Problems live in two worlds. Externally we see the task; internally we build a “problem space,” a mental map of the current state, the goal state, plus possible moves in-between. When the space is huge, random searching stalls. “We need not be concerned with how large the haystack is, if we can identify a small…

Benjamin Bloom found that tutoring and mastery learning were incredibly powerful ways to teach and learn. In the decades since, teachers and researchers alike have asked how those techniques can be used in a group setting. In fact, I conducted some research and wrote an article about it 13 years ago (Searching for the two…

I recall watching a fourth-grader tackle long division for the first time. Her shoulders slumped under the weight of those mysterious little “houses” and remainders. A few well-timed hints from her teacher, ​“First decide what you know; then pick one next step” ​and she began carving a workable path through the problem. This scene captures…