Abstract. Thurston defined invariant laminations, i.e. collections of chords of the unit circle S (called leaves) that are pairwise disjoint inside the open unit disk and satisfy a few dynamical properties. To be directly associated to a polynomial, a lamination has to be generated by an equivalence relation with specific properties on S; then it is called a q-lamination. Since not all laminations are q-laminations, then from the point of view of studying polynomials the most interesting are those of them which are limits of q-laminations. In this paper we introduce an alternative definition of an invariant lamination, which involves only conditions on the leaves (and avoids gap invariance). The new class of laminations is slightly smaller than that defined by Thurston and is closed. We use this notion to elucidate the connection between invariant laminations and invariant equivalence relations on S.

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Increasing integration of mathematics and biological concepts is an area of intense focus in education. Our goal is to develop a platform through which elementary mathematics and science instructors can collaborate with one another in order to demonstrate to their students the connectedness of the two disciplines. Our focus is to apply mathematics common core standards to biological phenomena. One strategy is to show how standards in geometry can be applied to cells. In order to do so, cells of various shapes were viewed under the microscope and then photographed. The images were incorporated into Geometer's sketchpad where perimeter, circumference, and/or area were determined based on the relative shape of the cell. Although this experiment was developed with elementary teachers in mind, we feel that extensions of this exercise would be well suited in secondary and higher education.

Increasing integration of mathematics and biological concepts is an area of intense focus in both secondary and higher education. Our goal was to develop a platform through which high school mathematics and biology instructors could collaborate with one another in order to demonstrate to their students the connectedness of the two disciplines. Our focus was to apply mathematics common core standards to biological phenomena. One strategy was to show how principles of mathematical modeling could be used to solve population genetics problems. In order to do so, we instructed teachers on how population genetics problems could be modeled and solved using the software, Stella®. We first taught instructors basic functions of the software and then demonstrated how Stella® could be used to answer problems in population genetics. Based on feedback from the instructors, we feel that this provided them with a unique experience that they will be able to use in their classrooms. Grant Funding Source: Supported by the Tennessee Higher Education Commission