"I argue that despite broad acceptance and rapid growth in enrollments, the consensus curriculum is still an unwitting prisoner of history. What we teach is largely the technical machinery of numerical approximations based on the normal distribution and its many subsidiary cogs. This machinery was once necessary, because the conceptually simpler alternative based on permutations was computationally beyond our reach. Before computers statisticians had no choice. These days we have no excuse. Randomization-based inference makes a direct connection between data production and the logic of inference that deserves to be at the core of every introductory course." - George Cobb
National standards for teaching statistics at the K-12 level and the introductory college level: Read this first.
An important article about how students learn statistics, including learning theories, what is most important to teach,
and ways we can help students learn.
A great set of examples why the Central Limit Theorem, and particularly the notion of variability of the mean relative to sample size, is
important in real applications.