Cooperative learning, or CL, is an instructional model commonly used in schools across the country, especially in mathematics. It involves the use of small group learning where students work collaboratively towards a common goal. Throughout my semester-long independent study, I researched how to incorporate cooperative learning into the secondary mathematics classroom and then made various lessons based on my findings. This presentation will discuss the meaning behind the term cooperative learning, its history, its benefits for both students and teachers, and why educators should consider incorporating this instructional practice into their classrooms. I will also discuss the various types and models of cooperative learning that I found in my research, along with best practices for how to successfully implement CL activities in the classroom. Finally, I will describe two mathematics lessons that I designed which incorporate various types and best practices of cooperative learning that I discovered throughout my research.
This presentation is based on Math 491- Differential Geometries taken in Spring 2021. We first define the coordinate patch of a surface and provide a few examples of surfaces. Then we construct the tangent space and normal vector of a given a surface. Afterwards, we compute first fundamental form, second fundamental form and Christoffel symbol of a surface. Then we define mean curvature and Gaussian curvature of a surface. We also will discuss geodesic and parallel vector field of a surface. In the mean time, we will utilize Mathematica technology to sketch the graphs of various surfaces.
Graph theory is the study of sets vertices connected by known as edges, which are depicted as lines. The graph coloring game is a game played on a graph with two players, Alice and Bob, such that they alternate to properly color a graph, meaning no adjacent vertices are the same color. Alice wins if every vertex is properly colored with n colors, otherwise Bob wins when a vertex cannot be colored using n colors. While strategies for winning this game may seem helpful, more interesting is the least number of colors needed for Alice to have a winning strategy, which is called the game chromatic number. We classified a specific tree graph noted as segmented caterpillar graphs that have vertices of degree 2, 3, and 4, for which the game chromatic number have not yet been explored.