Is it good practice to let students consult their text materials during exams? I teach undergraduate level courses in the humanities. Following practice in my department, I have let students take their texts for consultation during their written exams. They can choose a number of questions they want to answer from a set of questions. After a few semesters, I have begun questioning the validity of such an approach. 

I usually had one exam in this form and one final essay in the end of the semester. The issue is, although the subject dealt with in the first part of the course is more or less objective, I find students "copying" my classes much more than using the texts to answer the questions. A complicating factor is that most students cannot presumably understand the material, available only in English. To make it clear, most of my students cannot read English (I could mention the material is not available at the library, but that is another matter). And it is a required course.

What bothers me is that with this approach I cannot, as suspected, measure the level of understanding of the students. Some of the questions deal with very basic issues and concepts. Even then, the overall level of reading, understanding, and writing, as evidenced by their exams and final essays, is very low.

I have thought about changing the syllabus next semester, to one exam (without consultation), perhaps another exam and the final written assignment, but I am quite unsure of the results. Perhaps a lot of students will fail. 

Am I too concerned, or is this the way to go?
I take a compromise approach to the problem of bringing materials to an exam. I allow students to bring one or two sheets' worth of notes that they have prepared themselves. No magnifying glasses or other "reading aids" other than standard prescription glasses are allowed, so they can't simply photoreduce a whole bunch of pages and then use it—it's something they have to hand write or copy themselves.

Such an approach forces students to prepare the material, but still gives them some flexibility not to have to commit everything to memory (Is that sign positive or negative? Is that denominator regular volume or molar volume?).