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  1. Free, publicly-accessible full text available April 1, 2023
  2. Olanoff, D. ; Johnson, K. ; & Spitzer, S. (Ed.)
    In this study, we explore the relationships between the types of student exclamations in an enacted lesson (e.g., “Wow!”) and the varying dramatic tensions created by the unfolding content. By analyzing student exclamations in six specially-designed high school mathematics lessons, we explore how the dynamic tension between revelations of mathematical ideas at the moment and what is yet to be known connects with the aesthetic pull to react by the student. As students work through novel problems with limited information, their joys and frustrations are expressed in the form of exclamations.
  3. Olanoff, D. ; Johnson, K. ; & Spitzer, S. (Ed.)
    How does the design of lessons impact the types of questions teachers and students ask during enacted high school mathematics lessons? In this study, we present data that suggests that lessons designed with the mathematical story framework to elicit a specific aesthetic response (“MCLEs”) having a positive influence on the types of teacher and student questions they ask during the lesson. Our findings suggest that when teachers plan and enact lessons with the mathematical story framework, teachers and students are more likely to ask questions that explore mathematical relationships and focus on meaning making. In addition, teachers are less likelymore »to ask short recall or procedural questions in MCLEs. These findings point to the role of lesson design in the quality of questions asked by teachers and students.« less
  4. We propose a generalization of the popular nonlinear ARX model structure by treating its parameters as varying over time. The parameters are considered generated by linear filters operating on the model’s regressors. The filters are expressed as a sum of atoms that are either sum of damped exponentials and sinusoids, or sinusoids with time varying frequencies. This form allows us to enforce stability of the parameter evolution as well as leverage the atomic norm minimization framework for inducing sparsity. It also facilitates easy incorporation of smoothness related priors that that making it possible to treat these models as nonlinear extensionsmore »of the familiar LPV models.« less