More Like this

1. Party System Congruence and Bicameralism

   https://doi.org/10.1177/00104140241302767  

   Kim, Wooseok; Hicken, Allen; Kollman, Ken (November 2024, Comparative Political Studies)

   We compare the nature of party systems across bicameral legislatures using newly available data on upper chamber elections. We examine the similarity in the composition of political parties between the lower and upper chambers (partisan congruence) and introduce a novel measure that captures differences in the nationalization of parties between the two chambers (nationalization congruence). We explore variations in these measures across countries and over time and demonstrate that the power of the upper chamber (symmetry) is linked to both forms of congruence. Moreover, we apply these measures to understand how the interaction between congruence and symmetry—two key dimensions of bicameralism—influences policymaking, focusing on government spending patterns. Our findings reveal that partisan and nationalization congruence can have contrasting implications for government spending in symmetric bicameral systems but have negligible implications in asymmetric bicameral systems. 

   more » « less
2. Congruence RFRS towers

   https://doi.org/10.5802/aif.3532  

   Agol, Ian; Stover, Matthew (January 2023, Annales de l'Institut Fourier)
3. Congruence subgroups and super-modular categories

   https://doi.org/10.2140/pjm.2018.296.257  

   Bonderson, Parsa; Rowell, Eric; Wang, Zhenghan; Zhang, Qing (January 2018, Pacific Journal of Mathematics)
4. Prospective High School Teachers’ Understanding and Application of the Connection Between Congruence and Transformation in Congruence Proofs

   St. Goar, J.; Lai, Y.; Funk, R. (January 2019, Proceedings of the 22nd Annual Conference on Research in Undergraduate Mathematics Education)

   Undergraduate mathematics instructors are called by recent standards to promote prospective teachers’ learning of a transformation approach in geometry and its proofs. The novelty of this situation means it is unclear what is involved in prospective teachers’ learning of geometry from a transformation perspective, particularly if they learned geometry from an approach based on the Elements; hence undergraduate instructors may need support in this area. To begin to approach this problem, we analyze the prospective teachers’ use of the conceptual link between congruence and transformation in the context of congruence. We identify several key actions involved in using the definition of congruence in congruence proofs, and we look at ways in which several of these actions are independent of each other, hence pointing to concepts and actions that may need to be specifically addressed in instruction. 

   more » « less
5. Prospective High School Teachers’ Understanding and Application of the Connection Between Congruence and Transformation in Congruence Proofs.

   St. Goar, J. (January 2019, Proceedings of the 22nd Annual Conference on Research in Undergraduate Mathematics Education)