Open book exams are challenging, but how do we prepare undergraduate students for this type of exams? And what is best, multiple choice or essay type questions?
Multiple-choice type questions appear to me to not further enhance the students' knowledge - it is a too narrow scope. I see little chance of asking questions where the student can elaborate upon the question, and the latter type of question I find to be much better in order to see how deep the student's knowledge has reached.
If you are using open book you should use short answer, graphing, calculation, etc. exam questions. That way students can really show their level of understanding. Multiple choice exams are harder to write, easy to grade, but students can always just guess and they don't have to explain their reasoning behind their answers.
You prepare them by giving them exam-level difficulty open book practice questions either as a group problem, homework, or similar.
Open book exams still mostly relate to definitions of terms and other low-levels of knowledge.
Critical thinking should be evaluated in other ways, such as essays, case studies, or "take-home" tests featuring critical thinking questions/problems, with the requirement to employ concepts and terminology from class.
To my opinion multiple choice questions only show recognition of terms, so they are low level. However they are probably easiest to evaluate. If I use them, I ask students for some additional work for their final grade - a case study, project or similar. I find essays good to evaluate knowledge but very difficult to grade.
Prefer to give a formula sheet than allowing students to have full access to the book. In any case, the direct answer will rarely be available in the book. So why shall i waste their time and stress them?