Nano-Project Qualifying Exam Process: An Intensified Dialogue between Students and Faculty

An effectively designed examination process goes far beyond revealing students’ knowledge or skills. It also serves as a great teaching and learning tool, incentivizing the students to think more deeply and to connect the dots at a higher level. This extends throughout the entire process: pre-exam preparation, the exam itself, and the post-exam period (the aftermath or, more appropriately, afterstat of the exam). As in the publication process, the first submission is essential but still just one piece in the dialogue. Viewing the entire exam process as an extended dialogue between students and faculty, we discuss ideas for making this dialogue induce more inspiration than perspiration, and thereby making it a memorable deep-learning triumph rather than a wish-to-forget test-taking trauma. We illustrate such a dialogue through a recently introduced course in the Harvard Statistics Department, Stat 399: Problem Solving in Statistics, and two recent Ph.D. qualifying examination problems (with annotated solutions). The problems are examples of “nano-projects”: big picture questions split into bite-sized pieces, fueling contemplation and conversation throughout the entire dialogue. 1. “Teach Us How to Prepare . . . ”: Stat 399 as a Conversation Opener Over the more than half-century history of Harvard Statistics, the format of the Ph.D. Qualifying Examination has varied considerably and repeatedly, from the two week “Sleepless in Seattle” exam when one of us (XLM) was taking it in 1987 to the current format of a theoretical examination in two 8-hour parts, and a 32-hour applied examination (all take-home). But one thing has remained constant: there are no specific textbooks or courses around which the qualifying problems are designed. Indeed, many problems are inspired by research projects of individual faculty members. The underlying philosophy behind such problems is to require creativity and an ability to “connect the dots,” recognize patterns, and see when a new problem is essentially equivalent to a familiar problem. Such problems also provide a good opportunity for deeper learning, because they Date: October 31, 2010.