The Effects of Student-Teacher Ratio and Interactions on Student/Teacher Performance in High School Scenarios
We develop a model that incorporates the impact of sudden-teacher ratio on the performance dynamics of both teachers and students. The model assumes that the members of both populations may be found in three dynamics states: positive, discouraged and reluctant. The role of complex nonlinear interactions between students and teachers, as well as the role of recruitment and intervention, are studied via analytic and numerical studies. Using center manifold theory we find conditions for the existence of a backward bifurcation that support endemic stationary states below the critical threshold value, R0 < 1, when normally only a positive environment would be supported. Our simulations show that in order to maintain a positive environment for students and teachers, R0 must be reduced significantly. Since R0 is a function of student-teacher ratio this can be achieved by decreasing class size.
- Poster session award recipient at the 2004 AMS/MAA Joint Mathematics Meeting in Phoenix, AZ
Katie Diaz, Mills College - Oakland
Cassie Fett, Bemidji State University - Bemidji
Griselle Torres-Garcia, University of Puerto Rico - Mayaguez
Nicolas M. Crisosto, UC Berkeley-Berkeley