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.

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    $\begingroup$ Actually all of my classmates approved this course, so it was a good idea to do this. And I think we also learned. What could be a negative effect ? $\endgroup$ – user10026 Jul 6 '18 at 5:35
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    $\begingroup$ Actually all of my classmates approved this course --- This is a rather weak argument since your classmates are clearly not impartial judges. That said, I've done this often, and variations of it (notes only, books only, "formula sheet" with anything you wish written on it, etc.), but it's not appropriate in some situations, such as gateway calculus tests on derivatives or trig tests on basic trig facts and identities. $\endgroup$ – Dave L Renfro Jul 6 '18 at 10:01
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    $\begingroup$ Imagine ... if your first-grade teacher did not require you to memorize the alphabet ... and now, whenever you look something up in a dictionary, you have to pull out and look at your "alphabet card" to use in your search. $\endgroup$ – Gerald Edgar Aug 5 '18 at 13:18
  • $\begingroup$ @GeraldEdgar I understand your point. But sometimes it's really difficult to memorize all the definitions, ideas of theorems, ideas of the respective proofs, etc. A topology course is a good example of lot of these. Therefore notes/book would be very helpful in exams time. $\endgroup$ – user10026 Aug 5 '18 at 21:12
  • $\begingroup$ I've removed the (teacher-evaluations) tag, as that tag appears to refer to how teachers themselves are evaluated and not how teachers evaluate (test/assess) their students. $\endgroup$ – J W Aug 6 '18 at 10:32

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.

  • $\begingroup$ I really like this answer :) $\endgroup$ – user10026 Jul 12 '18 at 0:41
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    $\begingroup$ With respect to c - In some contexts the ability to perform under stress is a good indicator of mastery. When anxiety causes failure this often indicates that the student has not assimilated the material sufficiently. Put still another way, one practices so that success is achieved in spite of adverse conditions. This makes most sense with respect to routine, basic operations. Think of someone performing music on a stage, who has to play the notes correctly despite the pressure of public performance. This is what examinations that cause stress to the examined intend to test. $\endgroup$ – Dan Fox Jul 24 '18 at 10:01
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    $\begingroup$ "... it means it is not knowledge but data." Is it really so simple to draw a clear cut distinction between "retrievable data" vs. "knowledge"? Could you point me to an established (among cognitive scientists) definition of knowledge, that makes it clear that retrievable data is not knowledge? $\endgroup$ – Michael Bächtold Aug 5 '18 at 7:58
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    $\begingroup$ @DanFox: Following your simile, the pianists have the score in front of them. I agree with you that it is important teach how to handle stress, anxiety, .. and also some other issues as handle a conflict, public speech, ... but these are a few off-topic to this question and to math learning. $\endgroup$ – pasaba por aqui Aug 5 '18 at 9:51

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)

  • $\begingroup$ This is a good answer and all that you say here is true, but it's also true all that @pasabaporaqui says in his/her first paragraph of his/her answer. Don't you think? $\endgroup$ – user10026 Jul 12 '18 at 1:12
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    $\begingroup$ @Isa: No. Exams are a necessary means to verify what students have really learned/automated (i.e., the primary anti-cheating/outsourcing measure). $\endgroup$ – Daniel R. Collins Jul 12 '18 at 1:51
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    $\begingroup$ @DanielR.Collins, you state an absolute "exams are a necessary means to ...", instead say "exams are a method to ...", and support this uniqueness in the "primary anti-cheating" (?). In this way, you discard all evaluations of a practical activity or group activity. $\endgroup$ – pasaba por aqui Aug 5 '18 at 8:36
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    $\begingroup$ If the objective of the test is evaluate an automation, presence or absence of books and other external sources of information will be not a difference. Thus, tests of automation is not a rationale against allow them. Moreover, "working memory space" is a computer concept not applicable to humans. $\endgroup$ – pasaba por aqui Aug 5 '18 at 8:40
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    $\begingroup$ "given the choice between different pedagogical strategies, students tend to choose the strategy from which they learn the least": if this rule was true, one of the consequences is that self-training doesn't exists. $\endgroup$ – pasaba por aqui Aug 5 '18 at 8:48

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.

  • $\begingroup$ Terminal knowledge is very common in math classroom. Using very basic concepts: is "scalene" terminal ? it is the term "mixed fraction" ? $\endgroup$ – pasaba por aqui Jul 8 '18 at 15:44
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    $\begingroup$ Even for terminal things, I find that having learned it once decently is better than never having internalized it, in the odd times that you need to go back. For instance, not using organic chem for a couple decades, than needing it. Much easier having once learned it decently versus hazy. The pathways seem to still be there and get found again. Even psychologically there is an advantage, in that you think "I should know that, I did know that, will be easy to pick up again" versus "never really learned it". In the course of an education and a life there are a slew of things like that. $\endgroup$ – guest Jul 8 '18 at 19:39
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    $\begingroup$ Also of course there is a lot of content that you should internalize. The quadratic formula should almost be an icon (especially for science/engineering students)...it is everywhere, even all over the 2nd order diffyQ for feedback and damping. $\endgroup$ – guest Jul 8 '18 at 19:40

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.

  • $\begingroup$ '..the memory and recall in a test situation is much more powerful.' yes you are totally right but usually it's not easy to recall every definition, theorem, lemma, etc. so how to manage to recall all the knowledge? People usually recommend to draw figures in order to remember a certain theorem and but this helps just to remember the idea and not the complete conditions of the theorem. $\endgroup$ – user10026 Jul 7 '18 at 18:29
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    $\begingroup$ " it rewards students who are good at information retrieval": the alternative rewards students good in memorization. "memory and recall in a test situation is much more powerful.", not, it isn't, include as part of a method "consult table xxx" is as powerful (and safer) as "recall value of xxx". It is only a few slower. $\endgroup$ – pasaba por aqui Aug 5 '18 at 9:36

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.

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    $\begingroup$ I quickly learned that this discouraged students from studying --- Having "books and pages of notes" also results in students spending all their time flipping through page after page of stuff looking for ideas on how to solve a problem and not spending much time actually trying to solve the problem. Thus, you have this buzz of activity during the test, and you think there's all this work being done by students, but when you get the test papers you find very little written on them. (continued) $\endgroup$ – Dave L Renfro Jul 7 '18 at 17:49
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    $\begingroup$ I tended to use only a one-page "formula sheet" for major tests (if anything at all was allowed), and I reserved the more experimental situations that involved students using books and other things for short low-stakes quizzes. $\endgroup$ – Dave L Renfro Jul 7 '18 at 17:50
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    $\begingroup$ If a lot of students failed a first exam, they already learn that to have access to the book doesn't skips the necessity of previous study. Thus, this problem appears because books are infrequently allowed. If books are allowed always from 12 years old, this problem disappears. $\endgroup$ – pasaba por aqui Jul 8 '18 at 15:53
  • $\begingroup$ @pasabaporaqui, thanks, I had not thought of that. $\endgroup$ – Joel Reyes Noche Jul 8 '18 at 23:44
  • $\begingroup$ @pasabaporaqui you are totally right. I like the way you think. $\endgroup$ – user10026 Jul 12 '18 at 0:59

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.

  • $\begingroup$ If no one has a script, or page of notes etc. and everyone takes the same exam then it would seem more fair than the situation where different students have larger and smaller piles of books they haul with them to an exam. Even so, it seems far more fair than online courses where no judgement can be made as to who is actually taking given exams during the course. While perhaps it is nice to allow scripts (I tend to do this), it does not follow extensions of this policy are wise. A large part of having a test is verifying a certain pre-existing competence of the student, not their google-savvy $\endgroup$ – James S. Cook Jul 6 '18 at 14:28

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?

  • If the student needs to show that (s)he is able to use the course content to do something which is not stated in the course, then let the student use all the course material.
  • If the student needs to show that (s)he knows the course material by heart, then it obviously makes no sense to allow the course material during the exam.

As most of the course are of the second kind, in most cases course material is not to be allowed during an exam.


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