Example 3. How many ways are there to put m balls into n bins. Assume m ≤ n. 1. Balls are distinct and bins are distinct. Every ball has n choices. Hence n. Exercise 2. Why is the answer not m by looking at the opposite argument. 2. Balls are not distinct but bins are distinct. Take m identical balls and n− 1 identical sticks and permute them. Every permutation gives a different arrangement. So...

Eulogy for Jim Marshall (read at the funeral)Michael A. PetersBeijing Normal UniversityMy deepest condolences to Pepe, Dom and Marcus Jim’s grandchildren. Tina I spent a lot of time t...

In 1986, the Harvard Educational Review published Jim Cummins’s article “Empowering Minority Students: A Framework for Intervention,” which offered a theoretical framework for addressing the achievement gap of minority students. Despite considerable attention to this issue, educators have seen little encouraging progress. Even now, fifteen years after its original publication, Cummins’s article...