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.     

An Analysis of Student Grade Expectations and Marker Consistency

This study sets out to assess the extent to which final‐year students following a four year degree in education have a realistic sense of the strengths and weaknesses of an independent research study they are required to undertake. An analysis of the self‐assessment grades and those of their tutors reveals a poor match, whilst the criteria students use to assess their studies emphasise lower order criteria such as style and presentation, and largely ignore higher order criteria concerned with theoretical and conceptual understanding and the quality of discussion. The paper considers why students appear not to have theorised their experiences, and why there is only limited evidence of a critical understanding of academic writing.