Teachers’ Expectation About Geometric Calculations in High School Geometry

Abstract

This paper reports on a study of the instructional situation in high school Geometry that Hsu (2010) called Geometric Calculation in Algebra (GCA). In particular, we conducted a virtual breaching experiment in order to examine the extent to which high school teachers recognized breaches of two norms that we conjectured to describe geometry teachers’ expectations of this work context. The results of our analysis of the data (using z-tests and mixed effect regression models) provide evidence that, in the situation of GCA, (1) teachers appear not to take issue with giving students tasks that require them to set-up and solve equations whose solutions have no geometric meaning (e.g., the length of a side of the figure is zero), and (2) teachers do not appear to expect students to document the geometric theorem or property that justify the setup of those equations (highlighting the contrast between the situation GCA and that of doing proofs).