Geometry Representations in a Textbook

Abstract

The purpose of the study is to enumerate the representations in high school geometry, to narrow the focus to the most common ones, and to describe how the common representations are coordinated. To achieve this purpose, I analyzed several sections of a popular geometry textbook using thematic analysis, semiotics, and a pragmatic approach to capture the variety of representations into categories and to use descriptive statistics to narrow the focus to the most common representations and coordinations. The major findings are the bringing into prominence of representations like textbook gestures, ordered pairs, written language, tables, and their uses, and at the same time understating the importance of less common representations of physical objects. Other important findings are: (1) exposing which representations are most often coordinated like written language (WL), diagrams (D), numbers (N), and ordered pairs (OP), short geometry symbols (Sy), e.g., WL to D, WL+Sy to D, and N+OP to D; (2) some of the mechanisms in that coordination like using, numbers, point names, and textbook gestures, which include color, arrows, font changes, etc. Clarifying the representations in high school geometry and narrowing the scope to the most common ones allows researchers to study various combinations of representations and their impact students.