of the test, the TIF varies along the score continuum providing more information at certain points of the score range. The converse of the TIF, or the lack of information, is taken as the standard error of measurement at a particular score point. Because the TIF varies along the score continuum, so does the standard error of measurement. In Florida, the conditional standard errors of measurement (CSEM) tend to be larger at the extremes of the score distribution as illustrated in Figure 1. Because there is heteroscedasticity in the error term, the error-in-variables (EiV) regression model must directly take this into account to yield efficient estimates of the model parameters. Our derivation of the EiV model is based on these principles and is described in the next section. Figure 1It has been proposed that measurement error in the predictor variables can be ignored when the model conditions on at least three prior test scores (Sanders, 2006). It can, however, be shown analytically as follows that bias will remain, even when multiple scores are used.Suppose the true score regression is Y=X*β+e. Let X=X*+U where U is a matrix of unobserved disturbances with the same dimensions as X. The true score regression is then Y=(X-U)β+e. Taking the maximum likelihood estimator for the true regression asβtrue=(X*'X*)-1X*'yAnd then upon substitution we haveβtrue=X-U'X-U-1X-U'y=(X'X-X'U-U'X+U'U)-1X'y-U'yThis simplifies because E(X'U)=EU'X=E(U'U) and E(U'y)=0. Consequently, βtrue=(X'X-E(U'U))-1X'y, where as βobs=(X'X)-1X'y and the component EU'U propagates as bias.This shows that adding in additional predictor variables does not guard against bias due to the measurement error in the predictors. The bias is a function of the measurement error in the predictor variables, not a function of the number of variables. However, this illustration does shed light on a possible solution to the problem associated with measurement error in the predictor variables, which we present next.Accounting for Measurement Error in the Predictor VariablesWe first re-express the true score regression as: yt*=Xβ+r=1Lyt-r*γt-r+q=1QZqθq+eWe use * to denote the variables without measurement error. For convenience, define the matrices W={X,yt-1, yt-2,…, yt-L}, W*={X,yt-1*, yt-2*,…, yt-L*}, and δ'={β', γ'}. Label the matrix of measurement error disturbances U for disturbances associated with yt-1, yt-2,…, yt-L, and label the vector of measurement disturbances with the dependent variable, yt, v, hence yt=yt*+v . Let U have the same dimension as W, but only the final L columns of U are non-zero, so W=W*+U. If those disturbances were observed, the parameters {δ', θ'} can be estimated using Henderson’s methods (1950) by solving the following mixed model equations:W*'Ω-1W*W*'Ω-1ZZ'Ω-1W*Z'Ω-1Z+D-1δθ=W'Ω-1y*Z'Ω-1y*The matrix D is comprised of Q diagonal blocks, one for each level in the hierarchy. Each diagonal is constructed as σq2Iq where Iq is an identity matrix with dimension equal to the number of units at level q, and σq2 is the estimated variance of the random effects among units at level q. When concatenated diagonally the square matrix D has dimension m=q=1QJq.Two complications intervene. First, we cannot observe U, and second, the unobservable nature of this term along with the heterogeneous measurement error in the dependent variable renders this estimator inefficient. Addressing the first issue, upon expansion we see that W*'Ω-1W*=W'-U'Ω-1W-U=W'Ω-1W-U'Ω-1W-W'Ω-1U+U'Ω-1USince W=W*+U, we have EW'Ω-1U=EU'Ω-1U,EU'Ω-1W=EU'Ω-1U, hence W*'Ω-1W*=W'Ω-1W-U'Ω-1U. Furthermore, we have W*'Ω-1Z=E(W'Ω-1Z), Z'Ω-1W*=E(Z'Ω-1W), and W'Ω-1y*Z'Ω-1y*=EW'Ω-1yZ'Ω-1y.Addressing the second issue, both the right side and left side variables in the model equation measured with error contribute to the heteroscedasticity. While the correction U'Ω-1U eliminates the bias due to measurement error, we still do not have an error-free measure of y for any time period. Therefore, the residual is comprised of y-W'δ=-U'δ+v+ e.where y=y-Zθ, θ is the conditional mean of the random effects. The residual variance of any given observation is σti2=σe2+σv(ti)2+r=1Lδt-r2σu,t-r(i)2, where σv(ti)2 is known measurement error variance of the dependent variable for examinee i at time t. Similarly, σu,t-r(i)2 are the known measurement error variances of r prior test scores. Now, let Ω be a diagonal matrix of dimension N with diagonal elements σti2.With the above, we can define the mixed model equations asW'Ω-1W-U'Ω-1UW'Ω-1ZZ'Ω-1WZ'Ω-1Z+D-1δθ=W'Ω-1yZ'Ω-1yReplacing U'Ω-1U with Its ExpectationsAs indicated, U is unobserved and so solving the mixed model equation cannot be computed unless U is replaced with some observed values. First, we redefine the mixed model equations as:W'Ω-1W-SW'Ω-1ZZ'Ω-1WZ'Ω-1Z+D-1δθ=W'Ω-1yZ'Ω-1ywhere S is a diagonal “correction” matrix with dimensions p x p accounting for measurement error in the predictor variables, p=pX+L, and pX is the column dimension of X. The matrix S is used in lieu of U'Ω-1U based on the following justification. Recall that we previously defined Ω as diag(σt12, σt22, …, σtN2) and the matrix of unobserved disturbances is:U=0pX00ULwhere 0pX is a matrix of dimension of pX with elements of 0, andUL=u11u12…u1Lu21u22…u2L????uN1uN2…uNLThe theoretical result of the matrix operation yields the following symmetric matrix:UL'Ω-1UL=i=1N1σti2ui12…i=1N1σti2ui1ui2i=1N1σti2ui22…????i=1N1σti2ui1uiLi=1N1σti2ui2uiL…i=1N1σti2uiL2The theoretical result is limited only because we do not observe uip--it is latent. However, Euipuip=σip2 where σip2 is taken as the conditional standard error of measurement for student i. The theoretical result also simplifies because errors of measurement on different variables are by expectation uncorrelated, Euipuip'=0 where p≠p'. Because we now have a conditional standard error of measurement that varies for each student i and we can ignore the off-diagonals, let S be:S=diag0,…,0,i=1N1σti2σu,t-1(i)2, i=1N1σti2σu,t-2(i)2, …, i=1N1σti2σu,t-L(i)2where σu,j(i)2 denotes the measurement error variance for the jth, j = (1, 2, … L), variable measured with error.Empirical Bayes versus Fixed EffectsWe previously noted that the general model can estimate teacher impacts as fixed or random effects. We also note that the Florida value added teacher effects are empirical Bayes estimates and explicitly defined the teacher effects as such. These types of models are also referred to as “shrinkage” estimators as some of the teacher and school effects are pulled towards a conditional mean given their level of reliability. The “shrinkage” in the empirical Bayes estimates introduces a small amount of bias, but yields a smaller mean squared error. Conversely, fixed effects models produce unbiased estimates, but have larger mean squared error. As a result of this bias-variance trade-off, the empirical Bayes are, on average, closer to the true population parameter than the fixed effect estimator. We previously discussed with the Student Growth Implementation Committee that fixed and random effects measure the same quantity and would expect them to be highly correlated. Here we make that argument explicit and show how the fixed effects estimator is the same as the random effects estimator with a small constraint.Recall that the mixed model solution is based on Henderson’s equations: W'Ω-1W-SW'Ω-1ZZ'Ω-1WZ'Ω-1Z+D-1δθ=W'Ω-1yZ'Ω-1yThe system simultaneously solves for δ and θ. However, for illustration suppose we are interested only in solving for the random effects, θ: Z'Ω-1Z+D-1θ=Z'Ω-1y-Z'Ω-1WδNow suppose that we estimate teachers as fixed effects. The linear model would be:y=Xβ+ewhere y is an n x 1 vector of outcomes, X is an n x q design matrix β is a q x 1 vector of coefficients and e is a random error term, e~N(0, σe2). Because there are many teachers, suppose we partition X as X = [W Z], where W corresponds to non-teacher related fixed effects, and Z corresponds to teacher level fixed effects, similarly, we partition β as β=δ'θ' thus yielding:Y=Wδ+Zθ+eThe normal equation for a partitioned regression is (Searle, 1997):W'Ω-1W-SW'Ω-1ZZ'Ω-1WZ'Ω-1Zδθ=W'Ω-1yZ'Ω-1yAnd isolating the solution for the teacher fixed effects yields:Z'Ω-1Zθ=Z'Ω-1y-Z'Ω-1WδHence, we can see that the random effects estimator is the same as the fixed effects estimator when all elements in the matrix D are null. In fact, the matrix D is what controls the amount of shrinkage observed in the data.Standard Errors of Fixed and Random EffectsHenderson’s method provides that the standard errors of the fixed and random effects can be computed as:Varδθ=W'Ω-1W-SW' Ω-1ZZ' Ω-1WZ'Ω-1Z+D-1-1W'Ω-1WW' Ω-1ZZ' Ω-1WZ'Ω-1Z+D-1W'Ω-1W-SW' Ω-1ZZ' Ω-1WZ'Ω-1Z+D-1-1Note thatW'Ω-1W-SW'Ω-1ZZ'Ω-1WZ'Ω-1Z+D-1-1W'Ω-1WW'Ω-1ZZ'Ω-1WZ'Ω-1Z+D-1W'Ω-1W-SW'Ω-1ZZ'Ω-1WZ'Ω-1Z+D-1-1=W'Ω-1W-SW'Ω-1ZZ'Ω-1WZ'Ω-1Z+D-1-1W'Ω-1W-SW'Ω-1ZZ'Ω-1WZ'Ω-1Z+D-1+S000W'Ω-1W-SW'Ω-1ZZ'Ω-1WZ'Ω-1Z+D-1-1=W'Ω-1W-SW'Ω-1ZZ'Ω-1WZ'Ω-1Z+D-1-1+W'Ω-1W-SW'Ω-1ZZ'Ω-1WZ'Ω-1Z+D-1-1S000W'Ω-1W-SW'Ω-1ZZ'Ω-1WZ'Ω-1Z+D-1-1Let W'Ω-1W-SW'Ω-1ZZ'Ω-1WZ'Ω-1Z+D-1= ABB'C and W'Ω-1W-SW'Ω-1ZZ'Ω-1WZ'Ω-1Z+D-1-1= C11C12C12'C22. Then we have C11= A-BC-1B'-1, C12= -A-BC-1B'-1BC-1 andC22= C-1+C-1B'A-BC-1B'-1BC-1. Note that if we assume that no teachers teach at more than one school (and we order the columns in Z appropriately) and no student was associated with more than one school, the C matrix is block diagonal with a block for each school containing entries for each of the teachers teaching at that school. Under this assumption C-1can be computed efficiently and the other computations also become tractable even for very large datasets. If there are some students who were in two or more schools during the current year, we will have a few entries in the matrix that are not on the block diagonal, but these will simply be ignored for the purposes of computing the variance terms.We now havevarδθ= C11C12C12'C22+ C11SC11C11SC12C12'SC11C12'SC12The standard errors of the fixed effects are computed as:varδ=C11+C11SC11And the conditional variances of the random effects are:EVarθ|y=EC22+ C12'SC12In order to compute the variances we only care about the diagonal and C12'SC12 can be computed easily if C is block diagonal. That is, the ith diagonal block comes from the ith diagonal block Ci of C, and the ith block Bi of B. It equals: Ci-1Bi'A-BC-1B'-1SA-BC-1B'-1BiCi-1.Hence, at level q, the conditional variances are:EVarθq|y=1JqtrVarθ|yqwhere tr(.) denotes the trace of the matrix, and varθ|yq is the submatrix containing the entries at level q. We can now compute σq2 asσq2=Evarθq|y+1q-1θq-mθq1'θq-mθq1where mθq is the mean of θq and 1 is a vector of 1’s with the same dimension as θq.The residual variance can now be estimated as σe2=Vare-1Ni=1Nσv(ti)2+r=1Lδt-r2σu,t-r(i)2where e=y-Wδ and vare=e'eN-p, N is the total number of students and p is the number of fixed effect parameter puting the Value-Added ModelOur implementation of the value added model uses the well-known Expectation-Maximization (EM) algorithm (Dempster, Laird, Rubin; 1977) to solve the mixed model equations. All computing takes place within SAS IML, which has functions for sparse matrix methods, including a sparse Cholesky decomposition. These methods make computing more feasible to larger data sets when the matrices retain their sparseness. The solutions for the fixed effects and predictions for the random effects are obtained via the Expectation-Maximization (EM) algorithm via the following steps:1.Construct starting values for the variances of the random effects including σe2 and σq2 for all levels of q. These are used in the matrices Ω and D, respectively.2.Solve the linear system for δ and θ. The system is sparse and can be solved using sparse matrix methods.3.Update the values of the variances of the random effects including σe2 and σq2 using the methods described above.4.Iterate between steps 2 and 3 until δjt-δjt-1<con ? j where con is the convergence criteria by default set at 1e-5. If teacher and school effects are treated as fixed rather than random, the estimation method above is used with the constraint that all elements of the matrix D are 0 and the only variance parameter updated at each iteration is σe2 as justified in the previous section on fixed effects estimation.Final Estimates of the Teacher Value-Added ScoreWe previously noted that the SGIC wanted some of the unique school component to be added back to the teacher effect. We formally denote the teacher value-added score then as:θt*=θt+.5θ(s)tWhere θt is the empirical Bayes estimate of the teacher effect, θ(s)t is the empirical Bayes estimate of the unique school component and the notation s(t) is used to mean that teacher t is in school s. Because the revised teacher effect is a linear combination of the teacher and school effects, the final conditional variance of the teacher effect no longer applies and we require a new variance estimator. However, this is easily established using the conditional variances of the empirical Bayes estimates as the variance of the linear combination, which we denote as:var(θt*)=varθt+.25varθst+ cov(θt,θst)Classification ProbabilitiesThe standard errors of the teacher effects represent the measurement of uncertainty associated with a given effect. However, we can extend this to compute other measures that indicate the degree to which teachers could be inaccurately classified as having high or low value added measures. Suppose we begin with a true score measurement model for teacher effects such that the observed teacher effect is the sum of a true effect and measurement error:θ=θ*+eIn value-added models, the goal is to identify teachers whose effects are sufficiently large to judge them as being “high performing.” Hence, a teacher is deemed high performing within a VAM context when θ>t; or their observed effect is larger than a pre-determined threshold, t. Value-added modeling researchers often estimate θ in different ways and they often vary in how they define t. However, this section establishes a general framework for VAM classification accuracy for models that establish teacher effects using a classical measurement framework. Model-specific classification probabilities can be subsequently derived based on the following theory.Given this structural model for teacher effects and assuming normality of the error distribution, the marginal probability of a teacher being identified as effective can be derived as:Prθ>t=Prθ*+e>t=Pre>t-θ*=Pr?(e<θ*-t); fe~N0, σe2=Φθ*-tσewhere Φ(.) denotes the normal cumulative distribution function. Managing risk requires an examination of the false positives, or the identification of teachers classified as effective when they truly are not. Extending this to examine false positive rates requires the joint probability:Pr(θ>t, θ*<t)=Prθ*<tθ>tPrθ>t=-∞tΦθ*-tσefθ*μθ*, σθ2dθ*This yields, for each teacher, a misclassification probability. Introducing the subscript j to denote individual teachers (for i = 1, …, N), we can now establish:EFP= j=1NPr(θj>t, θj*<t)where EFP denotes the expected number of false positives given the data. Supposing we observe Q teachers falling above the threshold t, we can compare EFP to Q where it is expected that EFP<Q.Additionally, we can use the same assumptions made previously and justify the following in order to compute the false negatives Pr(θ<t, θ*>t)=t∞Φt-θ*σefθ*μθ*, σθ2dθ*EFN= j=1NPr(θj<t, θj*>t)SimulationsTo ensure the accuracy of the measurement-error corrected mixed model equations, AIR conducted a series of simulations. We constructed test data sets that varied along five dimensions. While the focus of the estimates is on teacher effects, the model should handle multiple levels in the educational hierarchy. We vary the simulated data according to the following:Magnitude of effect at each level.Measurement properties of the test. IRT tests have measurement variances that vary across the range of scale scores. Classical test theory (and existing programs based on it) assume a constant measurement variance across the range.Number of lags. The model controls for prior achievement. Simulations should include immediately prior and previous lagged achievement scores.Variation in school and class size. Selection model. We know that students are not sorted into classrooms randomly. This varies the extent to which students are sorted into classrooms based on observed scores.ConfigurationsThe chart below summarizes the parameter settings for four simulation configurations. Each run included approximately 200 top-level units (i.e., schools or districts), and were run on 800 independently generated data sets.Exhibit 1. Data configurationsSimulation modelMeas. PropertiesMagnitude of effect at each levelLevelsSize VariationSelection effectCovariatesTime LagsSimple/baselineConstantModerate (.2)2Low (m=20,v=16)NoneNone1(prior effect=.8)BasicAsymmetricModerate (.2)3Moderate(school: m=20, v=100; teacher m=20, v=80)Some (.0225 at each level)Some(2, both N(0,1); coef = .1,-.1)1(prior effect=.8)Two LagsAsymmetricModerate (.2)3Moderate(school: m=20, v=100; teacher m=20, v=80)Some(.0225 at each level)(2, both N(0,1); coef = .1,-.12(prior effect=.8)Small effectsAsymmetricSmall (.05)3Moderate(school: m=20, v=100; teacher m=20, v=80)SomeSome1Quality of model parametersStatistical indicators of model quality included indicators of: BiasPrecisionQuality of standard errorsBias of estimated teacher effectsQuality of standard errors of estimated teacher effectsExhibit 2 describes the indicators of bias and precision for the parameters of the model. Each simulation should recover unbiased estimates of the parameters.Exhibit 2. Indicators of bias and precisionIndicator of:Indicator for each model parameterObserved biasAverage estimate – true valueSampling errorAverage standard deviation of estimates across replicatesCombined sampling error and biasRoot mean square error across replicates Exhibit 3 summarizes the indicators of the quality of the standard errors.Exhibit 3. Indicators of unbiasedness and consistency of the standard error estimatorsIndicator of:Indicator for each model parameterObserved standard errorStandard deviation across replicatesEstimated standard errorAverage estimated standard error across replicatesUnbiasednessAverage of across itemsUnbiasednessProportion of 200 datasets where UnbiasednessProportion of 200 datasets where Quality of unit (teacher or school) effectsExhibit 4. Indicators of bias and precisionIndicator of:Indicator for each model parameterObserved biasAverage across replicates, average across teachers and schools: estimate – true valueSampling errorCalculate the mean, standard deviation, min and max of the standard error estimate for each replicate. Report the average of these statistics and put the 200 estimates in an bined sampling error and biasRoot mean square error across replicates Exhibit 5 summarizes the indicators of the quality of the standard errors.Exhibit 5. Indicators of unbiasedness and consistency of the standard error estimatorsIndicator of:Indicator for each model parameterUnbiasednessProportion of estimates across all 200 datasets (200*N teachers) where UnbiasednessProportion of estimates across all 200 datasets where To evaluate the quality of the school and teacher effect estimates, we propose to calculate the estimated effects and compare them to the true effects using statistics similar to those described in Exhibits 2 and 3.ResultsIn this section we provide summaries of the model results for reading and math across all grades for the 2010-11. The appendices provide tables showing results in further detail. Teacher and School Variance ComponentsFor each grade, the value-added models were fit to the data with both teacher and school random effects. The model decomposes total variation in the outcome into three orthogonal components: variance between teachers within a school, variance between schools, and variance between students within a class. Figures 2 and 3 below show the standard deviation of the student, teacher, and school components in reading and math across all grades.Figure 2. Magnitude of Teacher and School Variance Components: MathematicsFormal likelihood ratio tests are not performed between models with teacher effects only and those with both teacher effect and school component. However, using the visual displays as a heuristic to gauge the magnitude of the variance components, we observe that school components seem to account for a non-trivial amount of the variance in the outcome variable. The relatively sizable magnitude of the school components suggest that systematic school components exist and explain differences in how students perform, above and beyond that which is explained by the teacher effects. In general, the variance between schools tends to be smaller than the variance between teachers within a school. The notable exception to this trend is grade 6 math, where the two effects appear to have similar magnitudes.It is clear that the variance between students within a class is the largest of all variance components. In reading, there remains quite a bit of heterogeneity between students within a class across all grades. However, the math plots suggest greater homogeneity in students within a class as we look at the higher grades. It is also worth noting that in math there is an apparent, systematic decline in the variance between schools and the variance between teachers within a school as we look in the higher grades. Figure 3. Magnitude of Teacher and School Variance Components: ReadingTeacher and School Standard ErrorsWhen value-added models estimate teacher effects and school components, they do so with a certain level of uncertainty. Factors such as the variation in student scores, the type and number of students attributed to a school, and the number of teachers in a school can all influence this level of uncertainty. The level of uncertainty for a particular teacher effect or school component is summarized in the standard error for each estimate. Table 1 shows the mean of the conditional standard errors of the teacher and school empirical Bayes estimates disaggregated by grade and subject. Within each grade and subject, it can be seen that on average, school components are more precise than the corresponding teacher effects – as would be expected given that more students are typically attributed to a school than to an individual teacher. While the relationship between teacher and school precision seems to be consistent across grades, the standard errors vary considerably across grades. This variability indicates that the model for some grades is producing teacher effects and school components with less uncertainty than other grades. The standard errors of teacher effects for reading range from a minimum of 8.98 for grade 5, to a maximum of 16.37 for grade 10. For mathematics, grade 9 has the most precise teacher effects on average (7.9), whereas grade 5 has the least precise teacher effects (24.37).Table 1. Mean Teacher and School Standard Errors by Grade and Subject?ReadingMathematicsGradeTeacherSchoolTeacherSchool58.98(0.58)6.85(1.12)24.37(4.44)15.1(2.42)614.9(1.82)8.05(1.57)18.85(3.86)13.91(3.69)715.77(1.98)7.77(1.33)14.88(4.28)8.71(1.50)812.84(1.74)6.35(1.07)9.45(2.22)5.7(0.99)99.82(0.89)5.23(1.14)7.9(2.03)4.25(1.00)1016.37(1.85)6.86(1.57)6.46(0.84)3.51(0.92)Impact of VAM on Different Student GroupsIt is important to examine the possible disparate impact that the VAM has on different groups of students. A difference in expectations does not necessarily imply issues inherent in the model. Some of the observed differences are plausible. In this section we provide descriptive statistics showing how the growth-based model predictions may vary across different student groups. Below we use the term expected growth, a statistic which we compute as:gi=yit-yi,t-1Where yit is the predicted outcome and yi,t-1is the observed outcome. This expected growth is aggregated at various levels to examine possible differences in mean growth expectations. Differences in Student Growth Expectations by Gifted StatusTo examine whether student growth expectations differ for gifted and non-gifted students, conditional expected growth estimates were calculated separately for gifted and non-gifted students at each grade level for both mathematics and reading. Figures 4 and 5 below display these expected growth estimates by grade for mathematics and reading, respectively.Figure 4. Expected Growth for Gifted and Non-Gifted Status Students by Grade: MathematicsFigure 5. Expected Growth for Gifted and Non-Gifted Status Students by Grade: ReadingFigure 4 demonstrates that student growth expectations in mathematics were higher for non-gifted than for gifted students in all grades tested. For reading, Figure 5 demonstrates that student growth expectations were higher for gifted than for non-gifted students in grades 5, 9 and 10, approximately equivalent for grade 6 and lower for gifted than for non-gifted students in grades 4, 7 and 8. It is important to interpret any observed differences between students with gifted and non-gifted status with caution given considerable differences in the size of the population of students for which these estimates were calculated. For example, for grade 10 reading, the expected growth for gifted students is based on 194 students in contrast to 175,184 non-gifted students. A comprehensive display of the student growth estimates and associated sizes of the student populations used to calculate each estimate is provided in Appendix F. Together, these findings demonstrate higher growth expectations for non-gifted than gifted students in mathematics but no consistent relationship between gifted status and conditional expectations for student growth in reading.Differences in Conditional Student Growth Expectations by ELL StatusSimilarly, it is possible that English Language Learners (ELLs) differ from their non-ELL counterparts in expectations for student growth. To examine this possibility, conditional expected growth estimates were calculated separately for ELL and non-ELL students at each grade level for both mathematics and reading. Figures 6 and 7 below display these expected growth estimates by grade for mathematics and reading, respectively.Figure 6. Expected Growth for ELL and Non-ELL Status Students by Grade: MathematicsFigure 7. Expected Growth for ELL and Non-ELL Status Students by Grade: ReadingFigure 6 demonstrates that student growth expectations in mathematics were higher for ELL than for non-ELL students in all grades except grade 6. For reading, Figure 7 demonstrates that student growth expectations were higher for ELL than non-ELL students in grades 4 through 10. Again, it is important to interpret any observed differences between ELL and non-ELL students given considerable differences in the size of the population of students for which these estimates were calculated. For example, for grade 10 mathematics, the expected growth for ELL students is based on 123 students relative to 156,089 non-ELL students. A comprehensive display of the student growth estimates and associated sizes of the student populations used to calculate each estimate is provided in Appendix F. Together, these findings demonstrate higher conditional growth expectations in mathematics and reading for ELL than non-ELL students with one exception (grade 6 mathematics). Effects of Teacher Characteristics on Teacher Value-Added EstimatesWe can also examine whether value-added estimates for teachers are related to teacher characteristics such as teaching experience (years teaching) and teacher education (highest degree earned) as well as the characteristics of teachers’ classrooms such as the percentage of students who are ELLs and/or who have disabilities. To examine these possibilities, we calculated the correlations between teacher value-added estimates and the teacher (experience) and classroom characteristics (percent ELL, percent of students with disabilities). Additionally, we present the average teacher value-added estimate separately for teachers with different levels of higher education. Here we show the correlations across all grades (4-10, excluding grade 9 for mathematics; 4-10 for reading). Appendix G provides these same results separately by grade.Table 2 displays the correlations between teacher effects for mathematics and reading (separately) and teaching experience, the percentage of ELL students and the percentage of students with disabilities within teachers’ classrooms. Table 3 displays the average teacher value-added estimates for mathematics and reading for teachers with bachelors, masters, and doctorate degrees.Table 2. Relationship between Teacher Effects for Mathematics and Reading and Teacher and Classroom Characteristics ?MathematicsReadingTeacher/Classroom CharacteristicRNRNTeacher Experience (Years Teaching)0.02644,4010.04559,247Percent ELLs0.01145,8860.008a61,409Percents Students with a Disability-0.05545,886?-0.02261,409Note: a Correlation not statistically significant at the 0.05 level.Table 2 shows the observed correlations with the teacher characteristics. These correlations are all very small in magnitude, but are worth examining. For both mathematics and reading, teacher value-added estimates are positively correlated with the percentage of ELLs in teachers’ classrooms and teaching experience, and negatively correlated with the percentage of students with a disability in teachers’ classrooms. Teachers who have been teaching longer, who have a greater proportion of ELL students in their classroom, and a smaller proportion of students with a disability have larger effects. Table 3. Average Teacher Value-Added Estimates for Mathematics and Reading by Teacher Education ?Mathematics?ReadingTeacher Education (Highest Degree)MeanSDN?MeanSDNBachelor's Degree0.2130.7928,804-0.0918.9536,726Master's Degree1.4630.3414,4941.2319.1220,830Doctorate Degree-1.2627.69383?0.6018.75612Table 3 provides the mean value-added estimate in reading and math conditional on teachers’ highest degree. In mathematics, teacher value-added estimates were larger for teachers who had completed a master’s degree followed by teachers with a bachelor’s degree and a doctorate degree. For reading, teachers with a master’s degree showed the largest teacher value-added estimates on average, followed by teachers with a doctorate degree and teachers with a bachelor’s degree. Thus, there is not a direct relationship between teacher education and teacher value-added estimates; teachers with master’s degree demonstrate the highest value-added estimates in both mathematics and reading.Simulation ResultsQuality of Unit (Teacher or School) EffectsThe tables below provide summaries of the statistics outlined in the Methods section. In almost all cases, our EiV mixed model recovers the parameter estimates for both the fixed and random effects. In a few cases, there is a very small bias in the fixed effects parameters as observed in Table 4. We note that correction for measurement error reduces, but does not totally eliminate, bias in the parameters. All variants of the model produce unbiased estimates of teacher and school effects. Table 4. Unbiasedness of the Fixed Effects Parameters?Simple/BaselineBasicTwo LagsSmall EffectsObserved Bias Parameter 10.0130.0000.0000.000Observed Bias Parameter 2?0.0000.0000.000Observed Bias Parameter 3?0.0130.0120.011Observed Bias Parameter 4??0.003?Sampling Error Parameter 10.0090.0030.0040.003Sampling Error Parameter 2?0.0030.0050.003Sampling Error Parameter 3?0.0050.0110.006Sampling Error Parameter 4??0.010?Combined Sampling Error and Bias Parameter 10.0160.0030.0040.003Combined Sampling Error and Bias Parameter 2?0.0030.0050.003Combined Sampling Error and Bias Parameter 3?0.0140.0160.012Combined Sampling Error and Bias Parameter 4??0.010?Table 5. Standard Errors of the Fixed Effects Parameters?Simple/BaselineBasicTwo LagsSmall EffectsObserved Standard Error Parameter 10.0090.0030.0040.003Observed Standard Error Parameter 2?0.0030.0050.003Observed Standard Error Parameter 3?0.0050.0110.006Observed Standard Error Parameter 4??0.010?Estimated Standard Error Parameter 10.0080.0030.0040.003Estimated Standard Error Parameter 2?0.0030.0040.003Estimated Standard Error Parameter 3?0.0050.0110.005Estimated Standard Error Parameter 4??0.010?No bias appears in the teacher and school effects as the EiV model seems to always recover their true values. The coverage rates for the teacher and school effects are all very close to their nominal values. Table 6. Unbiasedness Bias of the Random Effects?Simple/BaselineBasicTwo LagsSmall EffectsObserved bias: Teacher0.0010.0000.0010.000Observed bias: School?0.0010.0000.000Sampling error: mean SE: Teacher0.1270.1660.1990.124Sampling error: mean SE: School?0.1100.1140.061Sampling error: standard deviation of SEs: Teacher0.0140.0340.0390.020Sampling error: standard deviation of SEs: School?0.0320.0330.017Sampling error: average min SE: Teacher0.0960.1100.1340.087Sampling error: average min SE: School?0.0700.0720.039Sampling error: average max SE: Teacher0.2030.4180.4360.221Sampling error: average max SE: School?0.2470.2540.134Combined bias and sampling error: Teacher0.1320.1720.2060.127Combined bias and sampling error: School?0.1140.1170.063Percentage outside estimated 95% confidence interval: Teacher5.6435.3665.3715.298Percentage outside estimated 95% confidence interval: School?4.9724.8665.104Percentage outside estimated 90% confidence interval: Teacher10.97210.58610.56810.386Percentage outside estimated 90% confidence interval: School?9.7079.76410.152ConclusionAs described earlier, the State of Florida has committed to the use of a value-added model as one component of its statewide teacher evaluation system as required by the Student Success Act of 2011 [Senate Bill 736], as well as its Race to the Top plan. With input from an advisory committee (the SGIC), the state selected a value-added model to be used with statewide assessments. The committee and the state began their work with a broad survey of the types of value-added and student growth models currently in use around the country. The committee then narrowed its focus to a set of value-added models which it felt could best illustrate the nature of student, teacher, and school interactions and was flexible in its ability to describe teacher effects and school components. The committee and the state then used information from analysis of 120 different model variants to inform their decision on a statewide value-added model, reviewing data on model precision, explanatory power, and other information. The selected statewide value-added model design represents the consensus of the committee about the factors that influence student learning which should be taken into consideration in order to produce a fair and accurate estimate of individual teacher and school effectiveness. It also represents the consensus of the group about how best to represent the relationships between students, teachers, and schools in a statistical model. While the selection of the value-added model to be used with statewide assessments represents one step along the path to a comprehensive teacher evaluation system, much work remains to be done. For example, the value-added model described in this technical report is applied to the Florida Comprehensive Assessment Test (FCAT) in reading and mathematics across grades 3 through 10. Moving forward, data from new and additional assessments will be analyzed and any necessary modifications to the existing value-added methodology to accommodate these new data will be made. Specifically, data from new end-of-course assessments as well as the statewide alternate assessment will be analyzed in order to produce measures of teacher effectiveness for more teachers. Similarly, the state will consider how other commonly used assessments (such as Advanced Placement) may be utilized with the existing statewide value-added model methodology. Information on the results of value-added analysis using these assessments will be published in future technical documents.In addition, key decisions about how to report and use information from the statewide value-added model must be made. For 2011-12, each local school district will determine how to use value-added scores in its teacher evaluation system. To assist districts and to comply with state law which requires that three years of teacher value-added data be used in making evaluation decisions, the state will need to provide guidance on a method to aggregate scores across years (and potentially across subjects or grades), so that districts can easily use value-added data in their evaluation systems. Moving forward, the state may also need to provide additional guidance on how best to use value-added data to classify teachers into performance categories (e.g. highly effective, effective, and so on). Finally, while this document provides detailed information about the value-added methodology for a technical audience, the state will now embark upon efforts to ensure that teachers, principals, district officials, and the public have an understanding of the statewide value-added model and how it estimates teacher and school effectiveness. ReferencesBallou D., Sanders W., Wright P. (2004). Controlling for student background in value-added assessment of teachers. Journal of Educational and Behavioral Statistics, 29, 37–66.Dempster, A.P.; Laird, N.M.; Rubin, D.B. (1977). Maximum Likelihood from Incomplete Data via the EM Algorithm.. Journal of the Royal Statistical Society. Series B (Methodological) 39 (1): 1–38.Kmenta, J. (1971). Elements of Econometrics. New York: Macmillan.Henderson, C. R. (1950). Estimation of genetic parameters. Ann. Math. Stat., 9:309.Lockwood J., McCaffrey D., Mariano L., Setodji C. (2007). Bayesian methods for scalable multivariate value-added assessment. Journal of Educational and Behavioral Statistics, 32, 125–150.Lord, F.M. (1980). Applications of item response theory to practical testing problems. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.McCaffrey D., Lockwood J., Koretz D., Louis T., Hamilton L. (2004). Models for value-added modeling of teacher effects. Journal of Educational and Behavioral Statistics, 29, 67–101.Meyer, R. (1992). Applied versus traditional mathematics: New econometric models of the contribution of high school courses to mathematics proficiency (Discussion Paper No. 966-92). Madison: University of Wisconsin‐Madison, Institute for Research on Poverty.Sanders, W. (2006). Comparison among various educational assessment value added models. White paper. A. SGIC Member RosterThe names and affiliations of the SGIC members are as follows:Sam Foerster, Chair, Associate Superintendent, PutnamSandi Acosta, Teacher (6th and 7th Science), DadeRonda Bourn, Consortium AdministratorAnna Brown, Representative for Superintendent MaryEllen Elia, HillsboroughJoseph Camputaro, Teacher (Elementary/Reading), LeeJulia Carson, Teacher (HS AP History, Geography), VolusiaCathy Cavanaugh, Postsecondary, UFDoretha Wynn Edgecomb, School Board, HillsboroughGisela Field, District Administrator – Assessment, DadeStacey Frakes, Teacher (3rd – 5th ESE), MadisonArlene Ginn, Teacher (7th Science), OrangeStephanie Hall, School-based Administrator (ES), BrevardLavetta B. Henderson, Postsecondary, FAMUEric O. Hernandez, Teacher (Honors Math), DadeLinda J. Kearschner, Parent, PinellasLatha Krishnaiyer, State PTAJohn le Tellier, Teacher (Music), MarionNicole Marsala, Teacher (8th History), BrowardLisa Maxwell, Local Union, BrowardLawrence Morehouse, BusinessJeff Murphy, District Administrator - Student Services, Virtual SchoolMaria Cristina Noya, School-based Administrator (HS), St. LuciePam Stewart, Assistant Superintendent, St. JohnsLance J. Tomei, Postsecondary, UCFGina Tovine, District Administrator – HR, LevyLori Westphal, Teacher (ESE), LakeTamar E. Woodhouse-Young, Teacher (High School Math), DuvalAppendix B. Florida Course Codes Used in the Value-Added ModelTable 1. Course Codes Used in the Mathematics Value-Added ModelYearCourse NumberCourse Name2008-09, 2009-10, 2010-111200300Pre-Algebra2008-09, 2009-10, 2010-111200310Algebra I2008-09, 2009-10, 2010-111200320Algebra I Honors2008-09, 2009-10, 2010-111200330Algebra II2008-09, 2009-10, 2010-111200340Algebra II Honors2008-09, 2009-10, 2010-111200370Algebra Ia2008-09, 2009-10, 2010-111200380Algebra Ib2008-09, 2009-10, 2010-111200400Intensive Mathematics2008-09, 2009-10, 2010-111200410Math for College Success2008-09, 2009-10, 2010-111200500Advanded Algebra with Financial Applications2008-09, 2009-10, 2010-111200700Math College Readiness2008-09, 2009-10, 2010-111201300Math Analysis2008-09, 2009-10, 2010-111202371Pre-AICE Additional Math III2008-09, 2009-10, 2010-111204000M/J Intensive Mathematics (MC)2008-09, 2009-10, 2010-111205010M/J Mathematics 12008-09, 2009-10, 2010-111205020M/J Mathematics 1, Advanced2008-09, 2009-10, 2010-111205040M/J Mathematics 22008-09, 2009-10, 2010-111205050M/J Mathematics 2, Advanced2008-09, 2009-10, 2010-111205070M/J Mathematics 32008-09, 2009-10, 2010-111205080M/J Mathematics 3, Advanced2008-09, 2009-10, 2010-111205090M/J Mathematics IB2008-09, 2009-10, 2010-111205100M/J Pre-algebra IB2008-09, 2009-10, 2010-111205370Consumer Mathematics2008-09, 2009-10, 2010-111205400Applied Mathematics I2008-09, 2009-10, 2010-111205410Applied Mathematics II2008-09, 2009-10, 2010-111205500Explorations in Mathematics I2008-09, 2009-10, 2010-111205510Explorations in Mathematics II2008-09, 2009-10, 2010-111205540Business Mathematics2008-09, 2009-10, 2010-111206300Informal Geometry2008-09, 2009-10, 2010-111206310Geometry2008-09, 2009-10, 2010-111206320Geometry Honors2008-09, 2009-10, 2010-111207310Integrated Mathematics I2008-09, 2009-10, 2010-111207320Integrated Mathematics II2008-09, 2009-10, 2010-111207330Integrated Mathematics III2008-09, 2009-10, 2010-111209810Pre-AICE Mathematics I2008-09, 2009-10, 2010-111209820Pre-AICE Mathematics II2008-091298010M/J Great Explorations in Math (GEM) 6th Pre-Algebra2008-091298020M/J Great Explorations in Math (GEM) 7th Algebra2008-091298030M/J Great Explorations in Math (GEM) 8th Geometry2008-095012000Mathematics-Elementary2008-095012010Functional Basic Skills in Mathematics-Elementary2008-09, 2009-10, 2010-115012020Math Grade K2008-09, 2009-10, 2010-115012030Math Grade 12008-09, 2009-10, 2010-115012040Math Grade 22008-09, 2009-10, 2010-115012050Math Grade 32008-09, 2009-10, 2010-115012060Math Grade 42008-09, 2009-10, 2010-115012070Math Grade 52008-09, 2009-10, 2010-117712010Mathematics K-52008-09, 2009-10, 2010-117755010Academics K-52008-09, 2009-10, 2010-117755030Academic Skills K-52008-09, 2009-10, 2010-117755040Advanced Academic Skills K-52008-09, 2009-10, 2010-117755050Developmental Skills K-52008-09, 2009-10, 2010-117812010Mathematics: 6-82008-09, 2009-10, 2010-117855010Academics 6-82008-09, 2009-10, 2010-117855030Academic Skills 6-82008-09, 2009-10, 2010-117855040Advanced Academics 6-82008-09, 2009-10, 2010-117855050Developmental Skills 6-82008-09, 2009-10, 2010-117912050Mathematics 9-122008-09, 2009-10, 2010-117912340Life Skills Math: 9-122008-09129800AM/J Great Explorations in Math (GEM) 6th Pre-Algebra2008-09129800BM/J Great Explorations in Math (GEM) 7th Algebra2008-09129800CM/J Great Explorations in Math (GEM) 8th GeometryTable 2. Course Codes Used in the Reading Value-Added ModelYearCourse NumberCourse Name2008-09, 2009-10, 2010-111000000M/J Intensive Language Arts (MC)2008-09, 2009-10, 2010-111000010M/J Intensive Reading (MC)2009-10, 2010-111000020M/J Intensive Reading and Career Planning2008-09, 2009-10, 2010-111000400Intensive Language Arts2008-09, 2009-10, 2010-111000410Intensive Reading2008-09, 2009-10, 2010-111001010M/J Language Arts 12008-09, 2009-10, 2010-111001020M/J Language Arts, 1 Adv.2008-09, 2009-10, 2010-111001030M/J Language Arts 1, International Baccalaureate2008-09, 2009-10, 2010-111001040M/J Language Arts 22008-09, 2009-10, 2010-111001050M/J Langague Arts 2, Adv2008-09, 2009-10, 2010-111001060M/J Language Arts 2, International Baccalaureate2008-09, 2009-10, 2010-111001070M/J Language Arts 32008-09, 2009-10, 2010-111001080M/J Language Arts 3, Adv2008-09, 2009-10, 2010-111001090M/J Language Arts 3,International Baccalaureate 2008-09, 2009-10, 2010-111001300English Skills I2008-09, 2009-10, 2010-111001310English I2008-09, 2009-10, 2010-111001320English Honors I2008-09, 2009-10, 2010-111001330English Skills II2008-09, 2009-10, 2010-111001340English II2008-09, 2009-10, 2010-111001350English Honors II2008-09, 2009-10, 2010-111001440Business English I2008-09, 2009-10, 2010-111001450Business English II2008-09, 2009-10, 2010-111001560Pre-AICE English Language2008-09, 2009-10, 2010-111001800English I Pre-International Baccalaureate2008-09, 2009-10, 2010-111001810English II Pre-International Baccalaureate2009-10, 2010-111001840IB Middle Years Program English I2009-10, 2010-111001845IB Middle Years Program English II2008-09, 2009-10, 2010-111002000M/J Language Arts 1 through ESOL2008-09, 2009-10, 2010-111002010M/J Langague Arts 2 through ESOL2008-09, 2009-10, 2010-111002020M/J Langague Arts 3 through ESOL2008-09, 2009-10, 2010-111002180M/J Developmental Language Arts Through ESOL (MC)2008-09, 2009-10, 2010-111002300English I through ESOL2008-09, 2009-10, 2010-111002310English II through ESOL2008-09, 2009-10, 2010-111002380Developmental Language Arts Through ESOL2008-09, 2009-10, 2010-111005375AICE English Literature II2008-09, 2009-10, 2010-111008010M/J Reading 12008-09, 2009-10, 2010-111008020M/J Reading 1, Advanced2008-09, 2009-10, 2010-111008040M/J Reading 22008-09, 2009-10, 2010-111008050M/J Reading 2, Advanced2008-09, 2009-10, 2010-111008070M/J Reading 32008-09, 2009-10, 2010-111008080M/J Reading, Advanced2008-09, 2009-10, 2010-111008300Reading I2008-09, 2009-10, 2010-111008310Reading II2008-09, 2009-10, 2010-111008320Advanced Reading2008-09, 2009-10, 2010-111008330Reading III2009-10, 2010-111008350Reading for College Success2008-09, 2009-10, 2010-112400000Sixth Grade2008-09, 2009-10, 2010-115010010ESOL English for Speakers of Other Language-Elementary2008-09, 2009-10, 2010-115010020Functional Basic Skills in Reading-Elementary2008-09, 2009-10, 2010-115010040Language Arts-Elementary2008-09, 2009-10, 2010-115010050Reading-Elementary2008-09, 2009-10, 2010-115010060Integrated Language Arts-Elementary2008-09, 2009-10, 2010-117710010Language Arts K-52008-09, 2009-10, 2010-117755010Academics K-52008-09, 2009-10, 2010-117755030Academic Skills K-52008-09, 2009-10, 2010-117755040Advanced Academic Skills K-52008-09, 2009-10, 2010-117755050Developmental Skills K-52008-09, 2009-10, 2010-117810010Language Arts 6-82008-09, 2009-10, 2010-117810020Reading: 6-82008-09, 2009-10, 2010-117910100Reading 9-122008-09, 2009-10, 2010-117910110English 9-122008-09, 2009-10, 2010-117910400Life Skills Reading: 9-12Appendix C. Fixed Effect EstimatesTable 1. Fixed Effects: Grade 4 Reading, 2010-11Effect NameEffectStandard ErrorConstant Term473.289488.0715626Language Impaired-39.43932.9372883Deaf or Hard of Hearing-27.5003328.293731Visually Impaired-28.1600337.685257Emotional/Behavioral Disability-35.3691919.751021Specific Learning Disability-19.54797.6782468Dual-Sensory Impaired440.46932162.78546Autism Spectrum Disorder-31.8146923.498643Traumatic Brain Injured-111.7807109.87965Other Health Impaired-20.6073111.333652Intellectual Disability-20.8997866.478877Enrolled in 2 or more Courses15.3743221.9531732Enrolled in 3 or more Courses9.23761572.1903717Enrolled in 4 or more Courses4.87964426.7319318Enrolled in 5 or more Courses-9.11833451.884447Homogeneity of Class 1 Prior Year Test Scores-0.020080.0047442Homogeneity of Class 2 Prior Year Test Scores0.01043820.0056998Missing Homogeneity of Class 2 Prior Year Test Scores11.820982.7854498Homogeneity of Class 3 Prior Year Test Scores0.01308470.0074043Missing Homogeneity of Class 3 Prior Year Test Scores12.012653.1546793Homogeneity of Class 4 Prior Year Test Scores-0.0004880.009586Missing Homogeneity of Class 4 Prior Year Test Scores5.6972593.8949402Homogeneity of Class 5 Prior Year Test Scores0.00790560.0137998Missing Homogeneity of Class 5 Prior Year Test Scores-0.3171215.7611271Homogeneity of Class 6 Prior Year Test Scores-0.0040620.0172575Missing Homogeneity of Class 6 Prior Year Test Scores8.89962866.9670777Number of Students in Class 10.22782130.0717638Number of Students in Class 20.04817380.0480817Number of Students in Class 30.10726510.0536661Number of Students in Class 40.04793650.048687Number of Students in Class 50.07784840.0880728Number of Students in Class 60.14171390.0972198Difference from Modal Age-37.260630.859862Gifted Student Indicator29.8530919.4171472English Language Learner Indicator7.58840461.72676Achievement: Prior Year0.77652280.0020639*Attendance and mobility variables are not included in the model because the data is not reported until August during the Survey 5 data collection.Table 2. Fixed Effects: Grade 5 Reading, 2010-11Effect NameEffectStandard ErrorConstant Term252.755928.2825155Language Impaired-0.0682823.1538825Deaf or Hard of Hearing4.268537722.992432Visually Impaired7.293661940.758719Emotional/Behavioral Disability-6.4365219.422141Specific Learning Disability-1.2075558.3594024Autism Spectrum Disorder-8.93258522.48474Other Health Impaired-4.25366910.83725Intellectual Disability8.474910472.253255Enrolled in 2 or more Courses6.0482311.8277423Enrolled in 3 or more Courses6.66781382.1180171Enrolled in 4 or more Courses1.45452736.5435769Enrolled in 5 or more Courses7.055179840.711496Homogeneity of Class 1 Prior Year Test Scores0.00062980.0048649Homogeneity of Class 2 Prior Year Test Scores0.00509580.0059813Missing Homogeneity of Class 2 Prior Year Test Scores-0.9744222.7331346Homogeneity of Class 3 Prior Year Test Scores0.00647450.0076982Missing Homogeneity of Class 3 Prior Year Test Scores0.28686533.0383583Homogeneity of Class 4 Prior Year Test Scores0.00152220.0099288Missing Homogeneity of Class 4 Prior Year Test Scores5.05980053.7625568Homogeneity of Class 5 Prior Year Test Scores0.00563360.0142427Missing Homogeneity of Class 5 Prior Year Test Scores-3.6887585.464738Homogeneity of Class 6 Prior Year Test Scores0.01183240.0193209Missing Homogeneity of Class 6 Prior Year Test Scores11.6749217.1307045Number of Students in Class 1-0.4314340.0750854Number of Students in Class 2-0.1747290.0544604Number of Students in Class 30.08869440.0537982Number of Students in Class 40.07102030.0476787Number of Students in Class 50.05937460.0717484Number of Students in Class 6-0.0722240.1072331Difference from Modal Age-21.746670.8452812Gifted Student Indicator26.525859.6284085English Language Learner Indicator11.6804569.0500104Achievement: Two Years Prior0.61572190.0049343Achievement: Prior Year0.28718290.004357*Attendance and mobility variables are not included in the model because the data is not reported until August during the Survey 5 data collection.Table 3. Fixed Effects: Grade 6 Reading, 2010-11Effect NameEffectStandard ErrorConstant Term185.1010915.220935Language Impaired-32.918743.6205578Deaf or Hard of Hearing-28.7174925.055512Visually Impaired16.34446337.652171Emotional/Behavioral Disability2.750239318.314297Specific Learning Disability-6.4676667.5383492Autism Spectrum Disorder39.79111923.979703Traumatic Brain Injured158.05119114.06117Other Health Impaired-5.13517210.794594Intellectual Disability-15.6795558.345302Enrolled in 2 or more Courses40.760352.3361209Enrolled in 3 or more Courses7.29549532.7675227Enrolled in 4 or more Courses-18.524497.2056249Enrolled in 5 or more Courses71.7123931.914473Enrolled in 6 or more Courses-103.1539112.03514Homogeneity of Class 1 Prior Year Test Scores-0.0243830.0045525Homogeneity of Class 2 Prior Year Test Scores0.03011480.0053888Missing Homogeneity of Class 2 Prior Year Test Scores22.5004933.4804005Homogeneity of Class 3 Prior Year Test Scores0.03721260.0085022Missing Homogeneity of Class 3 Prior Year Test Scores8.84975044.0602352Homogeneity of Class 4 Prior Year Test Scores0.00564580.0125294Missing Homogeneity of Class 4 Prior Year Test Scores12.0479225.8523024Homogeneity of Class 5 Prior Year Test Scores-0.0024970.0208034Missing Homogeneity of Class 5 Prior Year Test Scores-13.0662310.087556Homogeneity of Class 6 Prior Year Test Scores0.04281240.0305257Missing Homogeneity of Class 6 Prior Year Test Scores25.04890414.439612Number of Students in Class 1-0.8740860.1029611Number of Students in Class 20.12979290.1134076Number of Students in Class 30.36812580.1602223Number of Students in Class 40.26826210.2239495Number of Students in Class 5-0.2804730.3691364Number of Students in Class 60.31281810.5480409Difference from Modal Age-28.681920.7866967Gifted Student Indicator26.23589410.593017English Language Learner Indicator-7.39630611.468293Achievement: Two Years Prior0.54566520.0060109Achievement: Prior Year0.37956540.005862*Attendance and mobility variables are not included in the model because the data is not reported until August during the Survey 5 data collection.Table 4. Fixed Effects: Grade 7 Reading, 2010-11Effect NameEffectStandard ErrorConstant Term155.3637415.110568Language Impaired-14.229133.5817283Deaf or Hard of Hearing-21.3090324.847463Visually Impaired-61.3377133.697251Emotional/Behavioral Disability-51.9105512.863482Specific Learning Disability-13.154116.5911623Autism Spectrum Disorder-31.2138923.337236Traumatic Brain Injured53.36182784.280827Other Health Impaired-5.52414210.45156Intellectual Disability66.62765663.863361Enrolled in 2 or more Courses67.1943672.0401473Enrolled in 3 or more Courses3.8442242.7539806Enrolled in 4 or more Courses-20.714587.3352801Enrolled in 5 or more Courses-9.9633827.142661Enrolled in 6 or more Courses202.02481134.70919Homogeneity of Class 1 Prior Year Test Scores-0.0278590.0040749Homogeneity of Class 2 Prior Year Test Scores0.04621480.0051846Missing Homogeneity of Class 2 Prior Year Test Scores16.6949143.0635009Homogeneity of Class 3 Prior Year Test Scores0.03625930.0078308Missing Homogeneity of Class 3 Prior Year Test Scores3.30793913.7958Homogeneity of Class 4 Prior Year Test Scores0.02170780.0124716Missing Homogeneity of Class 4 Prior Year Test Scores23.070535.8059018Homogeneity of Class 5 Prior Year Test Scores-0.0008650.0213881Missing Homogeneity of Class 5 Prior Year Test Scores-11.556779.8111999Homogeneity of Class 6 Prior Year Test Scores0.02874110.0317961Missing Homogeneity of Class 6 Prior Year Test Scores25.95570113.486732Number of Students in Class 1-0.9012540.0962286Number of Students in Class 20.15846820.1053166Number of Students in Class 30.20124580.1478354Number of Students in Class 40.59723750.2255181Number of Students in Class 50.37257540.380186Number of Students in Class 60.09986840.5126824Difference from Modal Age-16.444470.6837645Gifted Student Indicator-13.154949.3731567English Language Learner Indicator2.176783211.386944Achievement: Two Years Prior0.80561860.006981Achievement: Prior Year0.12951940.0053304*Attendance and mobility variables are not included in the model because the data is not reported until August during the Survey 5 data collection.Table 5. Fixed Effects: Grade 8 Reading, 2010-11Effect NameEffectStandard ErrorConstant Term510.4960612.002591Language Impaired-11.215662.9756546Deaf or Hard of Hearing-3.1807316.191602Visually Impaired-36.8178327.275501Emotional/Behavioral Disability8.210836710.68379Specific Learning Disability-9.4943285.1545126Autism Spectrum Disorder6.584113916.937298Traumatic Brain Injured17.05647764.747293Other Health Impaired-5.0902647.7142389Intellectual Disability-18.1649650.290433Enrolled in 2 or more Courses45.5723321.5451605Enrolled in 3 or more Courses3.02053382.1703055Enrolled in 4 or more Courses-6.8647116.0855819Enrolled in 5 or more Courses7.587275921.488679Enrolled in 6 or more Courses29.61999967.212724Homogeneity of Class 1 Prior Year Test Scores-0.0414850.0036467Homogeneity of Class 2 Prior Year Test Scores0.0213260.0045318Missing Homogeneity of Class 2 Prior Year Test Scores11.7472752.3526687Homogeneity of Class 3 Prior Year Test Scores0.02255210.0070363Missing Homogeneity of Class 3 Prior Year Test Scores8.00944973.0045083Homogeneity of Class 4 Prior Year Test Scores-0.0182950.0110015Missing Homogeneity of Class 4 Prior Year Test Scores7.89142094.3811562Homogeneity of Class 5 Prior Year Test Scores-0.002210.016882Missing Homogeneity of Class 5 Prior Year Test Scores2.69023047.6050919Homogeneity of Class 6 Prior Year Test Scores0.03498120.025556Missing Homogeneity of Class 6 Prior Year Test Scores18.13110710.55741Number of Students in Class 1-0.6453690.0732871Number of Students in Class 20.16596040.0810282Number of Students in Class 30.29665070.116208Number of Students in Class 40.40302850.1651929Number of Students in Class 50.48986530.2967227Number of Students in Class 60.14265410.4275934Difference from Modal Age-20.066010.5260609Gifted Student Indicator17.7201238.1612659English Language Learner Indicator-1.0760969.0620833Achievement: Two Years Prior0.58827860.0061952Achievement: Prior Year0.1554930.0046034*Attendance and mobility variables are not included in the model because the data is not reported until August during the Survey 5 data collection.Table 6. Fixed Effects: Grade 9 Reading, 2010-11Effect NameEffectStandard ErrorConstant Term127.4044815.481277Language Impaired-0.8406784.1586213Deaf or Hard of Hearing20.68068919.605202Visually Impaired72.17126428.722217Emotional/Behavioral Disability10.65868512.7573Specific Learning Disability4.46125186.6694999Autism Spectrum Disorder45.55529924.694002Traumatic Brain Injured45.62533166.069946Other Health Impaired-8.68775710.139713Intellectual Disability-24.6451853.619393Enrolled in 2 or more Courses42.9617831.7596205Enrolled in 3 or more Courses4.66824082.552918Enrolled in 4 or more Courses-14.064068.5764983Enrolled in 5 or more Courses42.50582327.673554Enrolled in 6 or more Courses-174.062259.402781Homogeneity of Class 1 Prior Year Test Scores-0.0234680.0052577Homogeneity of Class 2 Prior Year Test Scores0.01938420.00667Missing Homogeneity of Class 2 Prior Year Test Scores7.95429162.6044556Homogeneity of Class 3 Prior Year Test Scores0.03652520.010047Missing Homogeneity of Class 3 Prior Year Test Scores9.39470163.5393383Homogeneity of Class 4 Prior Year Test Scores0.02399870.0155308Missing Homogeneity of Class 4 Prior Year Test Scores20.3860835.3169434Homogeneity of Class 5 Prior Year Test Scores0.010490.0242804Missing Homogeneity of Class 5 Prior Year Test Scores9.84319418.7922832Homogeneity of Class 6 Prior Year Test Scores-0.0027310.0356633Missing Homogeneity of Class 6 Prior Year Test Scores0.196738612.657417Number of Students in Class 1-0.1582050.0611601Number of Students in Class 2-0.1257010.0716625Number of Students in Class 30.2965680.1122744Number of Students in Class 40.47739060.1716203Number of Students in Class 50.45255740.2796822Number of Students in Class 60.37300670.3957175Difference from Modal Age-21.62270.6116351Gifted Student Indicator27.45859310.206285English Language Learner Indicator10.88919911.509281Achievement: Two Years Prior0.59352530.0088751Achievement: Prior Year0.35354650.0062352*Attendance and mobility variables are not included in the model because the data is not reported until August during the Survey 5 data collection.Table 7. Fixed Effects: Grade 10 Reading, 2010-11Effect NameEffectStandard ErrorConstant Term-431.188118.092754Language Impaired-9.972315.2509912Deaf or Hard of Hearing-61.1001726.715485Visually Impaired-45.6831551.321393Emotional/Behavioral Disability-42.6423316.004993Specific Learning Disability-19.175548.1293353Autism Spectrum Disorder57.92423431.22077Traumatic Brain Injured81.18805269.734566Other Health Impaired0.419988412.199827Intellectual Disability-108.701971.258538Enrolled in 2 or more Courses62.0596882.5594101Enrolled in 3 or more Courses-2.1297422.9216503Enrolled in 4 or more Courses-5.01511710.434636Enrolled in 5 or more Courses-79.852349.90915Enrolled in6or more Courses98.073897187.10616Homogeneity of Class 1 Prior Year Test Scores0.02558740.0058464Homogeneity of Class 2 Prior Year Test Scores0.03877350.0065963Missing Homogeneity of Class 2 Prior Year Test Scores-2.8803713.25385Homogeneity of Class 3 Prior Year Test Scores0.0381790.0094606Missing Homogeneity of Class 3 Prior Year Test Scores-9.0387223.4148536Homogeneity of Class 4 Prior Year Test Scores0.023950.0148029Missing Homogeneity of Class 4 Prior Year Test Scores8.85020435.2435971Homogeneity of Class 5 Prior Year Test Scores0.0277360.0261934Missing Homogeneity of Class 5 Prior Year Test Scores4.13898569.439345Homogeneity of Class 6 Prior Year Test Scores0.14219120.0423349Missing Homogeneity of Class 6 Prior Year Test Scores30.10912615.091074Number of Students in Class 1-0.6000120.0826493Number of Students in Class 2-0.9796780.0856548Number of Students in Class 3-0.6902890.1184854Number of Students in Class 4-0.1500250.1887817Number of Students in Class 5-0.0696480.3401006Number of Students in Class 6-0.5882130.5329186Difference from Modal Age-6.7317470.7739671Gifted Student Indicator-2.16280612.69541English Language Learner Indicator12.94452615.682365Achievement: Two Years Prior0.73246250.0094948Achievement: Prior Year0.49100350.008455*Attendance and mobility variables are not included in the model because the data is not reported until August during the Survey 5 data collection.Table 8. Fixed Effects: Grade 4 Mathematics, 2010-11Effect NameEffectStandard ErrorConstant Term385.5223123.339473Language Impaired-3.8402652.2364243Deaf or Hard of Hearing-21.9234120.422514Visually Impaired26.41933430.738627Emotional/Behavioral Disability-51.5870115.515694Specific Learning Disability-23.893846.052578Dual-Sensory Impaired-497.13251.98334Autism Spectrum Disorder-58.0008817.436335Traumatic Brain Injured-252.2642114.85163Other Health Impaired-28.206618.6586249Intellectual Disability-97.0566653.59785Enrolled in 2 or more Courses3.49898942.2309281Enrolled in 3 or more Courses-42.0327318.825657Enrolled in 4 or more Courses-368.5785133.77785Homogeneity of Class 1 Prior Year Test Scores-0.0033660.0050922Homogeneity of Class 2 Prior Year Test Scores0.01304930.0072015Missing Homogeneity of Class 2 Prior Year Test Scores18.3339752.6051637Homogeneity of Class 3 Prior Year Test Scores-0.0330510.0132369Missing Homogeneity of Class 3 Prior Year Test Scores7.30962644.5309252Homogeneity of Class 4 Prior Year Test Scores0.03259010.0223476Missing Homogeneity of Class 4 Prior Year Test Scores11.3375117.6242129Homogeneity of Class 5 Prior Year Test Scores-0.0014230.0440533Missing Homogeneity of Class 5 Prior Year Test Scores1.143140613.665091Homogeneity of Class 6 Prior Year Test Scores0.06078410.0630242Missing Homogeneity of Class 6 Prior Year Test Scores19.45216323.807657Number of Students in Class 10.58621140.0650804Number of Students in Class 20.28331420.0639089Number of Students in Class 30.32769350.0830953Number of Students in Class 40.08993910.202489Number of Students in Class 5-0.1534490.1965843Number of Students in Class 60.87209851.0114603Difference from Modal Age-20.854720.6392342Gifted Student Indicator-10.816657.4334099English Language Learner Indicator17.3237911.2702079Achievement: Prior Year0.76041990.0019948*Attendance and mobility variables are not included in the model because the data is not reported until August during the Survey 5 data collection.Table 9. Fixed Effects: Grade 5 Mathematics, 2010-11Effect NameEffectStandard ErrorConstant Term244.2376719.500574Language Impaired-5.6698532.3171212Deaf or Hard of Hearing6.160095117.802791Visually Impaired-28.4764227.251441Emotional/Behavioral Disability-29.0774214.503526Specific Learning Disability-21.682916.1518216Autism Spectrum Disorder-42.180617.442558Other Health Impaired-12.391817.9562714Intellectual Disability-93.0494153.300141Enrolled in 2 or more Courses-1.3196872.0525284Enrolled in 3 or more Courses20.8447816.691847Enrolled in 4 or more Courses-64.8428154.72298Homogeneity of Class 1 Prior Year Test Scores-0.0188240.0054563Homogeneity of Class 2 Prior Year Test Scores0.0073510.0075638Missing Homogeneity of Class 2 Prior Year Test Scores11.5343412.4500363Homogeneity of Class 3 Prior Year Test Scores-0.0213990.0137758Missing Homogeneity of Class 3 Prior Year Test Scores6.65510914.2433632Homogeneity of Class 4 Prior Year Test Scores-0.0686020.0222075Missing Homogeneity of Class 4 Prior Year Test Scores-9.9046537.2831844Homogeneity of Class 5 Prior Year Test Scores0.03662880.0416947Missing Homogeneity of Class 5 Prior Year Test Scores34.32682214.746744Homogeneity of Class 6 Prior Year Test Scores-0.1796570.051917Missing Homogeneity of Class 6 Prior Year Test Scores-16.9358520.531083Number of Students in Class 10.46210610.0578507Number of Students in Class 20.27185670.0651857Number of Students in Class 30.32149840.0771496Number of Students in Class 40.12476120.2014734Number of Students in Class 50.5945540.4095525Number of Students in Class 60.94898150.9697296Difference from Modal Age-26.477380.640783Gifted Student Indicator13.1589227.0424124English Language Learner Indicator-10.765926.8759636Achievement: Two Years Prior0.74133520.0088471Achievement: Prior Year0.16051770.0070271*Attendance and mobility variables are not included in the model because the data is not reported until August during the Survey 5 data collection.Table 10. Fixed Effects: Grade 6 Mathematics, 2010-11Effect NameEffectStandard ErrorConstant Term215.1692639.42855Language Impaired-3.5780542.7135199Deaf or Hard of Hearing3.232569918.248699Visually Impaired-37.4427628.841561Emotional/Behavioral Disability-12.1504614.321627Specific Learning Disability-12.048525.7694111Autism Spectrum Disorder38.64458817.710852Traumatic Brain Injured67.82083190.205902Other Health Impaired-19.992488.3185141Intellectual Disability-49.4143550.290204Enrolled in 2 or more Courses36.3449551.5058887Enrolled in 3 or more Courses-1.1637215.4352515Enrolled in 4 or more Courses-31.8554444.447289Homogeneity of Class 1 Prior Year Test Scores-0.0371420.0048198Homogeneity of Class 2 Prior Year Test Scores0.00608410.0075158Missing Homogeneity of Class 2 Prior Year Test Scores26.986042.7512198Homogeneity of Class 3 Prior Year Test Scores0.01827850.0148413Missing Homogeneity of Class 3 Prior Year Test Scores21.8037275.1053418Homogeneity of Class 4 Prior Year Test Scores-0.0132190.0289149Missing Homogeneity of Class 4 Prior Year Test Scores1.96475959.4642018Homogeneity of Class 5 Prior Year Test Scores-0.0445260.0716354Missing Homogeneity of Class 5 Prior Year Test Scores-3.50440625.140907Homogeneity of Class 6 Prior Year Test Scores0.2268560.1573563Missing Homogeneity of Class 6 Prior Year Test Scores-5.98991843.07707Number of Students in Class 10.05467730.0781862Number of Students in Class 20.6159980.0971443Number of Students in Class 30.55742550.1724428Number of Students in Class 40.02526680.2912048Number of Students in Class 50.50922250.9382771Number of Students in Class 6-2.9131451.5274348Difference from Modal Age-19.80030.5728757Gifted Student Indicator-8.1157386.748183English Language Learner Indicator-14.216518.6379161Achievement: Two Years Prior0.66545490.0069056Achievement: Prior Year0.22824010.0061245*Attendance and mobility variables are not included in the model because the data is not reported until August during the Survey 5 data collection.Table 11. Fixed Effects: Grade 7 Mathematics, 2010-11Effect NameEffectStandard ErrorConstant Term501.116833.944595Language Impaired9.56167692.457258Deaf or Hard of Hearing-9.1741417.010014Visually Impaired9.914763425.406372Emotional/Behavioral Disability9.68762219.4042094Specific Learning Disability2.39470864.5619344Autism Spectrum Disorder7.105490714.804152Traumatic Brain Injured89.86398654.581504Other Health Impaired10.4730047.2771765Intellectual Disability-35.9431645.337656Enrolled in 2 or more Courses33.7686581.1395593Enrolled in 3 or more Courses-1.1807033.8026075Enrolled in 4 or more Courses43.18067562.284664Homogeneity of Class 1 Prior Year Test Scores0.00108880.0035572Homogeneity of Class 2 Prior Year Test Scores0.01907240.0056438Missing Homogeneity of Class 2 Prior Year Test Scores15.8141712.1687938Homogeneity of Class 3 Prior Year Test Scores0.01922970.0113031Missing Homogeneity of Class 3 Prior Year Test Scores10.6172723.9666914Homogeneity of Class 4 Prior Year Test Scores-0.0001290.0226006Missing Homogeneity of Class 4 Prior Year Test Scores-4.8320157.504312Homogeneity of Class 5 Prior Year Test Scores-0.0150290.0468479Missing Homogeneity of Class 5 Prior Year Test Scores7.930956418.191022Homogeneity of Class 6 Prior Year Test Scores0.03125020.0983872Missing Homogeneity of Class 6 Prior Year Test Scores9.51611534.765109Number of Students in Class 1-0.1518850.0596904Number of Students in Class 20.389130.0782597Number of Students in Class 30.18921020.1344612Number of Students in Class 4-0.0121360.233502Number of Students in Class 50.23959930.6105321Number of Students in Class 6-0.0575931.1487586Difference from Modal Age-10.886870.4390447Gifted Student Indicator-0.2154785.1783613English Language Learner Indicator4.06896567.498834Achievement: Two Years Prior0.67647830.0053744Achievement: Prior Year0.07675840.004823*Attendance and mobility variables are not included in the model because the data is not reported until August during the Survey 5 data collection.Table 12. Fixed Effects: Grade 8 Mathematics, 2010-11Effect NameEffectStandard ErrorConstant Term614.8553626.888289Language Impaired10.8036282.066494Deaf or Hard of Hearing18.82400311.071911Visually Impaired32.53238523.114175Emotional/Behavioral Disability-6.1320187.7828823Specific Learning Disability10.2755973.6454513Autism Spectrum Disorder15.83431611.482713Traumatic Brain Injured5.235510643.167249Other Health Impaired2.38172835.5117007Intellectual Disability28.35589165.253012Enrolled in 2 or more Courses14.9564640.8741064Enrolled in 3 or more Courses-3.5611522.5547497Enrolled in 4 or more Courses44.97375820.952594Homogeneity of Class 1 Prior Year Test Scores0.00597850.0033737Homogeneity of Class 2 Prior Year Test Scores0.03035040.0050766Missing Homogeneity of Class 2 Prior Year Test Scores20.7748051.5353988Homogeneity of Class 3 Prior Year Test Scores0.01901570.009875Missing Homogeneity of Class 3 Prior Year Test Scores-0.3763432.83383Homogeneity of Class 4 Prior Year Test Scores0.01525130.0178199Missing Homogeneity of Class 4 Prior Year Test Scores6.56150445.0576898Homogeneity of Class 5 Prior Year Test Scores-0.0410890.0490118Missing Homogeneity of Class 5 Prior Year Test Scores-8.99807511.911559Homogeneity of Class 6 Prior Year Test Scores0.1214440.0961515Missing Homogeneity of Class 6 Prior Year Test Scores55.35603927.527077Number of Students in Class 1-0.0858740.0472429Number of Students in Class 20.66326290.0558654Number of Students in Class 30.16017290.0990379Number of Students in Class 40.20321720.171318Number of Students in Class 5-0.2956910.3921755Number of Students in Class 62.24426240.9671986Difference from Modal Age-6.1284620.3385457Gifted Student Indicator9.84694454.5067393English Language Learner Indicator-4.7475375.9790561Achievement: Two Years Prior0.58451320.0058883Achievement: Prior Year0.09321350.004312*Attendance and mobility variables are not included in the model because the data is not reported until August during the Survey 5 data collection.Table 13. Fixed Effects: Grade 10 Mathematics, 2010-11Effect NameEffectStandard ErrorConstant Term281.3153514.591631Language Impaired9.27141321.9721118Deaf or Hard of Hearing12.1139339.5204873Visually Impaired3.080017425.00785Emotional/Behavioral Disability8.28835815.8676514Specific Learning Disability4.15419612.9946882Autism Spectrum Disorder1.13274659.5835244Traumatic Brain Injured-16.9628537.23783Other Health Impaired-4.1685034.3417563Intellectual Disability3.223481825.434598Enrolled in 2 or more Courses13.7962680.630254Enrolled in 3 or more Courses4.10425321.8515109Enrolled in 4 or more Courses-22.474138.5776429Enrolled in 5 or more Courses-119.172756.524715Homogeneity of Class 1 Prior Year Test Scores-0.0163240.0023542Homogeneity of Class 2 Prior Year Test Scores0.0081510.0040097Missing Homogeneity of Class 2 Prior Year Test Scores8.14714430.8601868Homogeneity of Class 3 Prior Year Test Scores0.01872260.0087236Missing Homogeneity of Class 3 Prior Year Test Scores5.93212661.9389153Homogeneity of Class 4 Prior Year Test Scores0.00425550.0150524Missing Homogeneity of Class 4 Prior Year Test Scores2.33563583.3620025Homogeneity of Class 5 Prior Year Test Scores0.0805470.0322793Missing Homogeneity of Class 5 Prior Year Test Scores-0.6911267.5575477Homogeneity of Class 6 Prior Year Test Scores-0.1070140.0725176Missing Homogeneity of Class 6 Prior Year Test Scores-37.261114.208512Number of Students in Class 10.23959780.0234322Number of Students in Class 20.29565420.03489Number of Students in Class 30.28646380.0819374Number of Students in Class 40.1215520.1421114Number of Students in Class 5-0.6683940.3191165Number of Students in Class 6-0.8911070.5996503Difference from Modal Age-8.9714770.252136Gifted Student Indicator2.15135533.8364851English Language Learner Indicator15.7914095.3689794Achievement: Two Years Prior0.68917910.0071194Achievement: Prior Year0.20858410.0061022*Attendance and mobility variables are not included in the model because the data is not reported until August during the Survey 5 data collection.Appendix D. Teacher Value-Added Scores by DistrictTable 1. Mean and Standard Deviation of Teacher Value-Added Scores by District: Grade 4, 2010-11DistrictMathematicsReadingMeanStd. Dev.NMeanStd. Dev.NALACHUA-0.7946.721472.0521.75145BAKER-16.2761.5613-21.7021.8913BAY-3.2151.451233.4024.29130BRADFORD-25.9036.5414-15.3313.7216BREVARD4.8140.243873.1717.58416BROWARD9.2843.9410801.8922.251125CALHOUN-5.7820.756-3.3418.208CHARLOTTE-8.9329.88733.6521.9077CITRUS17.6536.59784.3522.9893CLAY-2.6038.12167-2.4418.86184COLLIER-5.2945.52206-0.5620.09253COLUMBIA-1.5534.5537-0.1111.8338DADE4.2548.9212505.1626.371476DEAF/BLIND**3**3DESOTO1.9345.7323-7.2517.8224DIXIE9.7540.6611-4.6717.4616DUVAL15.1744.81545-4.2022.47571ESCAMBIA-0.0945.97242-2.2821.90249FAMU LAB SCH**2**2FAU LAB SCH12.5628.1211-0.5219.7011FL VIRTUAL**2**2FLAGLER-20.0746.7242-3.9522.2154FRANKLIN-0.6054.705-8.8534.067FSU LAB SCH38.3727.591125.658.3114GADSDEN37.9246.13280.1631.4031GILCHRIST21.6359.651310.7139.0915GLADES-13.4825.968-3.2813.308GULF30.9145.66111.8326.0212HAMILTON2.0538.146-2.5111.2710HARDEE7.5637.4824-10.6417.6829HENDRY9.7436.6928-2.0921.1731HERNANDO-9.4540.48105-3.0221.65108HIGHLANDS-5.8145.5263-2.3019.5771HILLSBOROUGH-4.3841.289102.9519.84973HOLMES22.9337.03141.3633.0512INDIAN RIVER3.2635.64781.9120.3274JACKSON28.4845.553112.5117.5936JEFFERSON11.8653.72759.0231.987LAFAYETTE**4-7.6810.418LAKE-1.4845.03190-4.8618.12201LEE6.0542.294211.1120.67448LEON1.0735.32168-0.5720.51173LEVY-0.9527.5426-11.1813.2431LIBERTY-8.6933.566-3.2112.499MADISON-44.3957.0012-5.0223.9618MANATEE5.3639.602300.5019.31239MARION1.3942.49199-6.9018.76248MARTIN12.6035.2279-1.9320.8986MONROE18.9144.6237-12.7018.3644NASSAU10.7348.33458.0517.9848OKALOOSA-9.3535.3895-0.6118.38127OKEECHOBEE2.5035.0533-3.6923.7236ORANGE-0.2541.21848-2.0120.48892OSCEOLA-2.9936.662295.2717.75279PALM BEACH3.7043.955467.5519.76945PASCO-8.1638.91361-6.6719.36399PINELLAS-10.5839.92451-1.1419.02456POLK-8.7839.15528-3.7921.80531PUTNAM27.7044.18523.4715.6894SANTA ROSA-1.5544.221153.1620.04119SARASOTA-14.7647.221741.1021.15202SEMINOLE5.2036.482910.6419.20309ST. JOHNS-6.5039.851347.3022.94141ST. LUCIE0.3440.58187-10.8822.02202SUMTER12.3837.12278.1224.1739SUWANNEE9.0337.2429-3.8322.1729TAYLOR-20.7164.6083.7529.0512UF LAB SCH**3**3UNION38.3957.871215.1615.2912VOLUSIA-8.5836.80351-4.5117.26399WAKULLA-13.9949.23292.3424.8528WALTON10.5833.68346.3316.3636WASHINGTON3.6369.58153.6224.1815State Avg.1.0943.25117340.6521.6713157Table 2. Mean and Standard Deviation of Teacher Value-Added Scores by District: Grade 5, 2010-11DistrictMathematicsReadingMeanStd. Dev.NMeanStd. Dev.NALACHUA3.2739.771341.4918.60121BAKER-25.5437.5712-22.9612.3812BAY2.0739.811121.5316.07121BRADFORD-7.7437.2812-4.3716.3213BREVARD0.2231.51365-2.4914.46408BROWARD5.3734.111021-1.3818.321060CALHOUN3.8932.979-6.6111.5114CHARLOTTE-0.7938.00595.9917.6871CITRUS9.2431.08664.1913.9183CLAY0.0332.48132-3.4714.47157COLLIER-6.5436.54203-7.0914.07229COLUMBIA2.1011.12132.489.0414DADE-0.7643.6210973.4620.091345DEAF/BLIND**4**4DESOTO1.1134.4919-17.1731.5118DIXIE**415.0420.087DUVAL0.9135.98507-1.3516.89548ESCAMBIA-3.5042.86223-0.3918.98231FAMU LAB SCH**2**2FAU LAB SCH17.1323.5393.0017.7911FL VIRTUAL**2***FLAGLER-12.9841.51375.2515.5545FRANKLIN**4-0.788.676FSU LAB SCH4.6432.0792.329.659GADSDEN25.7549.31249.5840.2624GILCHRIST-16.6151.12139.0115.9214GLADES-8.4020.535-17.6025.519GULF-16.2339.929-1.7615.1112HAMILTON-3.4332.156-4.439.2010HARDEE-4.5833.9023-10.5712.8428HENDRY10.8045.25270.3715.9630HERNANDO-14.5827.5099-3.5216.23103HIGHLANDS-17.2439.3758-7.3817.7762HILLSBOROUGH-1.1530.708921.2314.73955HOLMES-14.2549.93113.0913.3513INDIAN RIVER8.6930.2075-3.5713.1374JACKSON-20.3563.69282.5714.2935JEFFERSON42.8029.43819.6525.488LAFAYETTE**3-0.439.235LAKE-2.7033.341630.2715.99182LEE12.2835.84382-4.8315.24396LEON3.4135.621686.6120.38166LEVY-15.2635.3328-3.8912.1034LIBERTY-3.5032.23621.8011.338MADISON-25.2535.39117.8817.1016MANATEE8.2533.15227-1.5412.94224MARION1.2828.97168-3.8817.51223MARTIN9.2830.74700.0413.2078MONROE4.2324.6230-4.4611.0338NASSAU3.3128.6840-3.2913.7746OKALOOSA0.8032.0385-1.8613.32123OKEECHOBEE6.2547.9424-12.3818.2432ORANGE3.3032.817651.5715.66808OSCEOLA8.5630.422212.9914.61276PALM BEACH-1.5834.765033.3315.40791PASCO2.1134.72351-2.0515.69378PINELLAS-5.7637.26454-1.6914.72455POLK-6.6833.95532-1.0416.62535PUTNAM11.0032.7051-2.4413.2077SANTA ROSA0.3535.391084.2718.56114SARASOTA1.5940.721544.3918.43185SEMINOLE3.9128.512882.4814.91292ST. JOHNS4.3133.201169.9715.92129ST. LUCIE5.0635.74165-0.0014.44187SUMTER17.8528.202110.8514.9935SUWANNEE13.3822.20183.5717.5618TAYLOR-33.2553.337-13.0513.7813UF LAB SCH**3**3UNION-12.9843.247-13.8127.487VOLUSIA-3.5533.82342-6.5513.51366WAKULLA1.4730.03266.2217.3526WALTON17.4926.55323.9312.6035WASHINGTON-80.4149.256-6.2412.4410State Avg.0.8635.82108780.1016.9012182Table 3. Mean and Standard Deviation of Teacher Value-Added Scores by District: Grade 6, 2010-11DistrictMathematicsReadingMeanStd. Dev.NMeanStd. Dev.NALACHUA-5.1627.1861-7.5914.7591BAKER48.0434.67142.477.8412BAY-2.9925.7954-6.5614.8878BRADFORD-9.7930.987-5.7611.0714BREVARD36.1427.503157.9715.54342BROWARD-1.3224.933262.6017.24556CALHOUN3.2523.488-6.4711.5610CHARLOTTE-12.3117.5826-0.8717.2936CITRUS-9.7017.0035-17.2512.8236CLAY19.8321.58964.2612.61126COLLIER11.2120.34719.0512.94131COLUMBIA-8.098.438-13.904.6311DADE-10.6827.727136.7019.50962DEAF/BLIND**2**4DESOTO-9.5220.3010-18.4819.7111DIXIE**218.437.345DUVAL-15.7923.49238-6.2315.19310ESCAMBIA-14.7621.9878-13.6417.14130FAMU LAB SCH**1**2FAU LAB SCH25.1419.11736.8610.1010FL VIRTUAL**1**1FLAGLER7.7419.59356.2910.8839FRANKLIN-19.5628.265-6.827.605FSU LAB SCH**3**3GADSDEN0.4830.3117-21.1725.2421GILCHRIST**3-4.794.229GLADES**4-6.3822.118GULF-24.3215.576-2.5710.358HAMILTON51.7642.096-12.4710.3412HARDEE-12.7213.128-3.8112.4311HENDRY-20.2221.309-19.169.5113HERNANDO-8.1623.0950-5.1912.0169HIGHLANDS15.8023.80344.3612.3539HILLSBOROUGH0.3121.51328-11.4115.50487HOLMES19.0427.4310-5.519.2810INDIAN RIVER2.0717.7336-5.8413.3246JACKSON-12.9214.3116-0.0914.9824JEFFERSON-3.054.8271.003.895LAFAYETTE**1**1LAKE-2.8623.7671-3.0415.53106LEE-3.0924.32147-8.9914.37229LEON3.9624.1071-2.2514.7092LEVY2.3522.9419-4.9915.1826LIBERTY24.5923.129**4MADISON-10.838.306-15.947.578MANATEE-5.8723.5583-1.3813.25114MARION-8.1617.98772.4012.02128MARTIN3.5123.5729-0.939.8652MONROE16.8017.122110.877.6735NASSAU0.3211.9522-6.8412.1228OKALOOSA4.3923.78642.2312.4157OKEECHOBEE8.2129.5912-4.0811.9321ORANGE-3.8422.772232.4314.35361OSCEOLA0.5222.341017.6313.57130PALM BEACH2.8325.503284.1416.89392PASCO7.5722.87137-2.2512.15240PINELLAS-13.6321.62199-11.6815.35240POLK-15.6622.76195-3.8512.46304PUTNAM-4.2234.2326-18.6515.5357SANTA ROSA-5.3520.67480.0411.2261SARASOTA5.7925.66918.8517.6387SEMINOLE-2.0623.781185.9711.20163ST. JOHNS1.6030.63728.9122.0165ST. LUCIE3.1623.57851.2512.30142SUMTER-6.5030.8710-13.1412.5723SUWANNEE-6.4812.16130.419.2817TAYLOR-0.7226.67119.6813.1112UF LAB SCH**1**3UNION-7.3410.99512.226.618VOLUSIA-10.4921.84110-12.1111.23179WAKULLA11.1221.0115-10.129.0716WALTON19.3522.3422-0.9715.8322WASHINGTON-8.9116.856-6.8413.757State Avg.-0.8827.485078-0.6617.067091Table 4. Mean and Standard Deviation of Teacher Value-Added Scores by District: Grade 7, 2010-11DistrictMathematicsReadingMeanStd. Dev.NMeanStd. Dev.NALACHUA-0.6716.6867-3.1414.2794BAKER-10.479.2187.4415.4211BAY3.9917.5861-1.2213.0475BRADFORD-0.1614.349-5.738.2113BREVARD-11.0516.87127-8.5215.45152BROWARD-3.4717.47364-2.5017.11572CALHOUN-0.3314.2910-20.019.8515CHARLOTTE7.1618.27268.8515.4243CITRUS2.5418.1444-11.8117.0947CLAY-5.8316.13651.4312.3780COLLIER7.2715.77635.1514.73123COLUMBIA-9.8611.2192.206.8810DADE-0.3617.778149.2716.94996DEAF/BLIND**2**3DESOTO-2.0230.06122.3514.7318DIXIE-4.404.1159.7210.607DUVAL1.7816.262701.9814.11342ESCAMBIA-3.0914.8981-9.4517.34124FAMU LAB SCH**1**2FAU LAB SCH-1.6212.8070.785.2011FL VIRTUAL**1**1FLAGLER2.8614.6831-1.5013.7229FRANKLIN**41.9919.607FSU LAB SCH**3**4GADSDEN-8.7314.4213-2.9220.2319GILCHRIST**4-14.449.348GLADES**4-15.889.3312GULF4.9913.688-1.3214.729HAMILTON**4-8.419.315HARDEE-14.0915.6862.2015.6610HENDRY-6.4116.398-10.7116.7914HERNANDO3.0815.01513.5813.8761HIGHLANDS8.7613.44326.0913.7435HILLSBOROUGH2.9215.77383-5.1015.39492HOLMES-0.0719.369-15.9116.5219INDIAN RIVER4.1515.4736-13.1417.8949JACKSON-2.0614.5117-9.1916.3527JEFFERSON-10.5211.897-0.502.247LAFAYETTE**2**2LAKE-0.4515.1579-0.0915.61112LEE7.9816.16170-2.4216.59279LEON1.2217.9194-0.3319.4489LEVY1.9617.4719-0.8222.4321LIBERTY7.7516.359-13.4116.529MADISON0.0813.1675.999.4310MANATEE1.7514.78991.7013.53122MARION-1.7317.77846.8011.40136MARTIN1.3014.5035-12.1716.7250MONROE1.3817.3325-2.3910.6738NASSAU-0.9315.90225.0512.5322OKALOOSA2.2916.10752.7817.2168OKEECHOBEE2.0812.4515-2.0715.2622ORANGE3.6416.882566.1116.13338OSCEOLA3.9714.141114.1915.94140PALM BEACH-0.0516.223713.3217.17421PASCO5.2012.651464.1911.32192PINELLAS-8.5214.31225-1.6419.55237POLK-3.9014.25220-6.7415.37327PUTNAM-5.5114.65221.2913.4137SANTA ROSA-1.8614.98511.8916.8850SARASOTA1.5916.87995.9017.3494SEMINOLE4.8417.141481.1014.45174ST. JOHNS5.0815.218610.0416.9773ST. LUCIE1.7615.5294-8.8915.47138SUMTER0.6816.6012-18.0621.8523SUWANNEE2.508.91122.2811.0917TAYLOR0.8512.0012-13.8114.4014UF LAB SCH**1**3UNION2.3212.26521.0913.8311VOLUSIA-3.6214.24145-13.6513.92209WAKULLA9.7418.5112-15.2814.9417WALTON12.4019.28186.7414.5826WASHINGTON0.4915.868-5.207.9012State Avg.0.2716.6954250.2317.177046Table 5. Mean and Standard Deviation of Teacher Value-Added Scores by District: Grade 8, 2010-11DistrictMathematicsReadingMeanStd. Dev.NMeanStd. Dev.NALACHUA7.7316.1162-0.009.9883BAKER-12.5911.338-0.725.5010BAY0.7318.6659-0.487.6771BRADFORD-1.009.7270.555.3412BREVARD-6.5012.75132-4.248.32144BROWARD1.6216.523511.6911.66544CALHOUN5.5313.2710-6.434.0213CHARLOTTE1.4912.07265.749.0438CITRUS2.7912.1236-1.9711.7539CLAY-0.1414.6064-0.107.8777COLLIER7.8114.22652.6810.75115COLUMBIA-3.377.068-5.586.1611DADE2.3316.157476.6811.39917DEAF/BLIND**3-4.795.816DESOTO-6.1816.2612-3.276.6318DIXIE**22.955.246DOZIER/OKEEC**1**2DUVAL-0.0214.232273.338.65277ESCAMBIA-2.3213.1480-6.249.13133FAMU LAB SCH**1**3FAU LAB SCH4.2716.5759.227.357FL VIRTUAL**1**2FLAGLER-2.1511.72301.459.3530FRANKLIN-11.756.216-7.855.406FSU LAB SCH**35.505.205GADSDEN4.7717.31152.4617.8517GILCHRIST**4-9.473.437GLADES**3-10.592.817GULF3.3414.355-14.656.615HAMILTON-15.028.655-8.5911.488HARDEE4.0917.246-8.0210.498HENDRY-0.7115.169-8.9114.9715HERNANDO-1.6212.2852-3.5310.1470HIGHLANDS1.3513.2536-0.658.7138HILLSBOROUGH-3.4314.92348-4.579.56463HOLMES-0.8412.8017-2.886.7419INDIAN RIVER-5.2214.6336-8.118.0848JACKSON-4.3312.2919-4.705.0823JEFFERSON**2**3LAFAYETTE**2**1LAKE1.5811.28760.279.58107LEE7.3617.40149-0.729.67243LEON3.5413.37812.848.7985LEVY0.3712.82203.6912.7322LIBERTY-11.486.426-0.683.378MADISON-0.539.388-16.738.6812MANATEE1.4812.9391-4.817.45114MARION2.2111.9486-0.137.96122MARTIN3.7012.0936-0.137.0555MONROE14.0714.38241.178.9131NASSAU-10.6912.23245.298.5530OKALOOSA3.7014.09696.1110.6368OKEECHOBEE-5.1814.8215-7.775.8425ORANGE-3.6915.552471.8310.34347OSCEOLA3.0811.90112-2.6110.56146PALM BEACH4.9514.713454.489.70395PASCO0.6914.44140-0.088.36198PINELLAS-7.4714.62205-4.3610.58212POLK-1.0114.21185-5.6711.49286PUTNAM-5.3611.54235.357.2031SANTA ROSA1.4115.25483.979.3948SARASOTA5.6815.66840.688.52103SEMINOLE5.1714.331182.149.44148ST. JOHNS3.1513.53767.979.1279ST. LUCIE3.7715.8486-5.8410.43118SUMTER-3.3510.5813-7.347.5725SUWANNEE-7.0412.0412-2.707.3111TAYLOR4.234.91160.824.6016UF LAB SCH**1**2UNION2.6710.496-2.165.4111VOLUSIA-1.4514.15139-10.779.03206WAKULLA-1.2010.2612-5.895.2420WALTON5.5214.85245.2811.1126WASHINGTON11.8918.237-3.508.7612State Avg.0.7715.2350700.1611.016633Table 6. Mean and Standard Deviation of Teacher Value-Added Scores by District: Grade 9, 2010-11DistrictReadingMeanStd. Dev.NALACHUA6.638.2859BAKER10.784.1113BAY1.678.0372BRADFORD3.564.077BREVARD5.046.56193BROWARD-6.918.82475CALHOUN-6.052.886CHARLOTTE3.666.8329CITRUS7.367.3744CLAY4.195.7792COLLIER1.018.79100COLUMBIA-0.191.308DADE-0.627.99841DEAF/BLIND0.174.477DESOTO-2.913.6030DIXIE**3DOZIER/OKEEC-2.675.466DUVAL0.146.57293ESCAMBIA-2.376.38157FAMU LAB SCH**1FAU LAB SCH**1FL VIRTUAL**1FLAGLER5.246.7933FRANKLIN-4.272.547FSU LAB SCH8.413.879GADSDEN-6.529.5018GILCHRIST1.782.4115GLADES-4.793.795GULF**3HAMILTON-4.543.129HARDEE-3.855.0411HENDRY-7.564.0519HERNANDO3.966.3667HIGHLANDS-1.185.4929HILLSBOROUGH-3.767.50450HOLMES-3.158.3615INDIAN RIVER4.226.7734JACKSON3.306.8023JEFFERSON4.370.917LAFAYETTE**3LAKE1.036.6978LEE-1.297.52155LEON3.696.5283LEVY3.444.6423LIBERTY-5.725.078MADISON2.062.2111MANATEE2.3011.40116MARION5.077.83118MARTIN-2.529.9731MONROE-2.606.2324NASSAU3.357.2422OKALOOSA2.1010.4973OKEECHOBEE-7.046.9415ORANGE-0.497.95312OSCEOLA0.386.02144PALM BEACH-1.199.21408PASCO2.305.87214PINELLAS-0.476.24233POLK-2.757.37237PUTNAM4.357.1125SANTA ROSA9.288.0953SARASOTA2.067.1299SEMINOLE-2.306.65160ST. JOHNS12.389.6175ST. LUCIE-3.357.5283SUMTER3.015.5118SUWANNEE4.046.5014TAYLOR-0.913.176UF LAB SCH**2UNION-4.473.1511VOLUSIA2.648.69177WAKULLA11.264.8816WALTON2.156.8831WASHINGTON1.858.089State Avg.-0.148.476256Table 7. Mean and Standard Deviation of Teacher Value-Added Scores by District: Grade 10, 2010-11DistrictMathematicsReadingMeanStd. Dev.NMeanStd. Dev.NALACHUA1.725.4870-0.1429.4776BAKER-5.782.59116.0523.1613BAY-0.856.3689-9.5128.3580BRADFORD-1.042.65104.5537.6513BREVARD1.805.77193-4.5325.91206BROWARD-4.595.936905.5431.12753CALHOUN3.193.8678.9722.8613CHARLOTTE-2.725.2947-8.3423.5050CITRUS-0.396.1958-6.0123.1554CLAY2.105.081042.4920.12138COLLIER3.946.42120-1.5030.01142COLUMBIA3.864.487-4.2615.7810DADE1.497.0389416.6132.441058DEAF/BLIND8.425.559-15.1018.9410DESOTO-2.405.7216-3.3225.4125DIXIE**412.9917.036DOZIER/OKEEC**4**4DUVAL-4.526.403281.3829.15434ESCAMBIA0.515.80111-7.5525.09167FAMU LAB SCH**110.8718.095FLAGLER-0.926.75346.2931.3433FRANKLIN-7.594.777-20.1220.046FSU LAB SCH2.156.81519.0819.466GADSDEN1.798.9216-11.0523.8821GILCHRIST2.193.4984.9422.9513GLADES**423.0521.396GULF2.634.5987.0534.287HAMILTON-1.202.8870.7817.888HARDEE7.756.44108.6025.1216HENDRY-0.387.4022-7.0724.5232HERNANDO0.835.2079-1.1424.4892HIGHLANDS-0.624.7928-4.8724.8239HILLSBOROUGH0.545.69483-2.6631.21631HOLMES-3.588.059-11.0117.4818INDIAN RIVER-2.515.2140-4.6519.4847JACKSON0.756.1524-0.6319.6228JEFFERSON2.181.776-8.2022.469LAFAYETTE**3**4LAKE-4.486.37107-0.5329.30132LEE1.385.832093.7927.75237LEON-0.374.9394-0.3524.8688LEVY-1.705.6423-10.8225.4028LIBERTY1.144.076-9.7116.3010MADISON3.855.499-23.5017.9817MANATEE0.666.14102-2.4626.42123MARION-0.455.93114-5.3024.99132MARTIN-0.465.7951-1.5925.9457MONROE1.954.79286.0819.9439NASSAU-1.664.0333-12.0825.9833OKALOOSA-0.195.8371-2.4427.7481OKEECHOBEE-0.874.38180.7536.9921ORANGE-1.005.923990.6227.81436OSCEOLA5.165.8916113.6423.61204PALM BEACH-0.316.254717.5426.15579PASCO1.795.60201-3.3422.26255PINELLAS0.365.863360.9526.76348POLK-0.015.71271-9.0727.00323PUTNAM-0.675.6230-2.7323.4430SANTA ROSA-2.264.83671.3321.5468SARASOTA1.095.85119-1.4928.15119SEMINOLE3.836.571860.7526.02190ST. JOHNS4.405.411121.6124.6299ST. LUCIE0.426.66901.7727.15112SUMTER-0.544.52201.1922.3423SUWANNEE-0.014.19207.2026.0917TAYLOR-4.594.918-6.3420.8910UF LAB SCH**3**3UNION-4.754.888-16.0023.6712VOLUSIA1.446.57202-6.5130.38228WAKULLA-0.155.90123.6620.3816WALTON1.146.1626-7.4318.8935WASHINGTON-1.0211.9612-14.6522.6317State Avg.-0.006.5671602.1528.958359Appendix E. School Component by DistrictTable 1. Mean and Standard Deviation of the School Component by District: Grade 4, 2010-11DistrictMathematicsReadingMeanStd. Dev.NMeanStd. Dev.NALACHUA-4.6535.85320.1119.5731BAKER-19.15NA1-34.64NA1BAY-9.6447.31243.1721.8124BRADFORD-21.7119.175-12.9410.865BREVARD3.6533.11694.0215.2569BROWARD9.9133.491800.6819.28180CALHOUN-2.7813.883-4.9916.273CHARLOTTE-11.8923.80106.1924.3210CITRUS22.8734.91135.4125.1413CLAY-5.0727.7027-4.2116.2427COLLIER-8.7434.3232-1.3319.1232COLUMBIA0.2331.9010-0.276.9110DADE3.4834.102555.4122.21255DEAF/BLIND**2**2DESOTO5.189.423-12.816.353DIXIE10.4017.862-6.743.802DUVAL15.6433.18111-6.2019.65111ESCAMBIA-3.7142.0639-4.7122.6139FAMU LAB SCH**1**1FAU LAB SCH14.855.1624.8626.402FL VIRTUAL**1**1FLAGLER-29.0227.148-5.4713.299FRANKLIN-11.9323.432-14.1718.872FSU LAB SCH48.8213.97233.882.772GADSDEN32.4429.6111-0.5817.0911GILCHRIST30.0913.38216.377.882GLADES-12.774.773-3.519.563GULF40.562.4924.9533.382HAMILTON5.8627.123-1.7311.853HARDEE8.4220.035-11.9813.845HENDRY12.9130.526-2.1319.826HERNANDO-15.4323.0712-4.7420.5212HIGHLANDS-9.3941.749-2.6921.399HILLSBOROUGH-6.4732.271612.8018.37161HOLMES23.0218.704-1.8816.924INDIAN RIVER4.3125.01171.6112.5817JACKSON24.4834.71812.5015.778JEFFERSON13.228.88244.3351.992LAFAYETTE**1-11.15NA1LAKE-6.5238.6930-6.2515.6130LEE5.6028.0460-0.3417.3361LEON0.4028.6627-2.3918.1227LEVY-6.0415.426-12.0212.216LIBERTY-0.1436.292-4.411.672MADISON-35.8050.374-3.6417.334MANATEE5.3132.1043-0.1317.3743MARION0.8927.0034-8.6815.8935MARTIN17.9324.1113-1.8222.7813MONROE22.4730.2311-10.0617.4511NASSAU12.8035.0168.5211.076OKALOOSA-10.8519.8425-2.3015.9625OKEECHOBEE2.5418.326-5.1721.516ORANGE-1.3832.95137-2.7317.93137OSCEOLA-2.5123.67346.0515.8434PALM BEACH3.1329.881239.4819.83123PASCO-10.9128.8652-9.3718.1352PINELLAS-14.8030.9385-2.1314.7184POLK-11.1732.8284-5.3820.4684PUTNAM23.0536.33115.4516.6311SANTA ROSA-5.9631.90143.1918.8314SARASOTA-16.2632.42332.1617.4233SEMINOLE4.3927.28400.6517.2440ST. JOHNS-8.5635.13199.6922.0519ST. LUCIE-2.4129.6530-14.9720.7630SUMTER13.8812.39511.7727.695SUWANNEE1.2824.173-5.0511.493TAYLOR-25.606.922-0.854.542UF LAB SCH**1**1UNION44.10NA124.30NA1VOLUSIA-12.1327.0548-7.3315.2948WAKULLA-14.5521.7853.3919.485WALTON11.748.3576.557.007WASHINGTON16.3248.8020.5319.652State Avg.0.1633.022,0830.0219.432,084Table 2. Mean and Standard Deviation of the School Component by District: Grade 5, 2010-11DistrictMathematicsReadingMeanStd. Dev.NMeanStd. Dev.NALACHUA1.7526.82310.7516.3331BAKER-39.24NA1-36.86NA1BAY-0.7428.99241.4812.6324BRADFORD-7.0118.275-3.009.765BREVARD-0.5423.3169-3.2113.4369BROWARD5.2626.33178-1.8716.98178CALHOUN3.1326.953-11.089.003CHARLOTTE-0.3518.42128.4814.9811CITRUS8.1717.36125.9113.4612CLAY-0.3524.6427-3.3314.6827COLLIER-10.7522.2434-9.6312.5934COLUMBIA1.669.0583.677.198DADE-1.9625.992554.0317.17254DEAF/BLIND**2**2DESOTO-1.165.073-27.997.703DIXIE**217.2917.702DUVAL0.9424.18112-2.0315.10112ESCAMBIA-5.8027.0139-0.7818.0839FAMU LAB SCH**1**1FAU LAB SCH9.9129.772-0.9222.422FL VIRTUAL**1***FLAGLER-10.1225.4485.607.318FRANKLIN**2-1.223.622FSU LAB SCH1.5827.2722.541.812GADSDEN15.5128.06104.4133.4010GILCHRIST-19.4354.69212.6723.332GLADES-5.786.633-16.6718.923GULF-18.191.552-4.2724.282HAMILTON-1.1417.603-4.119.693HARDEE-6.3623.755-14.379.285HENDRY3.6241.6360.737.026HERNANDO-17.9516.9313-4.8113.8813HIGHLANDS-21.6226.639-8.0318.789HILLSBOROUGH-1.9921.371651.3713.56165HOLMES-11.3228.6843.8710.314INDIAN RIVER12.5020.1016-3.509.4516JACKSON-20.0229.418-0.7411.518JEFFERSON34.1133.19215.4420.102LAFAYETTE**1-0.53NA1LAKE-2.6321.3930-0.7013.9430LEE14.1523.7559-6.4413.1060LEON3.7128.86277.0323.6127LEVY-14.5821.247-3.0710.157LIBERTY-7.3919.76225.556.252MADISON-19.9626.4745.3914.404MANATEE8.9322.2542-1.6010.9242MARION0.8019.8335-5.0814.6535MARTIN11.4825.1712-1.0010.0412MONROE2.3014.7611-4.429.3811NASSAU4.4212.396-3.4712.915OKALOOSA0.9818.3824-1.1310.3424OKEECHOBEE9.6846.515-12.8822.695ORANGE2.3525.521381.9214.22138OSCEOLA8.9719.94343.3615.3534PALM BEACH-1.4919.821233.7714.91123PASCO2.0523.6555-2.9913.9552PINELLAS-7.8727.2188-2.0713.3786POLK-8.5128.6385-1.5916.0385PUTNAM9.3422.1710-2.2715.9310SANTA ROSA-3.9326.79155.0317.3015SARASOTA1.8322.35336.2814.8133SEMINOLE4.9222.15403.2313.7640ST. JOHNS5.9015.992113.2112.6520ST. LUCIE5.8929.1130-0.1913.1330SUMTER16.0915.03614.6712.925SUWANNEE15.9613.9623.438.212TAYLOR-30.0410.692-9.6811.882UF LAB SCH**1**1UNION-17.10NA1-19.43NA1VOLUSIA-5.6320.6948-8.7213.0448WAKULLA2.8417.8353.2019.475WALTON20.4015.0275.4510.637WASHINGTON-75.5825.392-9.2615.872State Avg.0.0424.782,0920.0215.492,082Table 3. Mean and Standard Deviation of the School Component by District: Grade 6, 2010-11DistrictMathematicsReadingMeanStd. Dev.NMeanStd. Dev.NALACHUA-8.1234.5216-9.0918.9417BAKER89.28NA14.41NA1BAY-6.4724.5213-9.5318.9913BRADFORD0.1546.233-4.689.433BREVARD50.9238.807011.4919.3970BROWARD-2.0925.64782.2820.4179CALHOUN13.2027.243-4.1817.683CHARLOTTE-13.2020.7560.4521.436CITRUS-10.9218.606-22.0215.846CLAY28.9226.45256.4316.5725COLLIER16.0323.382110.8616.3521COLUMBIA-15.097.273-19.302.633DADE-12.2036.5614011.9824.98144DEAF/BLIND**2**2DESOTO-4.5325.043-19.6229.762DIXIE**128.74NA1DUVAL-21.4731.9039-8.0020.9740ESCAMBIA-19.6725.0615-17.8821.1315FAMU LAB SCH**1**1FAU LAB SCH29.1840.24244.4329.592FL VIRTUAL**1**1FLAGLER9.4419.6886.2715.258FRANKLIN-23.7037.512-4.8114.422FSU LAB SCH**1**1GADSDEN-1.6440.858-19.2132.758GILCHRIST**2-6.995.072GLADES**3-3.1027.523GULF-39.7121.382-3.039.462HAMILTON55.4255.854-13.3913.044HARDEE-18.495.722-4.763.642HENDRY-30.588.393-26.9913.313HERNANDO-6.7322.4810-4.9416.9410HIGHLANDS15.7332.1367.1716.585HILLSBOROUGH-0.2425.4171-15.5721.5870HOLMES28.4633.725-5.6111.185INDIAN RIVER7.3218.477-4.2416.717JACKSON-17.798.977-5.8213.696JEFFERSON-0.652.9230.464.842LAFAYETTE**1**1LAKE-4.1924.1616-1.8120.1316LEE-6.8025.7433-11.1719.5435LEON2.5827.0218-0.5119.2519LEVY2.5723.298-7.8817.918LIBERTY22.7141.883**3MADISON-16.240.762-18.4613.032MANATEE-10.2224.9423-2.9815.3024MARION-11.9717.60151.2313.7215MARTIN4.8421.606-3.579.436MONROE20.7421.99815.119.518NASSAU0.649.535-13.0612.215OKALOOSA8.3125.13172.7611.9517OKEECHOBEE13.904.862-5.856.193ORANGE-4.9724.06552.9816.3057OSCEOLA2.4223.802112.8816.0521PALM BEACH2.9028.50544.7722.1054PASCO12.6530.1422-0.9118.4622PINELLAS-19.3523.5733-17.0316.9633POLK-19.5430.4041-3.8116.0742PUTNAM1.7855.116-25.7126.986SANTA ROSA-8.5720.7313-0.4012.8613SARASOTA9.5730.531813.3721.2018SEMINOLE-5.2816.40158.6812.8315ST. JOHNS3.9641.761012.0628.9910ST. LUCIE5.5725.59203.4713.7620SUMTER-12.6641.065-11.5922.395SUWANNEE-9.634.4041.683.964TAYLOR-3.845.41214.522.402UF LAB SCH**1**1UNION-12.10NA120.78NA1VOLUSIA-15.4825.5420-18.1611.9720WAKULLA13.8614.114-14.3710.964WALTON36.9924.1658.8421.435WASHINGTON-13.110.202-8.0124.082State Avg.0.1433.701,1020.0321.631,112Table 4. Mean and Standard Deviation of the School Component by District: Grade 7, 2010-11DistrictMathematicsReadingMeanStd. Dev.NMeanStd. Dev.NALACHUA0.329.6320-4.188.9119BAKER-14.96NA111.95NA1BAY1.3913.3113-1.948.9214BRADFORD0.131.372-9.5312.442BREVARD-11.3412.0129-10.6012.8829BROWARD-3.0412.1777-2.9315.8679CALHOUN0.0310.133-22.3914.933CHARLOTTE6.1613.8068.9013.286CITRUS2.5415.707-14.6512.387CLAY-7.5712.4881.4911.608COLLIER6.4511.65173.3313.7618COLUMBIA-9.969.363-0.056.303DADE-0.5412.7614110.8416.20141DEAF/BLIND**2**2DESOTO-1.954.3542.326.104DIXIE-5.36NA114.03NA1DUVAL2.0112.48452.1812.3246ESCAMBIA-3.748.9715-13.6615.5115FAMU LAB SCH**1**1FAU LAB SCH-1.794.7422.262.002FL VIRTUAL**1**1FLAGLER0.2412.665-4.188.035FRANKLIN**24.7914.862FSU LAB SCH**1**1GADSDEN-7.789.726-4.2418.396GILCHRIST**2-17.519.542GLADES**3-16.988.543GULF6.226.902-2.7221.832HAMILTON**2-8.474.682HARDEE-18.56NA13.46NA1HENDRY-4.6011.383-11.5021.533HERNANDO3.288.17104.595.3110HIGHLANDS8.749.3265.8213.456HILLSBOROUGH2.9713.4074-5.2512.8575HOLMES-1.4912.585-15.1215.716INDIAN RIVER4.6610.427-11.7821.587JACKSON-2.557.928-10.2918.167JEFFERSON-7.1914.392-0.680.432LAFAYETTE**1**1LAKE-0.0212.78150.1111.9615LEE7.2813.9933-1.6615.9233LEON-0.9414.4520-1.8821.0620LEVY2.3312.718-3.5720.008LIBERTY1.5914.614-10.7911.504MADISON2.483.0033.768.763MANATEE1.3111.45250.6611.7925MARION-3.099.30157.3212.1115MARTIN1.2110.176-17.554.616MONROE2.2510.107-0.248.827NASSAU-0.5513.8953.8812.175OKALOOSA1.0213.24172.7911.8318OKEECHOBEE0.599.594-9.0916.753ORANGE4.0013.14546.4814.5555OSCEOLA4.1311.49205.3113.9520PALM BEACH-0.8313.46543.1616.4454PASCO4.829.65264.5110.0426PINELLAS-8.7011.1636-2.5715.9237POLK-4.749.4543-6.5816.7342PUTNAM-5.646.9864.4413.206SANTA ROSA-2.678.08121.2816.6012SARASOTA1.3612.46205.0814.5120SEMINOLE5.1813.5717-0.2013.0117ST. JOHNS5.6211.83139.4518.3014ST. LUCIE1.1410.8819-10.5814.2819SUMTER1.388.656-11.5223.456SUWANNEE1.154.4440.726.004TAYLOR-1.3911.122-9.5220.212UF LAB SCH**1**1UNION3.85NA124.8416.372VOLUSIA-4.139.3223-17.0412.9823WAKULLA6.759.904-12.2415.964WALTON7.8614.1086.0213.788WASHINGTON0.883.992-4.419.953State Avg.-0.0212.381,0710.0016.011,080Table 5. Mean and Standard Deviation of School the School Component by District: Grade 8, 2010-11DistrictMathematicsReadingMeanStd. Dev.NMeanStd. Dev.NALACHUA5.4310.21210.758.0319BAKER-18.66NA1-1.59NA1BAY-1.9213.7313-0.876.9714BRADFORD0.727.8531.746.332BREVARD-7.217.9630-5.376.9129BROWARD0.8511.19742.9712.1874CALHOUN5.229.133-8.755.643CHARLOTTE0.957.7666.969.866CITRUS1.913.998-5.4915.526CLAY-0.0711.8211-0.544.4110COLLIER5.9010.82201.3211.2319COLUMBIA-2.382.124-5.448.494DADE1.9812.331417.7412.97141DEAF/BLIND**2-1.4913.302DESOTO-5.733.574-3.374.775DIXIE**13.65NA1DOZIER/OKEEC**1**1DUVAL-0.3710.19414.029.7142ESCAMBIA-4.4310.0616-7.3110.5717FAMU LAB SCH**1**1FAU LAB SCH3.671.2029.7911.392FL VIRTUAL**2**2FLAGLER-3.766.786-1.359.216FRANKLIN-9.973.022-7.287.832FSU LAB SCH**16.73NA1GADSDEN2.2611.8860.7320.636GILCHRIST**2-12.371.002GLADES**2-13.153.102GULF3.020.022-13.771.602HAMILTON-14.204.932-4.6024.462HARDEE2.267.692-9.533.512HENDRY-1.128.034-10.8118.274HERNANDO-2.0710.5810-3.1711.5410HIGHLANDS-0.268.878-1.447.756HILLSBOROUGH-3.779.0176-5.2911.1077HOLMES-2.108.576-4.707.715INDIAN RIVER-5.8710.076-9.979.637JACKSON-3.838.687-6.603.546JEFFERSON**1**1LAFAYETTE**1**1LAKE0.647.6615-0.137.8915LEE6.8114.9634-1.2511.5734LEON1.819.44221.4011.0822LEVY0.368.5281.8513.828LIBERTY-8.874.033-0.522.685MADISON-1.494.133-16.3315.103MANATEE0.129.1024-5.627.2224MARION0.6411.5115-1.759.9715MARTIN3.397.0470.096.117MONROE13.4712.9071.1910.206NASSAU-9.9012.2853.615.957OKALOOSA1.2011.88206.7311.6218OKEECHOBEE-5.0015.803-11.714.473ORANGE-3.9811.96601.8611.5658OSCEOLA3.499.5920-2.6211.3420PALM BEACH4.5912.59575.4910.9153PASCO0.3011.3136-0.219.5726PINELLAS-7.398.6537-4.7910.2837POLK-1.528.5042-6.1113.7043PUTNAM-4.616.1085.765.336SANTA ROSA-0.6912.66113.9410.4613SARASOTA5.0812.24211.008.1120SEMINOLE4.6811.22171.8311.4917ST. JOHNS1.7111.08178.1712.2817ST. LUCIE3.2011.3319-6.6413.4119SUMTER-3.985.055-10.206.565SUWANNEE-6.752.585-1.603.525TAYLOR2.967.1822.312.002UF LAB SCH**1**1UNION3.54NA1-4.833.772VOLUSIA-3.269.2825-13.8311.1025WAKULLA-1.437.124-6.934.334WALTON5.2712.2583.6912.988WASHINGTON8.5612.423-3.669.963State Avg.0.0511.191,1140.0312.071,094Table 6. Mean and Standard Deviation of School the School Component by District: Grade 9, 2010-11DistrictReadingMeanStd. Dev.NALACHUA7.4410.8314BAKER19.53NA1BAY2.329.7114BRADFORD3.516.702BREVARD6.4010.2924BROWARD-9.1312.1160CALHOUN-8.323.742CHARLOTTE5.387.467CITRUS6.3510.8210CLAY6.647.979COLLIER0.0810.1116COLUMBIA-0.481.162DADE-0.719.2099DEAF/BLIND2.305.622DESOTO-2.184.476DIXIE**1DOZIER/OKEEC-2.527.052DUVAL0.918.0937ESCAMBIA-3.518.5817FAMU LAB SCH**1FAU LAB SCH**1FL VIRTUAL**1FLAGLER5.187.364FRANKLIN-4.644.182FSU LAB SCH14.71NA1GADSDEN-6.5812.765GILCHRIST2.971.132GLADES-7.68NA1GULF**2HAMILTON-4.528.122HARDEE-6.91NA1HENDRY-8.905.524HERNANDO5.577.498HIGHLANDS0.837.666HILLSBOROUGH-4.129.5253HOLMES-2.4810.596INDIAN RIVER5.237.855JACKSON4.4710.457JEFFERSON7.33NA1LAFAYETTE**1LAKE1.597.6013LEE0.6010.2125LEON3.747.7915LEVY5.906.836LIBERTY-4.706.244MADISON2.153.813MANATEE-0.8117.5213MARION4.4311.3514MARTIN-2.8911.365MONROE0.029.034NASSAU4.757.756OKALOOSA2.0212.5516OKEECHOBEE-8.8410.553ORANGE-0.919.7148OSCEOLA-0.677.8617PALM BEACH-0.7112.4148PASCO3.137.5921PINELLAS-1.025.5238POLK-1.929.4633PUTNAM4.1011.405SANTA ROSA6.9612.8711SARASOTA4.3810.0313SEMINOLE-4.398.2714ST. JOHNS14.4617.4312ST. LUCIE-2.6610.9414SUMTER2.537.435SUWANNEE2.5410.223TAYLOR-2.160.762UF LAB SCH**1UNION-4.855.022VOLUSIA1.1112.4625WAKULLA10.0417.742WALTON1.0110.276WASHINGTON3.3711.593State Avg.0.0410.64889Table 7. Mean and Standard Deviation of the School Component by District: Grade 10, 2010-11DistrictMathematicsReadingMeanStd. Dev.NMeanStd. Dev.NALACHUA1.323.9611-1.4915.0512BAKER-9.33NA17.63NA1BAY-0.686.2011-8.5812.2011BRADFORD-1.060.9523.330.192BREVARD2.034.8724-4.6211.5523BROWARD-6.186.25583.8416.8759CALHOUN3.820.6027.114.932CHARLOTTE-2.045.197-6.119.668CITRUS0.013.378-4.937.439CLAY1.974.59102.317.999COLLIER3.056.5618-3.9413.3017COLUMBIA4.585.332-2.821.662DADE2.577.869213.4519.8992DEAF/BLIND11.147.382-13.823.452DESOTO-1.104.895-0.5712.084DIXIE**14.678.362DOZIER/OKEEC**2**2DUVAL-4.967.0935-0.3615.5938ESCAMBIA0.053.0817-7.4710.8417FAMU LAB SCH**11.21NA1FLAGLER-3.246.8952.8116.805FRANKLIN-6.608.422-10.079.832FSU LAB SCH2.95NA116.82NA1GADSDEN3.4412.194-7.328.084GILCHRIST2.884.1324.2013.002GLADES**116.99NA1GULF3.415.9624.9816.922HAMILTON-1.042.3421.611.012HARDEE12.62NA111.66NA1HENDRY-0.154.834-8.4616.904HERNANDO0.137.187-3.9811.827HIGHLANDS1.084.175-5.536.236HILLSBOROUGH0.674.7346-3.589.2861HOLMES-2.904.944-6.508.405INDIAN RIVER-4.231.194-5.157.804JACKSON1.894.826-1.203.447JEFFERSON1.812.452-4.428.222LAFAYETTE**1**1LAKE-6.185.2611-2.429.6812LEE0.475.63301.9715.5530LEON-0.853.2512-2.1012.4513LEVY-1.352.587-7.429.496LIBERTY0.711.213-3.705.574MADISON1.596.463-13.759.734MANATEE-1.046.2315-2.258.7516MARION-1.565.3415-6.9111.6015MARTIN-1.084.016-1.039.806MONROE1.943.0355.244.395NASSAU-2.631.434-9.5211.385OKALOOSA-0.033.6416-1.9313.6017OKEECHOBEE-0.193.053-0.1214.233ORANGE-1.505.1243-1.8213.1344OSCEOLA5.137.721910.9014.8720PALM BEACH-0.766.29486.1315.5448PASCO1.855.0720-3.4810.1522PINELLAS0.134.0938-1.189.9038POLK0.045.2932-8.8610.8733PUTNAM-0.603.726-2.726.985SANTA ROSA-3.272.108-2.3312.159SARASOTA2.225.6313-1.2013.0213SEMINOLE5.056.63130.0012.1514ST. JOHNS5.405.68130.7915.1413ST. LUCIE-0.064.77131.2512.2014SUMTER-0.561.5050.856.145SUWANNEE0.641.7541.4612.494TAYLOR-5.940.312-2.768.022UF LAB SCH**1**1UNION-3.098.892-11.516.432VOLUSIA0.935.2523-7.6010.5026WAKULLA0.723.442-0.7512.982WALTON1.976.395-6.036.526WASHINGTON0.0718.022-10.0014.083State Avg.-0.036.318500.0314.49890Appendix F. Expected Student Growth by Student Characteristics Gifted and English Language Learner (ELL) StatusTable 1. Conditional Estimates of Student Growth in Mathematics, 2010-11 ?Gifted?Non-Gifted??GradeExpected GrowthN?Expected GrowthN?Difference42.064906443388.476418175993-86.41151588.30707335294.806761163861-6.499688622.39568626544.540499163134-22.14481761.926867266110.13964158809-48.21278846.24828222384.55398162877-38.30571037.53747218949.837181156023-12.29971?ELL?Non-ELL??GradeExpected GrowthN?Expected GrowthN?Difference4153.82121264983.20118216377770.620016588.53036431894.80498163895-6.274616642.7584619444.50666163205-1.74827163.83582157110.005915891853.8299268134.3136316284.45208116293849.861551081.997501123?49.796945156089?32.200556Table 2. Conditional Estimates of Student Growth in Reading, 2010-11?Gifted?Non-Gifted??GradeExpected GrowthN?Expected GrowthN?Difference4146.44818435184.83559176048-38.3874563.43332734943.20759616398320.225731683.64742226584.322599163500-0.675177737.42110727387.788687160446-50.36758812.55488322555.417656163607-42.86277977.07595419145.61202115630331.4639331029.283435194?25.894549175184?3.3888864?ELL?Non-ELL??GradeExpected GrowthN?Expected GrowthN?Difference4259.452312601178.9963716388280.455937570.38820831843.19793416401427.1902746101.5443219684.30086916356917.2434527118.7098215587.67319916056431.0366198131.1275616155.28425816367175.843303954.95093113945.6421541563559.30877741029.830353143?25.895089175235?3.9352639Appendix G. Teacher Value-Added Estimates by Teacher and Classroom CharacteristicsTable 1. Correlations between Teacher Value-Added Estimates in Mathematics and Teacher/Classroom Characteristics, by Grade, 2010-11?Teacher Experience (Years Teaching)?Percent ELLs?Percent Students with a DisabilityGradeRN?RN?RN40.013535114750.012355811734-0.0649321173450.047717810648-0.01885110878-0.0779371087860.05069774899-0.0151855078-0.044967507870.00234365212-0.0033855425-0.01070354258-0.0017074871-0.0182815070-0.0099765070100.04364826906-0.01022971600.00020187160Note: a Correlation not statistically significant at the 0.05 level.Table 2. Average Teacher Value-Added Estimate in Mathematics Conditional on Teacher Education (Highest Degree Completed), by Grade, 2010-11 ?Bachelors?Masters?DoctorateGradeMSDN?MSDN?MSDN40.70763143.30996574842.147843142.76588837693.057505545.886016250.454121336.04432368332.294290534.8786243567-4.90865733.474936656-1.32357327.35189832160.405139527.9524641528-6.06091531.2975074770.263442616.90371834300.656603116.29161116190.477319418.7951626180.611312515.31061331651.452128514.9016221575-0.33261519.2227695310-0.1014096.585640844040.37170486.50160612294-1.2963136.322068790Table 3. Correlations between Teacher Value-Added Estimates in Reading and Teacher/Classroom Characteristics, by Grade, 2010-11 ?Teacher Experience (Years Teaching)?Percent ELLs?Percent Students with a DisabilityGradeRN?RN?RN40.0748987128670.010545113157-0.0437961315750.050207711921-0.00244112182-0.0045871218260.03523156817-0.0128770910.0124078709170.015212467480.00736377046-0.010088704680.00923426350-0.00931766330.0138814663390.04167665989-0.0115946256-0.0151386256100.047410180260.0052328359-0.0528468359Note: a Correlation not statistically significant at the 0.05 level.Table 4. Average Teacher Value-Added Estimate in Reading Conditional on Teacher Education (Highest Degree Completed), by Grade, 2010-11 ?Bachelors?Masters?DoctorateGradeMSDN?MSDN?MSDN40.154785821.86904682651.507660721.26743243443.939464719.237942795-0.18816917.14061776300.775386516.4962784021-1.60395114.136687756-1.47921317.0206542130.537179516.9772282366-0.81150117.857964737-0.28520116.89327741550.916767217.64428523552.933406319.19087798-0.27094611.01172638770.878304811.0181342286-0.82058510.177734649-0.2408058.483850936060.33354858.53225022176-0.6736788.838740395101.426522428.60634246583.307611129.42524830701.315382127.1821139 ................
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