Characteristics of the College Geometry Course for Preservice Secondary Teachers

Based on 30 syllabi and 108 questionnaire responsesfrom randomly selected U.S. colleges and universities,college geometry courses were analyzed with respect tocontent, pedagogy, and assessment. About 40% of thecourses start with elementary axioms and emphasizeEuclidean geometry or a mix of Euclidean andnon-Euclidean geometry; 23% employ a survey approach;and 20% employ an analytic or projective geometryapproach. In about 63% of the courses, the instructorlectures most or all of the time; in 36% of thecourses a substantial amount of class time is devotedto group work; and about 27% of the courses reflectnearly all the characteristics of good mathematicsteaching as defined by the NCTM Professional TeachingStandards. In most courses, in-class examinations,homework, and a final examination are the primaryevaluation tools; in about half of the courses atleast one alternative assessment contributes to thefinal grade. Common characteristics are evident butwide diversity exists also. A typical geometry coursedid not emerge from the data.