This article explains findings of part of a research project that uses the social fabric matrix (SFM) (Hayden 2006, 73-143) to analyze Nebraska's State education finance system with regard to adequacy and rules. The emphasis is about how to approach such a problem and to demonstrate the use of mathematical expressions to articulate social beliefs as instituted through rules, regulations, and requirements.
Concern for equity through equalization criteria has a long history in the analysis of state education systems. Concern for adequacy has become important in analysis recently, although court rulings indicate that it should have been of analytical importance earlier because most state constitutions call for an adequate education for all children. Nationally, since 1989, plaintiffs in 20 states have won school adequacy cases for additional funding in supreme courts. Defendant states have won seven. There are 12 cases pending, two of which are in Nebraska. The settlements require the state legislature to fix the constitutional deficiencies in the state funding formula. The Kansas Supreme Court, in summer 2006, ordered the legislature to expand its support to local school districts by doubling state spending on K-12 public education. The shift from equity to adequacy, in legal terms, moves the legal theory from equal protection claims to claims made on the education provisions of state constitutions. Constitutional terms such as "free instruction," "thorough and efficient education," "sound basic education," and "knowledge essential for good governance" have more interpretative meaning with regard to the "qualities" or "requirements" of schooling. Adequacy has support from the "standards-based" movement in that it considers a basket of goods, services, facilities, and technologies as the requirements necessary to deliver skills and knowledge to public school students (Rebell 2004, 40; and 2005, 291-324).
While the concept for adequacy in educational finance has become more refined and grounded in reality, the concept of rules in economics has become more abstract and divorced from reality. Articles about rules are often completed without one mention of real-world rules or an indication of how rules are related to institutions, technology, and ecological systems. Much of the rule literature is becoming a case of layering abstraction upon abstraction without validation by recurrence to reality. Yet, for rule concepts to be about reality, they need to be actualized in real situations of particular time and space (Dopfer 2006, 4). In that way, abstractions can be enriched to be conceptually valid. To assist in enriching rule concepts, we identify and model social agents that make the rules, the organizational subjects that apply the rules, and the object rules associated with the organizations (see Dopfer 2006, 32).
Figure 1 is a reduced version of the larger project's SFM. The first six rows are a list of the normative belief criteria that influence institutional organizations, as indicated by the ones in the first six rows for columns 7 and 8. In turn, those same organizations in rows 7 and 8 deliver rules in the form of court decisions and laws to the organizations represented in columns 9 through 13. (The term rules will be used here as shorthand for rules, regulations, and requirements.) Our interest is with the deliveries in cells (7,12), (8,12), (8,13), and (13,12). Together these cells contain the State education finance system called Tax Equity and Educational Opportunities Support Act (TEEOSA). Different calculations for different parts of TEEOSA are made by different agencies and niches within agencies, and from many different databases and computer programs. A mathematical formula of the whole set of TEEOSA rules and their calculations has not existed until finalized for this project.
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The relevant SFM digraph and TEEOSA sub-model are demonstrated with the digraph created by the program ithink in Figure 2. Connected to each element in the sub-model is the ithink calculation process that contains the...