A MINI HISTORY OF GEOMETRY WITH AN EMPHASIS ON TRANSFORMATIONAL GEOMETRY AND AN ANALYSIS OF ILLUSTRATIVE MATHEMATICS GEOMETRY CURRICULUM

Abstract

Before completing an analysis of Illustrative Mathematics – Geometry, Congruence Unit two, two things needed to occur, there needed to be an understanding of the history of geometry and the standards to which geometry is taught. The focus of this mini history is Euclid’s geometry and Transformational geometry, so to develop an understanding of how the two are different. Until recently Wisconsin used the Common Core State Standards for Mathematics, in 2021 Wisconsin adopted the Wisconsin Standards for Mathematics. A comparison of the two sets of standards was completed to determine which standards should be used for the analysis of Illustrative Mathematics – Geometry, Congruence Unit. For the purpose of this paper, the Common Core State Standards for Mathematics were used. Since the Common Core State Standards for math claim to use a transformational approach to teaching foundational concepts of geometry, they were used to analyze the Illustrative Mathematics – Geometry curriculum to determine if Illustrative Mathematics also uses a transformational approach. For time purposes Unit 2: Congruence from Illustrative Mathematics was analyzed. To do the analysis, the standards covered in each lesson were compared with the activities from the lessons to determine if they were meeting what was required from the standards. After Unit 2: Congruence was completely analyzed it was determined that Illustrative Mathematics appears to use a transformational approach in this unit of the geometry curriculum.