As a middle school history teacher, I've given many many open book tests. I don't want my students to spend hours memorizing dates. I want them to understand the deeper "why" behind the issues. I may ask them to write an essay outlining three causes of the Civil War. Too many students get bogged down in the dates and can't explain the causes. Allowing it to be open book gives them a crutch to know they can look it up if they need to but they'll never finish a high quality essay in 45 if they don't internalize the information in some way.
I've found that open book tests also reduce test anxiety, even among very gifted kids. The fear of missing one is often paralyzing and creates such anxiety! Often they won't even open their books but knowing they can is a huge relief.
