This document provides a discussion of the relationships in Individually Guided Education (IGE) schools between the organizational and instructional features of schools and the mathematics achievement of second- and fifth-grade students. The theoretical positions that are part of the IGE model--some of them explicit and some of them implicit but evident--imply what some of the relationships should be. Thus, it was possible to form a theoretical model of how variations in different organizational and instructional features would be linked, and how, in turn, those variations would be linked to variations in achievement. This report presents that theoretical model and evaluates how adequately it fits data obtained from schools. The results of the causal analysis used suggest that the instructional and organizational features, as measured in this study, are not able to account for much of the variance associated with second- and fifth-grade mathematics achievement. (Author)