An algebraic model uses a set of algebra equations to precisely describe a situation. Constructing such models is a fundamental skill required by US standards for both math and science. It is usually taught with algebra word problems. However, many students still lack the skill, even after taking several algebra courses in high school and college. We are developing a short, intensive course in algebraic model construction. The course combines human teaching with a tutoring system. This paper describes the lessons learned during the iterative development process. Starting from an existing theory of model construction, we gradually acquired a completely different view of the skills required as we modified the tutoring system and the instruction. We close by describing encouraging results from a quasi-experimental study.