112b9edb_metry_for_Educators_Appendix_C___proficiency_in_each_standard_
Geometry and measurement from both abstract and concrete perspectives and to identify real world applications, and mathematical concepts, procedures and connections among them including: . Formal and informal argument. . Names, properties, and relationships of two- and three-dimensional shapes. . Spatial sense. . Spatial reasoning and the use of geometric models to represent, visualize, and solve problems. . Transformations and the ways in which rotation, reflection, and translation of shapes can illustrate concepts, properties, and relationships. . Coordinate geometry systems including relations between coordinate and synthetic geometry, and generalizing geometric principles from a two-dimensional system to a three-dimensional system. . Concepts of measurement, including measurable attributes, standard and non-standard units, precision and accuracy, and use of appropriate tools. . The structure of systems of measurement, including the development and use of measurement systems and the relationships among different systems. Measurement including length, area, volume, size of angles, weight and mass, time, temperature, and money. . Measuring, estimating, and using measurement to describe and compare geometric phenomena. . Indirect measurement and its uses, including developing formulas and procedures for determining measure to solve problems.
All of these content areas are prerequisite knowledges for the current course, but they are not a focus of the course, since they appear to reflect lower level geometric knowledge and this is a graduate level course; consequently, they are not formally assessed in this course per se, although teachers cannot demonstrate their complete understanding of this courses' topics without having a certain amount of proficiency with these lower level topics. There are two exceptions to the above statement; the first occurs in the area of spatial reasoning and the use of geometric models to represent, visualize and solve problems. In the study of spherical geometry, teachers use Lenart spheres and spherical compasses to visualize spherical geometry concepts and solve problems. They are assessed on their use of these models and their problem solving ability in spherical geometry on homework, exams, projects, and presentations. The other exception is in the area of using measurement to compare geometric phenomena. Angle sizes and sums of angles in various spherical and hyperbolic polygons are compared to results from Euclidean geometry. Teachers knowledge is assessed on homework, exams, and projects.
Geometry for Educators Appendix C
In this column, indicate the nature of the performance assessments used in this course to evaluate student proficiency in each standard.