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Recently two friends of mine have come back to Australia after having done 2 semesters of 3rd and 4th year subjects (about half mathematics) at different branches of the University of California.

They said that the tests would only ask questions directly from or similar to material covered in lectures and example sheets. If questions deviated from the lectures or example sheets very much students would complain to the lecturer. Thus, if one studied the example sheets enough they got an A relatively easily. They returned with A or A+ in all of their maths subjects, but they average about 75-80 for their maths subjects here. In Australia, about 70% of the exam is usually like that. The rest are questions that we learned enough theory to feasibly do, but we hadn't seen that type of question before so it requires some level of cleverness to get it within the time limits of the exam.

My questions are

Can anyone corroborate that the maths tests at american universities are actually like this?

If so, is this well known and accounted for by the people who look at grad school applications from international students?

How do they fairly evaluate the performance of international applications? How are Australian applicants generally viewed by them?

Edit: Chris's answer below seems to answer the first question by "not quite", which is what I expected I suppose. The other questions still stand.

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    For the first question: there's no general answer. Instructors design their own classes, including the exams; some may decide to have exams like you describe, and others may be just the opposite. Commented Jul 7, 2013 at 14:38
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    I don't think you can make such a broad generalization about American universities. In my first year math course, for example, we had exams in which none of the material was directly from the homework/readings, and the first page consisted entirely of definitions we had not seen which we would need for the questions on the exams. The average was on the order of 30-40% for some of these. Commented Jul 7, 2013 at 15:23
  • @AlexBecker I did not mean to overly generalize or insult people in any way. I indeed expected that at the best universities the tests would be harder. I think people evaluating your transcript will know that this is the case because of the prestige of your university. I am wondering how one might judge this for an applicant from an unfamiliar university.
    – Craig
    Commented Jul 7, 2013 at 15:57
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    @Craig I took no offense. I'm just trying to point out that a couple of universities in the UC system doing things one way does not necessarily mean that this is even the norm at American universities. Commented Jul 7, 2013 at 17:07

4 Answers 4

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Repeating a bit other remarks: in the U.S., exams in upper-division courses are usually designed by the individual instructor, and vary widely.

There is a tradition in top-tier places in the U.S. to "challenge" students on exams, and students seem to expect this, while, yes, in some local cultures students expect/demand exams that contain no surprises.

For that matter, it is not clear to me that "testing cleverness" is necessarily an important goal for timed exams. I am well aware that there is a huge tradition in which quickness and cleverness are construed as fundamental skills/talents. Certainly these are important for math contests, and occasionally useful in the practice of mathematics, but I don't think our classes teach these things, in any case. Thus, testing for quickness and cleverness is testing for something outside the course content. Thus, in many regards it is an irrelevant challenge to the students.

That is, substantial mathematics often has genuine complications and difficulties that exist despite examples and forthrightness, and it is sometimes (often?) counterproductive to create "challenging (surprise) problems" from material that should be straightforward.

But, yes, people on admissions committees are well aware of such traditions and their variations, don't worry.

For me, the letters of recommendation from math faculty are far more important than grades on the transcript, in any case. Similarly, the statement of purpose of the applicant tells much more than the transcript. And, one more time, the skill set relevant to surprise questions on timed exams becomes ever less relevant throughout grad school.

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  • Thank you for your informative answer. I've spent the last few hours reading through your other answers on this website. In particular, point 5 and onward of your answer here addresses some of my questions. As for this answer, the last paragraph is certainly eye opening and raises new issues for me. I picked my honors essay (the largest part of my final year) to be in an algebraic area that I am relatively weak in.
    – Craig
    Commented Jul 7, 2013 at 19:11
  • I did this because I wanted to branch out and fill in the gaps in my foundation after having focused on analysis and (elementary/analytic) number theory excessively for most of my undergrad degree. As a result, I have struggled more than I would in other topics and my thesis adviser is probably less than impressed with me as he has only seen me understand things slowly. The letter of the person supervising my activities in the final year of my degree probably vastly outweighs the letters from lecturers that I have only done a course with recently.
    – Craig
    Commented Jul 7, 2013 at 19:11
  • Do you have any advice on what I can do in such a situation? If I were to write this in my personal statement, would it seem like I am trying to sweep my inability under the rug?
    – Craig
    Commented Jul 7, 2013 at 19:12
  • It's better to engage with more serious things and have to think about them, rather than be glib about easy, elementary things. Faculty with any sense don't expect serious projects to be dispatched as blithely as standard coursework. It's a completely different thing. Perhaps we too often think that that "easy" feeling is supposed to persist forever, but it cannot. In any case, you can put a positive spin on "having to work harder" by noting that you deliberately chose a more challenging project. And, again, no one cares so very much about "speed" at some point. Commented Jul 7, 2013 at 19:40
  • Your replies have been invaluable to me. I have a better idea on how to write my application and realize I must place more emphasis on doing well on my thesis to collect a strong recommendation than getting high marks on coursework. Thank you for your help Professor Garrett.
    – Craig
    Commented Jul 7, 2013 at 19:54
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Can anyone corroborate that the maths tests at american universities are actually like this?

Some are, some aren't. Grading standards are heavily influenced by national and departmental culture, but ultimately they're entirely up to the instructor, just as they are in Australia.

But I expect that most upper-division exams in strong departments require enough mastery of the material (as opposed to memorization of examples) to answer a completely novel question that requires the same techniques. The key word here is mastery, not cleverness.

(I go further than Paul Garrett. Cleverness is not only inappropriate to test on exams; it's actually a dangerous habit to cultivate. My most frequent advice to students in my classes is "You're trying to be clever. Stop it. Just solve the problem, one step at a time.")

If so, is this well known and accounted for by the people who look at grad school applications from international students?

Yes, admissions committees are well aware of significant differences between universities, both within the US and internationally.

How do they fairly evaluate the performance of international applications?

Generally, by comparing them with other international applicants, preferably from the same country, if not the same university. In other words, exactly the same way we judge American applicants.

In my department, if we get an otherwise strong application from a university we've never heard of, we try to judge by the recommendation letters. But sometimes we just have to gamble, so we admit one or two of the very best students from an unknown university just to find out how good it is. If they do well, we admit more from that university later; if they do badly, we don't.

How are Australian applicants generally viewed by them?

Well, that depends on the individual applicant, doesn't it?

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  • Thank you for your answer, I was not aware of this technique of comparing to other students from the same university/country. By my last question, I was asking if perhaps some reputation has been formed by e.g. previous Australian applicants with high marks having excelled in the program once accepted or on the other end of the scale, cases of students struggling in the program indicating that perhaps Australian undergrad degrees often do not adequately prepare students well enough for a phd at a top US uni.
    – Craig
    Commented Jul 7, 2013 at 16:23
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The rest are questions that we learned enough theory to feasibly do, but we hadn't seen that type of question before so it requires some level of cleverness to get it within the time limits of the exam.

The math and science classes I have taken at top tier universities in the U.S. have had these types of problems as a significant part of exams. As a caveat, those were also classes designed for math and science students. I have tutored students in non-math fields who have taken math and science classes that were less rigorous in that regard (e.g., "Calculus for Business majors").

Suffice it to say that as undergraduates progress deeper into their respective field, they will generally experience more challenging material on the exams.

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You have two very different questions here:

  1. how the international applicants are being treated, and
  2. how are math courses being evaluated.

The site would have been better off if you split them, as they are conceptually unrelated to one another. Ah well.

JeffE gave a good answer regarding the former question. His answer seems generalizable, as I've heard of other departments doing similar things. The admissions committees usually try to identify the countrymate among the faculty of their university and ask them whether the school the applicant is coming from is a worthy one. It is more difficult to do with applicants from Kenya or Morocco than those from Australia -- most academics will know about the top AU schools (and if they don't, I just gave them the link :) ).

For your latter question, there is no good answer as there are 4000 colleges * 5-50 math instructors in each. Oversimplified hand-holding you described is typical of the intro classes where the students will bitch about the letter $\theta$ and the sign $\forall$ as they have never seen it before. This creates huge impediments to instructors in trying to challenge the more inspiring and better prepared students who have to be held back at the level of the rest of the crowd.

I had a British prof in my Stat program, and he said that the British exams are usually written so that 70% completion gives you an A. I.e., the instructor reasonably expects that the top students will get 70 out of 100 on this exam. His exams were like that. As the system down under is built after the British system, you probably have the same approach.

The silly American "grading curve" system is 90-100% for "A", the top grade; 80-90% for "B", the second best grade; 70-80% for "C", which few students want to get; 60-70% for "D", which is a very low pass, and often requires retaking the course. Students want higher grades, and do not hesitate to give lower evaluations to instructors who grade less generously, so the professors, especially whose main responsibility is teaching (vs. research on the tenure track), have the incentives to make the exams simple so that the students are happy. The system produces a lot of students with nominal "A"s who know little to nothing. Only the top 20 or so universities (arguably stronger than the Australian G8 schools) have stronger incentives to maintain the university reputation, and tell their profs to make the exams real. I would expect that the stronger campuses of the Univ of California system (Berkeley, UCLA, UCSD) would know better than just hand everybody an "A".

As an artifact of the grading curve, the instructors have to populate their exams with 70% of very simple problems to let the bottom students accumulate enough credit for their "C"s, and can basically afford only one or two problems on a typical 90-120 minutes test to distinguish between the top "A" students and solid but not the top "B" students. This all is a matter of habit and tradition. Some instructors try to override it by making the total sum of scores in the course to be 431 or some prime number like that, so that there will be an extra step for the students to convert their 301 score to the familiar 100% range -- and most will fail without a calculator, and won't be able to tell whether getting three extra points they can squeeze for a homework would change their grade to pass from 69.93% to 70.05% into the next letter category. Professors coming from other countries may sometimes bring their own evaluation ideas (as my British prof did), and those interested in teaching and learning devise their own systems -- I described mine here.

Best luck with your applications, rest assured that you won't have any issues with the US schools just because you say it "todie" instead of "today" :).

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    The silly American "grading curve" system is 90-100% for "A", — To repeat myself and others: There is no single American grading system; every instructor decides their own.
    – JeffE
    Commented Jul 8, 2013 at 15:52
  • Oh come on, Jeff. Most instructors write and grade their own tests (unless that's a centrally administered bubble sheet). But how many instructors in your department do deviate from the 70/80/90 grading scheme? Please count, you are getting me VERY curious at this point, now that you downvoted my answer.
    – StasK
    Commented Jul 8, 2013 at 20:36
  • Most of them. In fact, none of the theoretical CS faculty In my department use those cutoffs.
    – JeffE
    Commented Jul 9, 2013 at 12:28
  • (Also, I didn't down vote your answer.)
    – JeffE
    Commented Jul 9, 2013 at 13:24
  • Wow. Double wow. (I thought you were a mathematician though; CS classes may be more project based, and you probably teach few if any Programming 101 classes that benefit from the standardized approach.) My apologies.
    – StasK
    Commented Jul 9, 2013 at 13:52

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