To explore the mathematics knowledge of teachers in two alternate route programs, the authors analyzed questionnaire and interview data collected at the beginning of the teachers' programs and at the end of their first year of teaching. Most of the teachers could use algorithms correctly, but many had difficulty representing or explaining them. Moreover, although some teachers learned some mathematics from teaching the subject, fundamental mathematical ideas appar ently continued to elude them. The authors call for further inquiry into the assumptions policy- makers make about the subject matter knowledge that arts and sciences majors bring with them to alternate route programs and what these majors can learn about a subject from teaching it.
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