Little agreement exists on which school expenditures and resources are most likely to improve student resources or whether resources really matter at all. This study compiles a national database of school finance information and analyzes the data to address the importance of school expenditures. Data were collected from the National Assessment of Educational Progress, a nationally representative sample of fourth and eighth graders, the Common Core of Data of the U.S. Department of Education, and a Teacher's Cost Index, which measures variations in the costs of education. Data were analyzed with multivariate techniques to produce flow charts for grades four and eight of how dollars and resources influence student achievement in mathematics. The study found that expenditures affect the achievement of fourth graders in two steps and eighth graders in three. For fourth graders, the process begins with increased expenditures on instruction and school district administration which then increase teacher-student ratios. The increased teacher-student ratios raise average achievement in mathematics. For eighth graders, the first step is the same. Then increased teacher-student ratios reduce problem behaviors and improve the social environment of the school. A lack of problem behaviors and a positive social environment then increase average achievement in mathematics. Expenditures related to capital outlays, school level administration, and teacher education levels were not found to increase achievement. Findings support both a productivity perspective and a traditional perspective on school finance. An appendix discusses the research methodology. (Contains 3 figures, 3 tables, and 41 references.) (SLD)