The theoretical and practice-based framework is presented for a study that explored the effect of teachers' use of alternative assessment on their mathematics teaching. A model for the impact of alternative assessment on teacher knowledge and classroom teaching processes is proposed, building on work by E. Fennema and M. L. Franke (1992) and P. L. Peterson (1988). A research study to test the model is described, including a description of the coursework provided and a discussion of the methodology and data sources. Subjects were 17 female teachers and 1 male teacher (4 African Americans and 14 Whites) in grades 4 through 10. In addition to data from observations of teachers, results from informal data are presented, including class notes, teacher-made tests, and summaries written by the teachers describing assessment strategies. These data, along with those from observations and student reports, provide evidence that knowledge and use of alternative assessments did help mathematics teachers change their teaching strategies to reflect approaches shown by research to result in higher order thinking. One table gives a sample course syllabus, and one figure illustrates teacher concepts. (Author/SLD)