Studies have demonstrated that norms have considerable influence on human behaviour, in particular, that of teachers and students in mathematics classrooms. Studies have also shown that breaches of norms are frequently sanctioned, sometimes positively, but typically negatively. The present study builds on that literature by investigating two other potential consequences of breaching norms of mathematics instruction: that breaches of one norm of a given instructional situation may lead teachers to abandon their expectations that other norms of that situation will be followed and/or alter their attitudes towards breaches of those norms. I focus on the relationship between two hypothesized norms of geometric calculations with algebra (GCA) in U.S. high school geometry. One of them, the GCA-Figure norm, stipulates that the GCA problems that U.S. high school geometry teachers assign are expected to have geometrically-meaningful solutions. The other, the GCA-Theorem norm, stipulates that, when solving GCA problems, students are expected to document their algebraic work, to occasionally verbally state the geometric properties that warrant the equations that they set up, but not to document those properties. To confirm the existence of those norms and investigate whether breaches of the GCA-Figure norm would have either of the aforementioned consequences, I conducted a virtual breaching experiment. This consisted of randomly assigning U.S. high school mathematics teachers to one of three sets of multimedia questionnaires. Each questionnaire confronted the participant with a storyboard representation of a classroom scenario in which each of the two norms is either breached or followed. Their reactions to each storyboard were captured through a set of open- and closed-response items. Scores, based on coded open-responses and closed-responses, were compared across experimental conditions, using statistical models. This was done to predict whether experienced geometry teachers would be more likely to recognize decisions to breach either norm than decisions to follow it (evidence that the hypothesized norm exists), to deem decisions to breach it more acceptable than decisions to follow it, and/or to remark or disapprove of decisions to breach the GCA-Theorem norm when the GCA-Figure norm is followed than when it is breached. Results suggest that experienced geometry teachers’ expectations of GCA problems are well-represented by the above statement of the GCA-Figure norm, but that their expectations of solutions to GCA problems are slightly different than hypothesized. Namely, they suggest that experienced geometry teachers expect students to document their algebraic work, but not to share their geometric reasoning (verbally or in writing). In terms of attitudes towards breaches, results suggest that experienced geometry teachers are generally opposed to problems that breach the GCA-Figure norm, but do not provide much information about their attitudes towards students sharing their geometric reasoning, suggesting the need to develop alternate ways of measuring such attitudes in future research. Lastly, results suggest that experienced geometry teachers’ attitudes towards breaches of the GCA-Theorem norm are not dependent on whether the GCA-Figure norm is followed, but that such teachers may abandon their expectation that the GCA-Theorem norm will be followed when the GCA-Figure norm is breached. While the dissertation’s main contribution is to our understanding of norms of mathematics instruction, it also has implications for instructional improvement. Namely, the latter result suggests that changing even a very specific behaviour may alter whole systems of expectations—something that reformers must consider when anticipating what their recommendations will require.