Alternate assessments based on alternate achievement standards are designed to measure the academic achievement of students with the most significant cognitive disabilities. Because this population has not previously been included in large-scale testing programs, these assessments present unique measurement challenges. Probably the most significant issue is the inherent need for individualization in item presentation and response while maintaining rigorous levels of standardization. Additional measurement challenges are presented as states move toward implementation of growth models for accountability. In this report, we discuss four approaches to modeling the growth of students with significant cognitive disabilities. We apply several variations of transition matrix growth modeling for one state's alternate assessments and discuss the measurement challenges and policy considerations related to our findings.