A cross-national study of calculus

The results from a cross-national study comparing calculus performance of students at East China Normal University (ECNU) in Shanghai and students at the University of Michigan before and after their first university calculus course are presented. Overall, ECNU significantly outperformed Michigan on both the pre- and post-tests, but the Michigan students showed a larger gain and normalized gain, and hence narrowed the gap. ECNU\u27s superior performance was especially striking on the subset of problems requiring only a pre-calculus background. On those, Michigan\u27s post-test scores were below ECNU\u27s pre-test scores and, indeed, ECNU\u27s higher performance on both the overall pre-test and overall post-test is attributable to its success on these problems

Products of Geodesic Graphs and the Geodetic Number of Products

Given a connected graph and a vertex $x ∈ V (G)$, the geodesic graph $P_x(G)$ has the same vertex set as $G$ with edges $uv$ iff either $v$ is on an $x − u$ geodesic path or $u$ is on an $x − v$ geodesic path. A characterization is given of those graphs all of whose geodesic graphs are complete bipartite. It is also shown that the geodetic number of the Cartesian product of $K_{m,n}$ with itself, where $m, n ≥ 4$, is equal to the minimum of $m, n$ and eight