| The Shulman model of teacher knowledge for successful instruction describes several distinct areas of understanding that the teacher needs. This study investigates two factors in the Shulman model with respect to geometry in general, and transformation geometry in particular. These aspects are (a) the origin, rationale, and structure of the geometry curriculum, and (b) knowledge of available curriculum materials in the form of textbooks.;The research into the first question reveals that the National Council of Teachers of Mathematics' (NCTM) Curriculum Standards and its Addenda are the best representation of a common USA curriculum for mathematics, including geometry. This curriculum was evaluated and categorized into specific aims and objectives for geometry. Six high school geometry textbooks, one high school integrated mathematics textbook series, three middle school textbook series, and four primary school textbook series were evaluated to see how they complied with the aims and objectives of the NCTM Standards, with respect to geometry, something they all claimed to do.;The research into the second question reveals that high school texts fail to meet the principle aims of the NCTM Standards, that middle school texts comply, and that primary school texts exceed the requirements of the NCTM Standards in geometry in general, and transformation geometry in particular. |
