  The maximum rectilinear crossing number of a graph $G$ is the maximum number
of crossings in a good straight-line drawing of $G$ in the plane. In a good
drawing any two edges intersect in at most one point (counting endpoints), no
three edges have an interior point in common, and edges do not contain vertices
in their interior. A spider is a subdivision of $K_{1,k}$. We provide both
upper and lower bounds for the maximum rectilinear crossing number of spiders.
While there are not many results on the maximum rectilinear crossing numbers of
infinite families of graphs, our methods can be used to find the exact maximum
rectilinear crossing number of $K_{1,k}$ where each edge is subdivided exactly
once. This is a first step towards calculating the maximum rectilinear crossing
number of arbitrary trees.
