## Congratulations Dr. Boileau!

Dr. Nicolas Boileau, a researcher from the GRIP lab, defended his dissertation titled “An Investigation of the Relationship Between Two Norms of the Instructional Situation of Geometric Calculation with Algebra in U.S. High School Geometry” on Wednesday, December 16. Nic originally became interested in mathematics education research while working as a high school math teacher, specifically, when he realized that he wanted to spend more time thinking about questions around math teaching and learning that he did not have enough time to think about as a teacher. This led Nic to pursue a masters in teaching mathematics degree from Concordia, and a Ph.D. in educational studies at the University of Michigan. In Nic’s dissertation, he focused on the relationship between two hypothesized norms of an instructional situation in U.S. high school geometry, called geometric calculations with algebra (GCA). To do this work, Nic conducted a virtual breaching experiment. The experiment consisted of randomly assigning U.S. high school mathematics teachers to sets of multimedia questionnaires, each of which confronting the participant with a storyboard representation of a classroom scenario in which each of the two hypothesized norms is either breached or followed (depending on the experimental condition) and captures their reactions using a common set of open- and closed-response items. He was able to provide some evidence that his two hypothesized norms—the GCA-Figure norm and the GCA-Theorem norm—exist, as well as demonstrate that, while experienced U.S. high school geometry teachers’ attitudes towards breaches of the GCA-Theorem are independent from whether the GCA-Figure norm is followed, breaches of the GCA-Figure norm may cause them to abandon their expectation that the GCA-Theorem norm will be followed. Nic is currently continuing his scholarly work as a research associate at the University of Michigan.