Friday 15 February 2019
Sasha Wang (Boise State University)
Constructive Mathematics Learning Pathways: An Integrated STEM Approach
Currently, the development of mathematics content knowledge for prospective elementary teachers (PSETs) takes place in undergraduate courses (CBMS, 2012; AMTE, 2017). In many teacher education programs, PSETs are required to take one or more mathematics content courses from a mathematics department prior to admission into the program. Teacher education and research communities have been examining ways to help PSETs develop a deeper understanding of mathematical concepts, situate mathematics learning in meaningful contexts, and create learning communities in which teachers and students engage in rich mathematical discourses. Some researchers suggest that providing the opportunity of an early field experience to PSETs while they are learning the mathematics could enhance their content knowledge and beliefs. However, very little research has studied PSETs mathematics learning in a mathematics content course through the integration of STEM inquiries that extends their learning experiences beyond mathematics.
Friday 8 March 2019
There is a need to elevate the mathematics learning experiences for PSETs in acquiring mathematics knowledge through inquiries, exploring the role of mathematics in other STEM disciplines, and solidifying knowledge and skills in teaching contexts as sustainable practices. During the colloquium talk, I will introduce an ACE course design model and will discuss its potential for creating an active learning environment to engage PSETs’ mathematics learning. In addition, a framework of designing integrated STEM inquiry will be shared to demonstrate the learning opportunities that PSETs are engaged in.
Marcelo Disconzi (Vanderbilt University)
Recent developments in relativistic viscous fluids
Relativistic hydrodynamics, the study of fluids in regimes where relativity theory cannot be neglected, is one of the most widely used tools in the study of relativistic phenomena. It is fundamental in the construction of the standard model of cosmology and has a wide variety of applications in nuclear high energy physics and astrophysics. The last decade has witnessed a spark of interest in the study of relativistic fluids with viscosity, in part due to the rich dynamics of the quark-gluon plasma and the growing awareness of the importance if viscous dissipation in neutron star mergers. Despite its importance, the construction of consistent models of relativistic viscous fluids has proven to be quite challenging. The simplest and most natural models have been showed to be unstable and to violate causality, the latter being a fundamental property of relativity theory. More sophisticated models have been showed to be causal and stable near equilibrium and at the linearized level and in Minkowski background (i.e., without coupling to gravity). Besides these restrictions, in all such models it is not known if solutions to the equations of motion exist and are unique (except for highly symmetric situations). In this talk, after introducing the appropriate background, we will discuss some recent results that settle the question of causality, existence, and uniqueness of solutions for different models of relativistic viscous fluids.