Geometry is the only domain which is present in every grade, K-12, in the Common Core State Standards for Mathematics (CCSSM), but despite—or perhaps because of—this, it is also under-emphasized in almost every grade. This module is designed to deepen participants’ knowledge and understanding of the CCSSM expectations for Geometry in Grades 7-12, with a brief look-back to the standards from earlier grades to emphasize the overall K-12 coherence of the geometry domain.
One important difference between the CCSSM and earlier geometry standards is an increased emphasis on transformations (translations, rotations, reflections, and dilations) and transformational arguments in the Common Core. Transformations are not necessarily studied for their own sake, but rather because they afford a quick and intuitive approach to more advanced results and applications of geometry. Nevertheless, the transformational approach is new and unfamiliar to many teachers of geometry, and this module will present teachers with a grounded introduction to transformations so that they can make an intentional decision as to the extent to which they will study transformations in their own classes.
Topics to be studied in the workshop include: an introduction to translations, reflections, and rotations; geometry and measurement standards in early grades and the van Hiele levels; and the transformational approach to congruence and similarity. The CCSSM Standards for Mathematical Practice, and their appearance through a geometric lens, will be addressed throughout.
- Become familiar with the progression of standards for geometry across Grades 7-12.
- Deepen understanding of the transformational approach to geometry advocated by the CCSSM.
- Explore the nature and importance of conjecture and proof in geometry.
- Deepen understanding of the ways in which students’ geometric understanding grows and implications for classroom instruction.