Last semester I had a teacher who let us use any type of information in the exam, for example the course notes, books, solved exercises, etc. The only thing he did not let us use was something electronic like smartphone. Of all the teachers that have given me classes (like 30) this is the first one to evaluate in this way and I do not think I will have it again.
Why do not all teachers evaluate in this way?
Personally, it served me enough to have these freedoms to be able to pass the course.
An exam is a totally artificial scenario. In real life you will never be in a scenario with all these fact at same time: a) you can not consult external resources or colleagues; b) you have limited time; c) you do not known the activity before to start it. As conclusion, exams should be deprecated in all forms, with or without consultation of external resources. They exists only because they are a fast and practical way to obtain a numerical evaluation for a big (massive) group of students.
Starting from this point and returning to the question about usage of external sources of information, we can analyze some different scenarios:
a) if a concept is basic, could be it is already acquired before the exam (not the same than memorized) or student will fail the test, because he/she has no time to acquire the concept and use it only during the time allowed for the exam.
b) thus, to have or not to have access to external sources of information is only a difference in the case of specific items of data information, like some particular formulas, taxonomies or algorithms. In these cases, allow notes or books has only advantages. In fact, if something can be successfully retrieved during the exam it means it is not knowledge but data.
c) allow notes minimizes some of the usual drawbacks of the (artificial method) exams: when anxiety causes a fail in the memorization of a data term; a question that fails into a paragraph that has been ignored as unimportant; it made useless hidden notes that benefits only cheaters; ... .
d) if the student has not acquired confidence in its book, course notes and/or write own abstracts, the presence of them during the exams will not help. Thus, allow these resources encourages the necessity of write abstracts, organize sources, ...
One classical example is the periodic table in chemicals. It is the perfect example of a resource to allow, not to memorize, and instead use this time to most conceptual activities (in my country, students loss months memorizing it).
In conclusion: skip usage of exams; if exams are a must, allow books, notes, even intranet.
Making a course easier to pass is not the same as making a good course. There is a certain corpus of knowledge with which practitioners are expected to have instant recall (a.k.a: "automaticity"). If one were to be looking up all of these basic facts constantly, one would not be able to accomplish anything practical. These basic topics are the ones mostly likely tested by standard college exams. Cognitive scientist Daniel Willingham writes (link):
Automaticity is vital in education because it allows us to become more skillful in mental tasks. An effective writer knows the rules of grammar and usage to the point of automaticity—and knows automatically to begin a paragraph with a topic sentence, include relevant detail, etc. The effective mathematician invokes important math facts and procedures automatically. Readers who are able to visualize a map of the world will find various books and assignments easier to read (and learn more from them). In each field, certain procedures are used again and again. Those procedures must be learned to the point of automaticity so that they no longer consume working memory space. Only then will the student be able to bypass the bottleneck imposed by working memory and move on to higher levels of competence.
Secondarily (as stated in a comment), "all of my classmates approved this course, so it was a good idea to do this" is not a valid justification. There is evidence that given the choice between different pedagogical strategies, students tend to choose the strategy from which they learn the least. See Clark, "Antagonism between Achievement and Enjoyment in ATI Studies", Educational Psychologist 17, no. 2 (1982)
I think that allowing students to use resources on exams can work well in certain situations, such as when the knowledge they can pull from those resources is peripheral (not of core importance to the course) or terminal (not going to be built upon in the future). However, I think it is very rare for all of the material in a math class to fall into one of these categories. For peripheral knowledge you'd want the instructor to select specific items and include something like a formula sheet.
Terminal knowledge is quite rare in mathematics. Math curriculum is generally cumulative. A math course builds on previous courses and sets a foundation for future courses. Suppose for example that I ask you "what is three times five?" and you have to first look up how multiplication works. This will slow you down, but perhaps it won't cripple you completely and you'll be able to answer in a few minutes. But if we take it a step further, suppose you have to look up what the quantities "three" and "five" refer to, how to add quantities, and (eventually) how to multiply quantities.
You might correctly argue that this example is too extreme, and of course students will internalize these concepts along the way. This is true, but exams say to students "you should have this concept internalized now". If you teach material one semester, but let students wait until a future semester to actually internalize it, in practice I think they will forget it and have to learn it all over again.
I think it is usually counterproductive. Instead of building skills, it rewards students who are good at information retrieval. And I say that as one of those advantaged.
Still remember a P-chem course where prof said he would do this AND he also curved the course. I ended up with highest grade, but did not "master" the course as I had calculus, freshman chem, etc. Would have gotten much more benefit from the opposite policy.
And...I am 50+ and routinely work with things where I used the Internet, books, etc. So this is not something I don't grok. But to really master a subject, the memory and recall in a test situation is much more powerful.
Just a contrary view to others, but hope it has some additive insights.
I allow students to have one index card of notes during their exams. I believe this allows me to test for understanding and skills that are more important than the ability to memorize. I also believe that it reduces student anxiety and creates a level playing field (instead of having only a few students using "cheat sheets," all of them are given this advantage).
I do think, however, that allowing students to use a lot more resources (such as books and pages of notes) during exams is counterproductive. The first time I taught, that was what I did, and I quickly learned that this discouraged students from studying. They believed that they did not need to study before the exam because they could study during the exam. A lot of students failed that exam, but, more importantly, a lot of students didn't learn.
When you have to solve a problem later, in real life, you will also be allowed to use all available sources of information (even including internet and your coworkers). Therefore it is a good idea to let students use their notes, scripts, books (including dictionaries if their native language is not that of the exam).
But, to answer your question, there are some disadvantages. Some students may not afford to buy all helpful material (if, for instance, there are only few copies of a useful book in the library) and the situation easily becomes unpracticable and confusing when students hide behind mountains of material. Too much material may even be a handicap. Further it is obvious that no material must be allowed when there are questions to check pure knowledge and memory.
But in case of exams where problem solving is the major topic, like it is often the case in mathematics or physics, it is certainly a matter of fairness, when a script or formulary is allowed. I used to allow students to write into their formularies whatever they wanted (if they owned personal copies, not taken from the library) and I allowed them to write one sheet of paper for use in the exam. But it must be handwritten by themselves! I always told this during the very first lesson. The idea behind was that they sit down at home immediately after the lessons and write down what they find important. Of course after some lessons the space was filled, and they had to sum up and to rewrite their sheet. So they wrote many sheets and learnt the important formulas - and often did not need at all the sheets in the exam.
I believe the choice is based on the expectations: what does the teacher expect the student to be able to do with the course content?
As most of the course are of the second kind, in most cases course material is not to be allowed during an exam.
