This paper provides an overview of the four major aspects of the PIXIE Intelligent Tutoring System: the field work undertaken to determine how teachers diagnose and remediate in introductory algebra; the set of experiments run to determine the relative effectiveness of Model-Based-Remediation (MBR) and Reteaching; systems work carried out to remedy shortcomings noted earlier in the Intelligent Tutoring System, PIXIE; and an experiment conducted to determine whether it is possible to enhance teachers' diagnostic capabilities. The major conclusions from the four phases of the work are: (1) the teachers involved in the study, essentially tutored algebra procedurally; (2) for algebra, when taught procedurally with this age group, reteaching seems as effective as MBR; (3) the initial basic PIXIE system has now been enhanced so that it can diagnose and remediate in several domains; and (4) this experiment concluded that exposure to the TPIXIE program did enhance the teacher trainees' ability to diagnose student errors. (Author/TW)