Search

In most school achievement research, the relationships between achievement and explanatory variables follow the Newton and Einstein concept/principle and the viewpoint of the macro-observer: Deterministic measures based on the mean value of a sufficiently large number of schools. What if the relationships between achievement and explanatory variables followed Planck's quantum concept/principle and the viewpoint of the micro-observer; that is, the nondeterministic measurement of individual schools, each with its own probability? What influence would a quantum theory of school achievement have on research, training, and practice? The author argues that there is no set of generally accepted concepts or mathematical principles underlying the multiple diverse studies estimating the relationships between school achievement and various explanatory variables; in short, there is no comprehensive theory of school achievement. In this article, the purpose of the analyses and thought experiments, culminating in a series of postulates, is to define the fundamental concepts and mathematical principles of such a theory. These issues are addressed in this article through discussion of the following: (1) Why achievement measures are quantum in nature: discrete integer values with upper- and lower-limits requiring probabilistic measurements; (2) Why normal curve statistics commonly used in achievement research are based on continuous variables with no upper- and lower-limits and implied deterministic measurements; (3) How normal curve statistics can accommodate the quantum nature of achievement by considering the relationships between achievement and explanatory variables as nonlinear, nondeterministic, and probabilistic; (4) How nonlinear relationships allow for the calculation of achievement levels and probabilities unique to each individual school (Planck's microview); (5) How the nonlinear interpretation leads to a calculation of cost-effectiveness; (6) How conceptually and statistically related variables can be combined to measure their collective influence on achievement; and (7) How normal curve statistics and combinations of explanatory variables can be used in a comprehensive theory of school achievement and mathematical model simulating how changes in individual school policies could influence the probability of improved achievement. (Contains 1 table, 10 figures, and 23 endnotes.)

Combining explanatory variables into factors instead of using individual variables in an achievement production function is advocated in several of the articles in this special issue. This article provides a brief overview of factor analysis explaining and illustrating the reasoning for this technique. There is a linchpin: Factor analysis is an aspect of regression analysis which is used to estimate the relationships between an outcome and the explanatory variables of a production function. While different in purpose, factor analysis and regression analysis share similarities. Regression estimates the relationships between an outcome and several explanatory variables, taking into consideration the relationships among the explanatory variables. Factor analysis, in contrast, estimates the relationships only among combinations of explanatory variables. (Contains 4 tables and 4 endnotes.)

The author believes that a unified theory might provide ideas helpful for improving research; professional training and practice; and therefore, student achievement. Little attention was paid to how several variables might work together and there is little discussion regarding how they might work together. The author stresses that there are reasons why a comprehensive, coherent, and unified modeling and testing process can be applied to achievement production. The purpose of this article is to identify these reasons. (Contains 5 endnotes.)

This article focuses on a method of policy analysis that has evolved from the previous articles in this issue. The first section, "Toward a Theory of Educational Production," identifies concepts from science and achievement production to be incorporated into this policy analysis method. Building on Kuhn's (1970) discussion regarding paradigms, the second section, "Characteristics of an Achievement Production Theory and Model," describes a comprehensive, coherent, and unified theory and a mathematical model of achievement production substantially different from other theories and models. Using sample data, section three, "Example of the Policy Analysis Model," demonstrates the implementation of the model. (Contains 7 figures, 3 tables, and 22 endnotes.)

One of the most influential studies affecting educational policy is Glass and Smith's 1978 study, "Meta-Analysis of Research on the Relationship of Class-Size and Achievement." Since its publication, educational policymakers have referenced it frequently as the justification for reducing class size. While teachers and the public had long believed lowering class size would be advantageous, Glass and Smith gave the idea legitimacy. This article is a review and reanalysis of the Glass and Smith study. While this review maybe considered much too late, it does serve the purpose of re-evaluating a frequently cited study to either support or challenge various aspects of the original findings. To that end, the article is divided into six major parts. It begins with an overview of the Glass and Smith study for those who may not be familiar with the specifics. This is followed by a description of their findings and comments upon these by the author. The fifth section presents a reanalysis of their data. The article closes with observations and conclusions. (Contains 7 figures, 2 tables, and 15 endnotes.)

Class size may be important in achievement, but it is not the only decision for policymakers. Class size plays a role, but the role is effectively fulfilled only when the other players are successful. Therefore, it is appropriate to address several questions: What goals are to be accomplished; what is the best distribution of personnel related to these goals; what roles do curriculum, instruction, time, and home support play; and how do the personnel work together effectively to achieve those goals? In the broadest sense, the fundamental question is: How are decisions made? For the sake of discussion, three levels of decision making related to class size are presented. Generally speaking, there are three broad categories or levels: (1) Professional and public opinion; (2) A critical analysis of educational research evidence; and (3) A decision-making process. The premise of this article is to provide some rationale and ideas regarding how policymakers can move through the more sophisticated levels of the taxonomy--the critical analysis of educational research evidence and a structured decision making process. This article is divided into three parts. In the first, "Does Class Size Make a Difference: A Brief Overview of the Research," a sampling of studies is presented. The second section is titled, "How Much of a Difference Does Class Size Make on Achievement?" The 1978 meta-analysis of Glass and Smith suggested the possibility that achievement increases faster as class sizes become smaller. The third and final section closes with some observations. (Contains 3 figures, 9 tables, and 11 endnotes.)

The previous articles on class size and other productivity research paint a complex and confusing picture of the relationship between policy variables and student achievement. Missing is a conceptual scheme capable of combining the seemingly unrelated research and dissimilar estimates of effect size into a unified structure for policy analysis and decision making. This article builds a rationale for a unifying structure and consistent method of estimating effect size. This article develops a policy analysis paradigm by combining the various estimates of effect sizes into a coherent structure with a consistent method of measurement; and building a rational and analytical method to accommodate the effect ceiling and effectiveness components. (Contains 2 figures, 16 tables, and 17 endnotes.)

The purpose of this article is to illustrate how a valid and reliable state accountability system could be developed that identifies effective schools and school districts in a comprehensive, understandable, and practical way. The author presents an overview of the strategy used in the analysis, discusses the use of education production functions and the assessment of school effectiveness, and proposes a model of education production. The data and analysis processes used are described, and the empirical results are presented. The results from the presented method are contrasted with results from a "change score" approach, and conclusions and implications for school accountability policy are discussed. (Contains 6 figures, 3 tables, and 11 endnotes.)

The never-ending organizational challenge is to allocate available resources to best achieve its goals. Out of this fundamental question several models have evolved. One is a conceptual model--a way to think about how organizations operate. A second is a statistical model estimating the magnitude of relationships among goals and elements of the organization. This article presents a third model, an optimization model building upon the other two in order to analyze various policy options by simulating "what if" situations arising in organizations. These three models are complementary rather than competing. (Contains 6 figures, 3 tables and 20 endnotes.)

How do district policies, leadership, and support services influence the quality of teaching and learning in public schools? This article uses a rich longitudinal school-level database to estimate a model of student achievement and analyzes the residuals in the model to obtain estimates of the contributions of unobserved school and school district characteristics to student performance. The second section of the article reviews recent research on current approaches to determining school quality on the basis of student achievement test scores. Section three presents an alternative approach to assessing school and district effectiveness using an educational production function. A production function model is specified in the fourth section, and empirical results are presented in section five. A summary of findings in presented in the final section, along with implications for state and federal policy and programs regarding school accountability. (Contains 3 figures, 5 tables and 23 endnotes.)

A survey of one national and three statewide studies (in Tennessee, Texas, and Alabama) of class-size achievement effects revealed no consistent pattern across various subjects and grade levels. However, smaller classes can improve student achievement, particularly in early grades and when teacher quality remains constant. (Contains 36 footnotes.) (MLH)

Discusses the conflicting goals of school finance reform--educational equity, equality, and excellence--and their effects on the district power equalizing (DPE) method of achieving school equity. Describes the experiences with DPE in California, Ohio, Illinois, and Michigan. (RW)

Regarding shortcomings in guaranteed tax base (GTB) school aid formulas, especially difficulties in measuring district fiscal capacity, the authors cite Michigan data to argue that inequities resulting from measurements using property wealth can be mitigated by property tax relief, intrastate cost differentials, and a unique aspect of Michigan's GTB formula. (RW)