The changing expectations for the reading of geometric diagrams

Abstract

Students studying geometry at the secondary level are expected to read diagrams in different ways than those in elementary school. In this paper, we present an analysis of the changes in diagrammatic expectations by comparing the geometric diagrams found in Grade 1 U.S. textbooks with those in U.S. high school geometry textbooks. This work included developing and using a coding scheme that recognizes dimensions of reading a diagram geometrically, including the type of object represented, use of deduction, use of mental redrawing, interpretation of markings, and the necessity of the diagram. The way in which elementary and secondary students are expected to interpret diagrams was shown to change along several of these dimensions, posing potential learning barriers for students. We end our paper with a discussion of what our results mean for the learning of geometry