The Bell Curve

I chuckled when I read this article:   Desperate undergrads pray to ‘bell curve god’

 

Superstitions aside, students correctly know that the bell curve does affect them in some way or other. However, I hope that no one is feeling haunted by the bell curve.

 

What is this ‘bell curve’ all about?

 

In probability theory, the normal distribution is a continuous probability distribution that has a bell-shaped probability density function, known as the Gaussian function, or informally, the bell curve. The normal distribution is the most prominent probability distribution, because many large sets of data are approximately normally distributed.

 

 

 

 

For example, the heights of all students in NUS are likely to be normally distributed. The weights of NUS students probably follow a normal distribution too.  Likewise, if I set exams targeted at the average competency of a group of students, and if the class is large enough, the exam scores are likely to follow a normal distribution curve. Setting such an exam is, by no means, easy. Pitch it tough, most students will fail. Set it too easy, and many will score very high grades, and the resulting scores are hardly differentiated.

 

 

Grading and Moderation

 

Differentiation is necessary for CAP purposes, and for Honours classification, and these are here to stay for the foreseeable future. Most if not all major universities have variants of degree classes or GPA scores.  And because of the need for differentiation, many institutions from North America to Asia, use the bell curve as a mechanism to moderate marks.

 

Module requirements may encompass different modes of assessment such as tutorial presentations, laboratory reports, projects, essays, as well as mid-term and final examinations.  Grading may be based on absolute performance, relative performance, or a combination of the two.  Higher-level modules with small enrolments typically grade a student based on his absolute performance; larger lower-level modules take into account a student’s performance vis-à-vis the other students in the same module. Where necessary, the final grade which a student receives for a module may be subject to moderation.

 

One important reason for grade moderation is that examiners come from diverse academic backgrounds and may be accustomed to different marking regimes.  While we do make every effort to make sure modules are designed with clear learning outcomes, and professors are responsible to ensure their exams are pitched at the right level, grade moderation will prevent grade inflation or deflation, and helps to achieve consistency in assessment grading across modules. 

 

 

 

How NUS Applies the Bell Curve

 

At the end of the semester, a student is awarded a grade (and not specific marks) for each course taken. As such, NUS adopts a ‘recommended grade distribution’ in the following manner. I shall illustrate with an example – bear in mind that this is meant for illustrative purposes and is not the actual distribution that we are currently practising.

 

Example of a Recommended Grade Distribution: 

Grade A+, A, A- B+,B, B- C+,C D, F
Proportion Not more than 25% Not more than 40% About 30% Not more than 5%

   

One could compute the average grade point:

(5 x 0.17 + 4.5 x 0.08 + 4 x 0.14 + 3.5 x 0.13 + 3 x 0.13 + 2.5 x 0.15 + 2 x 0.15 + 1 x 0.05)

which is approximately 3.34, or roughly B grade.

And here are 3 possible course grade profile scenarios after moderation. For the first module, the test/exam may have been too easy, resulting in high cut-off marks for each grade. The average mark was 83 for a class of 630. The department will also look at the paper before moderation.

 

 

 

In the next scenario, the resulting cut-off marks for each grade after moderation, are moderate.

 

 

In this final scenario, the resulting cut-off marks for each grade after moderation are rather low.

 

 

 

I must emphasize that the recommended grade distribution is not applied blindly, and there are ample opportunities, within reason, for discretion and flexibility.  

  • First, the class size must be large enough, preferably above 30. For smaller classes, Professors are given discretion on an appropriate grade distribution because small sets of data may not be normally distributed.
  • Second, we are not looking for a perfect fit, i.e., we usually ignore small deviations. 
  • Third, if Professors have strong reasons to deviate from the recommended grade distribution, we are usually amenable to acceding to their requests. For example,  some modules belonging to special programs in the various Faculties/Schools have their own distributions.
  • Fourth, we sometimes also look at the CAP profiles of a class, and tweak the grade distributions appropriately. For example, if many students with high CAP choose a particular course, it will not be fair to apply the recommended grade distribution to this class. Another example: for Honours classes comprising students with an average CAP of at least 3.5, the grade distribution will be skewed higher.

 

Additionally, much goes on post-exams, before the grades are finalized and released to students. First, the grade profiles for individual modules are examined and compared at the Department level, and then across Departments at the Faculty level. All grades are carefully scrutinized by Department and Faculty Boards of Examiners before they are submitted to the Board of Undergraduate Studies and the Board of Graduate Studies for approval. Further checks are conducted at the University level by the Board of Undergraduate Studies and Board of Graduate Studies to ensure that there is consistency of assessment across Faculties/Schools.

 

In conclusion, I hope that this post has given a better picture of how the bell curve works at the NUS, and hopefully this helps to alleviate some bell curve anxiety. The bell curve is used primarily as a tool to moderate grades, and as a guide to prevent grade inflation or deflation. We do not apply the bell curve mindlessly or excessively. Students are sometimes worried about falling on a ‘wrong side’ of the bell curve. Do not worry too much, more often than not, we err on helping students along.

 

Here’s also wishing everyone a joyous Lunar New Year!

 

85 comments:

  1. Its quite interesting in Singapore that the school system seems to be based on the British education system but the university is based on the American system.
    Also I see little point in having a CAP system for graduate courses where the out come of a Masters or PhD is a pass and employers don’t really care whether you got a A+ in your modules. A simple pass fail grade would be more appropriate.

  2. never know that the percentage of ‘A’ is sooooooooooooooooo small.
    ><
    seems really need to work very very very hard to get a 1st honor degree.

  3. The bell curve system itself is a good system, but also imbalanced system. For course with high quality students (look at admission IGP), is it fair to use the same grade system to judge them? If the exemption for honor class or class with good student applied ,one can abuse it to push their CAP up, thus inflation, too.
    I don’t really care much about my CAP, as I want to enjoy the holistic approach of studying whatever I want to, no matter how hard they are. Then, thanks to the system, I also put myself in disadvantages, as I am judged by how high my CAP is, and what honor class I have.
    Quote from my favorite academic staff (who take care of every batches of our course for 3 years): “All of you are very bright student, so if possible, I want to give all of you A”.

  4. Dear Prof Tan,

    Thanks for sharing with us this information, makes the system a lot more transparent. Personally, I think this all makes sense, but it’s going to be a hard pill for alot of people to swallow. We’re all normal-curved anyway, in many aspects not just grades, and in some calsses I’m at the bottom in others I’m a bit nearer the top but it doesn’t matter cos I enjoy most of my classes anyway.

    It’s going to be a hard PR war for you to wage (I can’t imagine most students willingly voting for this, even though it really makes sense to me– kind of like the ministerial pay wage conundrum, we just cannot accept the fact that we *can* fall down to the bottom half of the curve and everyone just wants As anyway) but I’m glad you are taking the bull by its horns.

    My main gripes with school are mainly administrative inefficiencies and *SOME* really bad teaching, but otherwise I’m pretty content.

    Cheers,
    Koalaaa!

    1. I agree with this point of view. I often takes modules because I like it and gladly accept the grade, good or bad, as it reflects how I understands the class and performed in it, compared to other people.
      On the flip size, I realize this is not the case for everyone. In fact, seemingly a lot of us are coming for a module for grades. Take Living with Math – a very popular GEM-A module, for example: the course is extremely easy and everyone with good understanding in Math will be able to score >95% of the content. Hence, a single flaw will bring you from A+ to B, B+. Students obviously don’t really like it, especially when many of them take the class because they thought it’s easy to score.

      My thought on this is to actually try to compensate for this grade-oriented mindset, by making the modules more interesting and compelling to the students, so that when they finish, they actually feel that they learned something valuable and keep trying harder, even if their grades are not high

  5. My biggest objection to bell curve is its reward system. I feel like the system rewards students not necessarily for mastering the material taught, but by being better than the rest of the cohort.

    Moderated grade is certainly non-indicative of how much of the material one has mastered. To illustrate, I have scored B+ on modules I understand very little about. However, since I understand a bit more than the rest of the cohort I managed to get that grade. There are also modules for which I scored B- even though I would be more comfortable and able to engage in prolonged discussion on the topic as compared to my B+ modules.

    I took a management module during my 1st year (MNO 1001) and one of the topic touches on how a perception of fair reward would positively affect one’s performance. I got a C+ for that module. However, I can still talk at length about the content of MNO1001 rather than another module for which I scored B+ but can’t even remember the module code.

    My point is that allowing grades to not be moderated (even though it may lead to our benefit) would actually give us more incentive to learn as we know the grade we receive is a fair reflection of our effort and knowledge at the end of the course, not how many people we manage to “beat” and how many we “lost” to.

    Another thing I want to ask is about “preventing of inflation and deflation of grades” as stated in the post. What I cannot understand is why is there a need to prevent them?

    Isn’t grade deflation indicative that something is not working with the way that module is conducted?

    Isn’t grade inflation indicative that something in the module is conducted well and have had positive impact on the overall teaching-learning process?

    Why is it that the university choose to ignore these valuable signals ? These signals could provide excellent feedback that, in turn, can be used to improve the teaching-learning process. Why does grading consistency takes precedence over them?

    At least from my point of view, this is not the way to go if NUS wants to continue to be a robust leading university in the region.

    I hope you don’t take any offense from my response, Prof. Tan. If I appear to be heavily opinionated, it’s because grading policy is one of the things that would directly affect us as a student and as such I am heavily invested in the topic.

  6. Not to speculate or anything, but the first example on the grades seems to be that of ACC1002X I took last semester.

    The paper was too easy, that when I stepped out of the examination hall, I was too afraid. Too afraid that any careless mistakes, it would bring me down not just 1, but 2 grades.

    Simply speaking, there was no margin of error. Is that what the University is solely trying to inculcate in us? I believe that this is as such in many computational modules (taking MA1505/1506 for example) in NUS. Shouldn’t understanding the concepts be as important, if not critical as well?

    (Come to think of it, 630 students, that rang me a bell.)


  7. Punctual Koala:

    Thanks for sharing with us this information, makes the system a lot more transparent. Personally, I think this all makes sense, but it’s going to be a hard pill for alot of people to swallow. We’re all normal-curved anyway, in many aspects not just grades, and in some calsses I’m at the bottom in others I’m a bit nearer the top but it doesn’t matter cos I enjoy most of my classes anyway.

    I think that is the most important. If we like learning, grades would not matter too much as long as they are reasonably fair. However it is my personal opinion that bell-curve grading should never be used. Rather, the examination should be set such that it is entirely within the capability of a student who completely understands the course content, yet one that is as challenging as possible but not tedious or routine. This also means that the course content has to be carefully prepared. But I do think that if everyone has learned the concepts and techniques well, they should all be awarded an A/A+, regardless of how many there are. Also, the examination’s maximum marks should be more than 100%, with the extra marks awarded for solutions to problems that are directly related to but not taught in the course. In this way, students who can handle the course content with facility will still be able to obtain full credit, yet students who learn more than “from the book” will be rewarded. In fact, there are some interesting competitions in which original solutions are given special prizes. If courses and examinations at NUS were like that, I think we hardly have to be concerned about needing a bell-curve at all. And as I mentioned before, there will be absolutely no necessity for tight time constraints, which will be always be diametrically opposed to true application of what one learns. I heard that one professor gave his students essentially as much time as they needed for their mid-semester examination. And why not?


    Punctual Koala:

    My main gripes with school are mainly administrative inefficiencies and *SOME* really bad teaching, but otherwise I’m pretty content.

    I suggest that the deans and department heads attend at least two lectures per module, halfway through the module, such that they can directly assess the teaching of each module. This would also be a very good source of feedback to the lecturers, because currently the only way they get feedback on their teaching is from students. Some professors are well known among students to be extremely good in teaching, and I think it would be great if all the professors could learn from one another.

  8. You’re making a very important assumption here – that the assessment method is directly reflective of the aptitude/understanding achieved of the module.

    There are also ways in which you can fail an assessment even though you achieve nearly perfect understanding of a topic. I had that experience in JC for Economics, scoring only 24/100 for the paper in my first year. If I recall correctly, I was the single lowest scorer in my cohort.

    That didn’t indicate anything about my understanding of the topic. I was already applying economics principles to daily living at the time. Of all the subjects I took, Econs was the single most impactful one to me, even though it has nothing to do with my area of specialisation.

    After the second year, in which my J2 teacher focused on teaching me how to fulfil the required answer format, I got an A for that topic.

    The point I’m trying to make is that because exams are imperfect tools, they will introduce artifacts into the assessment.

    In addition, on that point, deflation and inflation create some highly negative effects, such as certain modules being abandoned, and some others being oversubscribed. In addition, the students who were in an inflated module would have an unfair edge in upping honours class, while those who were in the deflated ones will be unfairly penalised. A moderated system keeps the field somewhat level, which makes the honours class ultimately more reflective of your capabilities. This is important not only to the student being assessed, but to the reputation of the university as well.

    Nobody would trust a university who first classes a low-capability student who takes ‘mickey mouse modules’, as they’re sometimes called, and thereby gets his grade, while a third classer is actually a genius who took the hardest modules because he was interested in them.

    I do not believe the university ignores the signals either. It is obvious from the raw result if indeed something was amiss in the way the module was conducted, and in addition to the feedback we give every Semester, I believe that in their cumbersome multilevel moderation process, any such issues will be highlighted, and improvements will be scheduled for the next module run.

    I do actually think the same way that you do in that I would like my grade to reflect my absolute level of ability as opposed to a relative one, but recently I’ve realised that the alternative of using an absolute test may not always be reliable at doing this.

    If I understand 12 topics out of 15 and the 3 I didn’t get were tested, I would score lower than someone who only understood the very 3 that were tested, as a hypothetical example. Of course, the probability that would happen is low, but the probability of such a misreading of ability is even lower when normalised into a bell curve.

    The very marginal increase in diagnostic accuracy of a test by reverting to an absolute form is outweighed by the very significant side-effects that form may bring, in most cases.

    That said, an absolute system may merit consideration in a case where the modules are fixed in a syllabus, since in that particular scenario inflation and deflation will be of little impact since the entire cohort against whom the student will be scored will experience the same effects at the same time. The only cohorts for whom this apply seem to be Law, Medicine, Dentistry, and to a more limited extent Pharmacy and Nursing. Majors for which the module structure is somewhat more elective will suffer badly if there was no grading consistency.

    Ultimately though, the main societal function of grading in the first place is to help employers decide who to hire relative to the other people in the same batch and training, which is what bell curves do. Hmm.

    This is not to say that this is the function of education. I still do believe learning should be for its own sake and for the betterment of society, and that this assessment and differentiation role should be just a side effect, for better or for worse. But the idea of assessing learning in the first place, as opposed to simply skipping that cumbersome process, is for the aforementioned purpose.

    The university can get so much more done, and students learn in so much less time, if assessments were not required by society, but that is something that cannot be changed at this point in time.

    The primary problem I had with bell curves was that they do not properly take into account exceptional samples, where everyone really deserves an A but the system refuses to grant it. However, it seems that the CAP-moderated result shift that is already in place addresses that relatively well, and that if that ever does happen, the Provost, at least, has more or less indicated that such a result is possible. Its chance of occurrence will, of course, be the chance of such an exceptional batch occurring, which is very small.

    My only remaining gripe about the assessment mode is that the honours class, while good for differentiating within a cohort, will not differentiate effectively between students of different cohorts. While this is not relevant for careers which use work experience and testimonials after the first job, it may result in problems for those careers that care too much about honours class. Like any job in the civil service, really.

    =====

    Hey Prof Tan, any chance we can shift the module evaluation till after exams and before result release instead? As of now we gotta rush like hell to do it in the midst of our exam prep, and also, we can’t give any feedback on whether the final assessment has areas of improvement or excellent qualities that should be kept. If it was after, we’d be able to provide proper feedback on it. Though it should probably be before release so that people who did well won’t say the exam sucked, and so on.

  9. Thank you for sharing the information, but what about exchange students? Is it fair to give them low grades based on how they compare with other NUS students when they can come at the top of there classes at their home universities? Many of them are not graded on a pass/fail basis by their home universities during exchange.

  10. Thanks a lot for enlightening us on the bell curve in NUS.

    I agree with Kim who said, “The bell curve system itself is a good system, but also imbalanced system. For course with high quality students (look at admission IGP), is it fair to use the same grade system to judge them?”.

    The main problem I see with the bell curve lies in core modules or other optional but almost essential modules in the sense that we have to choose 6 out of 8 modules in a list for example, so it is theoretically an elective but 6/8 of the cohort will probably take it.

    The problem I see is that there is a lot of repeated competition with the exact same batch of students, who may be of very high quality. An anecdotal example would be say, Physics or Chem. Engineering in NUS, both with highly talented students and small cohort. Looking at CAP profiles of a class may not help much, since the CAP profiles of the batch would be affected by the internal competition in earlier years, eg. year 1, year 2.

    What I mean here is that, this results in clusters of groups of students in NUS competing in the same bell curve, over and over again. Hence, an A from a Physics module may not be “equivalent” or “equivalently difficult to get” as, say, an A from a Arts module. (just for comparison sake)

    ———
    I recommend this website: http://www.cbsnews.com/8301-505145_162-37241878/5-hardest-and-easiest-college-majors-by-gpas/

    A new study from Wake Forest University suggests that a huge reason why so many students abandon their pursuit of science and engineering majors is this: Their professors are grading too hard.

    Students, who hope to be science and engineering majors, get discouraged by their grades, which are significantly lower than students in other disciplines. Consequently, they flee for easier “A’s”. Male students are more likely to bail because of grades than would-be women STEM majors.

    During this period, the science geeks earned grades that were consistently below other students. Brainy STEM graduates left their school with four out of the five lowest grade point averages.

    ———–

    What I humbly recommend is that perhaps, Bell Curve for Core Modules & “Almost Core” Modules be slightly relaxed compared to GEMs, SS, etc. Furthermore, we cannot S/U Core modules, while GEMs and SS can be S/Ued up to 3 times.

    Thanks

  11. I believe bell-curve is a fair system as it is basically impossible to set exam questions such that the difficulty lvl is consistent across different professors or even from the same professor over a different semester. It is also a good gauge of the caliber of a student for both employers and faculty should the student wish to apply for specific courses which only accept the best. But im glad that we just need to be at 20-25th percentile to get aleast an A-.

  12. Errr, the previous comment by me was regarding Michael’s comment.

    I should mention that there’s another issue related to the bell curve, though it wouldn’t go away completely even if an absolute system was used.

    That is, intense rivalry between students of the same cohort on the same major in several instances. Enough for some to pull stunts like ‘teaching’ their friends the wrong things to sabotage them so that they can increase their relative performance.

    I would like to strongly discourage any readers from doing something of such a low standard.

    But in addition, the common view of always looking at it as if we’re opponents in a war has severe drawbacks. For one, peer-to-peer learning is highly restricted to being done only within cliques in most cases I know of. The kind of open exchange of information that is typical of several of the top higher learning institutions in the US, or so I hear, appears to be absent in NUS.

    The style of learning is primarily lecturer driven, and secondarily personally driven. However, increased peer-to-peer interaction can lead to insights beyond the capabilities of any single student, or even any single lecturer, no matter how skilled one might be.

    Current peer to peer interaction type learning is limited to either voluntary participation via limited cliques, or group work assignments, which are limited to a few people, and usually cliqued as well unless random assignment is used.

    I’d propose the following to enhance this kind of learning I believe we lack:

    1. IVLE forums to be created BY DEFAULT for every module, every semester, with all students given the ability to post, and to create new topics.
    2. Some form of CA assessment on the quality and quantity of posts by users on the forum. Helping your fellow students understand a topic, for example, would be good posts, as would be asking questions that unlock further investigation, but only on the modules for which such types of assessment are appropriate.
    3. Forming avenues by which senior students who have already completed the module can address queries by, and facilitate the learning of their juniors.
    4. Making all forms of traditional group assessment such as practicals and projects mandatorily randomised to ensure students get the maximum chance to interact with people with whom they have not yet worked.

    Ultimately societies are formed by cooperation, not competition. Without being able to cooperate effectively to a common goal will adversely affect the ability of people to do so to a company’s goals, which will affect the employability and quality of graduates.

    1. Hi Jack, I think even though we are of different attitude towards the system, essentially we share the same set of concerns.

      I do recognize that one-off testing is really not a good way to evaluate a student’s progress, especially if it does not encompass all of the materials for that particular module. That is actually why I prefer modules that skews more on CA in terms of mark distribution. To a certain extent it gave me a sense of fairness on the resulting grade since I know that my effort throughout the semester is recognized and valued equally as the 2-hour major exam that checks our overall understanding.

      Regarding the inflation / deflation of grades I think we approach it from differing angle; I approached it from teaching process and you from content.

      I do agree with you that if approached from content angle, having a heavily deflated curve might deter people from registering for that module. I am also guilty of that to a certain extent. There are modules I am actually interested in but ended up not taking because i’m afraid it will drag down my CAP. In the end I pursue that topic haphazardly on my own rather than taking NUS’ module.

      Thank you for providing a counter-balance to my opinionated argument. Hopefully something good will come out of this (hopefully) constructive discussion.

      Cheers.

  13. Too bad for exchange students, those not used to being graded on the bell curve, and those not familiar with the sheer competitiveness of the Singapore education system. Many of them often regret going to NUS, or any local university, for that matter.

    How often have we heard the refrain from these students that our courses are too tough, too loaded with assignments, exams are harsh, grades are incredibly hard to score for? Yes, they might seem mediocre here, but are they really? Probably many of them find success just fine back where they are.

    Are we being too demanding, simply to identify what our meritocratic society deems as the cream of the crop, i.e. the elite, who are probably just exam smart? Is that worth constantly crushing the aspirations and self-esteem of university students?

    Just a disclaimer: I don’t subscribe to the self-esteem school of educational psychology.

  14. Hi all,

    I would like to share with you an inspirational story (true) that I use to inspire myself when my grades are low.

    Once upon a time, there was a student studying mathematics and physics. His sophomore and junior years were marred with mediocre grades, mostly Bs, Cs and even an F in nuclear physics. He went on to graduate school (shows that he has perseverance) but yet again, he performed poorly his first years, earning a C average as a graduate student.

    Now the burning question you must be asking is, who is this average guy and what is so special about him?

    Answer: He is Steven Smale, Fields Medal recipient (the mathematical equivalent of Nobel Prize). He was awarded the Fields Medal in 1966, and spent more than three decades on the mathematics faculty of the University of California, Berkeley (1960–61 and 1964–1995).

    (http://en.wikipedia.org/wiki/Stephen_Smale)

    I think the moral of the story is perseverance is very important. Late bloomers exist, and you and I *may* be one of them. If we give up, we will never find out..

  15. The bell curve is unfair to Computer Engineering Students.

    Computer Engineering students compete in the same CS classes as the CS majors, who will naturally (not necessary by hard work) be more proficient in CS because they have more CS modules and hence more CS practice and experience.

    Computer Engineering students compete in the same EE classes as the EE majors, who will naturally (not necessary by hard work) be more proficient in EE because they have more EE modules and hence more EE practice and experience.

    So Computer Engineer students need to put in a lot more time and also effort in mugging and practising exam questions.

    Time is one of the most precious commodities students have. If CEG students have no time for other more enriching pursuits that could lead to better job opportunities — many employees are looking for people who have other pursuits, and have real passion and experience in those pursuits — then it is a natural disadvantage.

    In a way, CEG students are forced to choose between good grades (being a nerd) vs having good real world experience (eg mobile developers are commanding over $10k per month).

    The bell curve is currently just unfair for CEG students.

  16. The idea of the bell-curve is a kind of macro-policy in which few individuals can digest easily. From an individual perspective, the bell-curve obviously means you are competing with your fellow peers and as a result, there will always be some who fall into a lower percentile and get lower grades. At the same time, getting As are very difficult. What are not so apparent are the macro-policy needs of the institution and economy. Firstly, it is very difficult for lecturers to know how hard to set a paper for each cohort. This job of setting assessment gets even more difficult with increasing cohort sizes. Easy papers will produce more ‘As’ and the real problem that results is ‘too many’ honours and therefore diluting the reputation and standing of the NUS degree. If the papers are set too hard, then more people will have a poor result which is simply evil… (we didnt pay so much money to fail) Secondly, the country’s economy is already rather degree ‘saturated’ (25% of the population is set to be graduates). That is , there are too many degree holders for the avaliable jobs therefore making it difficult for graduates to find a job as well at the same depressing graduate wages. When it used to be that having a degree was a differentiating factor when finding a job, now it seems not enough as the Provost had contemplated in his last post on graduates needing to “sell” themselves better. The University needs some way to measurably manage the ‘production’ of graduates and natually hence the gaussian function.

    Due to the stress of peer competition we have blamed final exams and demanded more continual assessment. However, if you notice, CA is also usually moderated, in the end making little difference in raising the grades for all. Its a valid argument that CA should be a balanced component of grading but I do not like it when things like active participation through forum dicussion come about or required asking questions in tutorial; basically using poorly-thought out methods as CA components. If I don’t know how to do the tutorial then my participation would be very low and therefore I would lose out more. Infact for some modules I learn far more in an hour’s tutorial with a good tutor or the lecturer him/herself who helpfully discuss the tutorial and makes useful summaries than with 4 hours of lectures.

    I believe the fundamental problem is due to the large cohorts. Fair grading based on content understanding and knowledge is the method we all seek. I think that cohort sizes should not exceed 200 for year 1 common modules and 100 or less for modules in year 2 onwards. It has been known for some time that small cohort sizes are more managable to teach as well as being easier for the teachers to guage the student’s understanding and manage the teaching pace. Therefore the MOE policy to increase the teacher-student ratio in schools. However, in University it seems to be reversing trend even as some modules move towards seminar style teaching because of the push for our universities to continually increase the intake of undergraduates. In the end, not only are the structural resources like our buildings more heavily taxed, the human resources that are the academic staff are also stretched out in an effort to increase module intake. If anyone notices, due to the increased traffic and heavy vehicle (shuttle buses…) frequency around NUS, our poor single lane two-way roads have been growing pot-holes just as fast as they can be patched up. This is an obvious strain on our structural facilities. As more and more students perceive a poorer quality of instruction as well as more difficulties with administration, its a sign of the strain on the human resources.

    Smaller cohorts will allow the teaching to be adjusted better as well as better assist slower students. Large cohorts will just have the lecturer giving a lecture with little room to adjust pace due to the number of people. Also, larger cohorts require more and more macro-policy making (for example setting difficult restrictions on administrative matters) to enable a single lecturer to manage everyone.

    Macro-policy will always feel distant from the individual thinking because the human brain is not naturally built to think beyond a couple of persons. That is why its very difficult to find individuals with that ‘big picture’ thinking ability to think far. What is good for everyone isn’t necessarily the best for the individual and vice versa. Having a balanced workforce is desired, but everyone wants to have honours degrees. As a result, things like the bell-curve, or most obviously government policies are difficult to like.

    I am not out to defend the bell-curve but only to give an alternative view becasue I have more or less understood the need for a ‘lesser’ evil to prevent greater problems. I too have taken ACC1002X last semester and felt that the paper was too easy despite the lecturer saying that the exam would be very difficult and became very worried at the end due to the sure application of the bell-curve. In the end, I got two grades below expectation even though I was confident of the content.

  17. I agree totally with Michael (#5). I find it disturbing that the department looks at the examiner’s paper only AFTER the marking is done to decide the paper’s difficulty, and to apply the bell curve. I am a huge proponent of absolute grading – I feel it is the professors’ duty to set a reasonably challenging (or very challenging) paper that assesses true conceptual understanding (not purely on memory, for that would defeat the purpose of education and critical thinking).

    I am a Chemistry major and a few minutes before the exam for a Level 4 module, the professor walked around to chat with us. I asked if the module is bell-curved, to which he said no – but in the end, the marks would end up looking like a bell curve anyway. That is what I believe to be successful assessment and difficulty pitching.

    I cite McGill University, where I went on SEP. To my surprise, the transcript had a column ‘average grade’. The modules I took had average grades of B- and B+. They do not curve their students, and one of the modules (they leave their module forums open even after the exams for students to comment on the exams etc) had the examiner commenting that the B- average will stand and not be moderated because they felt that the assessment covered all the learning objectives. This is despite complaints that the paper was too long and many couldn’t finish it in the 3 hours.

    I also cite ETH Zurich, which is Einstein’s alma mater and is one of the toughest schools for Science and Engineering in Switzerland. All first-year students undergo the Basisprufung, first-year examinations in their first summer, and I believe they are not curved either. They are scored on a 1.0 to 6.0 scale, of which an average of 4.0 is required to promote to the second year. More than 50% of Science students fail their Basisprufung, and have to retake their entire first year, or drop out, or switch to another course. Compared to the NUS system, I think we are much more forgiven for being incompetent (not to make any judgements of NUS students here but we slip up once in a while as human) yet we often do not see that other countries, such as Korea, Japan and China, have probably much nastier, unforgiving systems that see more student suicides and ‘cram schools’ just to cope and pass.

    That NUS gives just about most modules an average grade of 3.5, takes away much incentive to excel, and as many have said undermines the strength of the Honours degrees conferred due to people taking easy modules to out-curve other people. It also instills cut-throat competition, such that my personal strategy is to ‘help a few, and kill the rest’. A module grade distribution that is too high or too low, means the professor has not assessed the students fairly enough and instead of curving every exam, an after-action review should be done instead to evaluate the paper and for the same module and perhaps subsequent year modules, tweak the level of difficulty. If the board feels that the learning objectives have been covered in the papers then there is no reason to curve any grades and just let them stand.

    That is probably how world-renowned, and probably notoriously difficult, universities get their sterling reputation – because when you pass through their ranks and earn their degree, you have been truly tested and proven. Maybe graduating from NUS with an Honours just meant that I was slightly better than my peers at answering exam questions, and if you don’t screw up too much, you should be able to scrape through and pass everything minimally to graduate with a pass degree as well. So that kind of reduces the value of a degree, which is already oversaturated in the market.

  18. Addendum:
    Let’s say you are a CEG student and you are a fast learner. But the thing is people in the EE and CS courses would be around your level since people in university are generally smart. A lot less “feeders” so to say.

    However, the CEG student who is just as smart as a EE or CS student would not get the same grade due to the difference in module-preallocated time for practice. (As mentioned previously, EE and CS students take more EE mods and CS mods than CEG students, while CEG has to compete in both.)

    This in itself is unfair.

    As for the grade inflation hoohaa, there’s a simple solution that I wonder why a “world-class” university does not want to implement.

    Get lecturers not involved in the setting of the paper to do the test itself. The lecturer should know what the difficulty and quality of the paper is like by doing it.

    If lecturers are unable to determine paper difficulty/quality after doing it, they should be sacked without questions asked.

    My impression is that NUS has a sizable pool of good lecturers; hence the suggestion. Unless of course, my impression is wrong… then the implications for NUS would be well… sad.

  19. My apologies for so many opinions. This is a proposal from me. To encourage students to take difficult modules or whatever their interests are, an absolute grading system can still be used. However, modules can be ‘rated’ in difficulty level (like maybe on a scale of one to ten) and these will be part of the results, although not part of the grades. If the concern is to differentiate the Honours classifications awarded, what I heard of other universities doing (and the Yong Loo Lin School of Medicine it seems) is to have ‘Honours interviews’ which evaluate the student’s true potential, which might include the overall difficulty level of modules taken in his undergraduate career. In fact, some Science courses in NUS have poster and oral presentation rounds for Honours Projects, during which the examiners are looking not just for project progress and results, but also general undergraduate concept understanding. That is also a kind of ‘Honours interview’ as well to prove the student’s worth as an Honours student and which class he deserves to graduate with.

  20. As a NUS graduate, I was severely disadvantaged when I applied for post-graduate school in the US as my GPA was grossly lower than other American school college graduates. I did eventually get admitted to an Ivy for graduate school, and had to explain at length to the admissions director why my GPA was “low” (i.e. bell curve grading), but I was passed over for more prestigious scholarships. NUS, please remember that you are doing a disservice to your own graduates.

    1. From exchange students, we can really see how we deflated the grade/effort of NUS students. Grade should also be adjusted according to not only class size, but also difficulty. Non-honor classes (lvl 3k-5k in Engineering, SDE) is generally require twice the effort compare to lvl 1k-2k, and yet don’t get the same privileges as honor classes.

  21. (Proposal: Different bell curve for 30 students vs 600 students)

    Hi, I would like to humbly propose a different bell curve for small/medium-sized classes (eg. 30-100 students) and huge classes (600 students).

    I am almost graduating, and from personal experience, it is much more difficult to score (in the bell curve) in a small-medium class than a huge class.

    Reason: Small classes are small precisely because they are usually: specialised (require a lot of prerequisites); harder (so less people take them). Hence, it would not be too much to presume that those people who take a course in a small class would be of “higher expertise and skill”. Hence, the assumption of the students being in a normal distribution is invalid.

    This “small class” effect has great effects on people who major in a subject with a small and selective cohort. Imagine competiting with a small cohort (~100 people), all with 4As in ‘A’ Levels or better. (think chemical engineering for example) To get ‘A’, one would need to be the top 10 to 20. In a huge class (~600 people), being the top 100 to 150 would more than suffice.

    I humbly propose the following formula. Define a multiplier K:=log(600)/log(n), where n is the number of students in the class (n>=30). The maximal percentage of ‘A’s should then be multiplied by this multiplier.
    P’=KxP
    ,where P’ is the adjusted percentage, K is the multiplier, and P the current maximum percentage of ‘A’s

    Some numerical values are (suppose P=25%):
    (n=40 (small class) ), P’=47% (around half the class *can* get A)
    This may seem very high, but it is actually less than 20 people.

    (n=100 (medium class) ), P’=34.7%.

    (n=600 (huge class)), P’=25%, which reduces back to the current status quo.

    Thanks for reading.

    The basic tenet is this: Imagine putting Newton, Galileo, Einstein, Leonardo da Vinci in a class. Surely it is not too right that only 25% of them (ie. 1 person) get an A grade?

  22. Ex-NUS student here. Would like to comment on NUS bell curve and exam practices from the student perspective:
    1) There is NO TRANSPARENCY in the way grading is done, which is why students don’t like it. Why the need to keep it top secret? Even basic information like what is the percentage of students who can get A-/A/A+ is not released to us. Let’s not talk about the fact that we can’t even get back our exam papers…
    2) I have been to other universities and they work in a fairer and more transparent manner. Many professors tell their students at the start of the course the minimum score needed to get a specific grade, but have to the option to moderate/normalize it down in the event the course is too difficult. That way students have a target score to work to where they can be “guaranteed” a grade, and professors have some leeway in case the exams are too difficult.
    3) Bell curve systems with forced quota makes the entire education system in NUS a zero sum game. In only reinforces the kiasu, kiasee and selfish mentality that Singaporeans have. If everyone in the class has achieved a mastery of the subject matter, then they should all be given As. Under the bell curve, it doesn’t matter how much I have learned or how good I am, cause if I am still average (and yet average in this case is good), I get a B.
    4) Why on earth does there need to be 101 levels of bureaucracy in approving grades? No wonder it takes A WHOLE MONTH to get the results back where in other universities it takes a few DAYS or one WEEK at most!

    This is so typically of the bureaucratic, non-transparent and selfish nature of Singapore and NUS. I’m glad I have put those days behind me.

    FYI, I graduated with 1st class honors, so this is not a case of sour grapes. Have lived through and “won” the system, I still say that it is a lousy system.

    1. As written already there is an important function bell curves have in the allocation of employment here. The employer is not looking at your absolute ability either but your ability relative to your peer, since you’ll be competing for the same job. If everybody gets As and graduates with first class honours, employers would have to look at co-curricular activities, interview more comprehensively etc in order to determine the optimal ability-salary mix they need. Not everyone needs a honours graduate to fulfill a role, provided a non-honours graduate can perform equally well in the required job scope with a lower expected pay.

      Also, if the number of first class honours graduates were to increase, the prestige of the class will drop, which will then negatively impact all those possessing it. Our education is already suffering from this effect at large, as the average % of people with a bachelor’s or higher has increased by a lot over the past 30 years.

      However, your point that transparency would help stands. Even if the grades are fixed, for learning’s sake there would certainly be an improvement if the marked papers were released to us.

      Those who seek to know their absolute ability will be able to find out precisely where they need to improve their knowledge. Most students would rather know they got 95%A+/45%B+ as opposed to knowing only the grade and not knowing anything else.

      As opposed to abolishing the bell curve system, it would be better to work on the transparency of it. The Provost’s post is a good first step, but more can be done.

  23. From what I see, bell curve grading removes the DC content of the cohort score, so information regarding the quality of the cohort is discarded.

    There is a way to solve the problem of people choosing modules which are easy for the sake of scoring, and averting modules which are deemed to be hard, either because of the intrinsically hard to digest or over-subscription by able students.

    That is to report the mean (and optionally the variance) of the CAP of the cohort taking that module, along with the student’s grade. Some kind of mathematical formula can then be used to balance a student’s grade together with the cohort quality.

  24. This article really clears up the air surrounding the bell curve issue. I do understand how the bell-curve is important as a differentiating mechanism and that it will not be forced upon a class if the work submitted are equally outstanding.

    However, one point that Prof Tan mentioned caught my attention.

    “Fourth, we sometimes also look at the CAP profiles of a class, and tweak the grade distributions appropriately. For example, if many students with high CAP choose a particular course, it will not be fair to apply the recommended grade distribution to this class.”

    In Business Faculty, it is apparent that Finance is the specialization of choice for most high CAP students, for interest, pragmatic reasons or otherwise. I cannot see how NUS can “tweak the grade distributions appropriately” for finance majors relative to other majors in Business where competition is less stiff. Do finance majors get a more favorable grade distribution?

    If that is so, then shouldn’t business students have a more favorable bell curve as a whole during year 1 because the intake mainly consist of students with higher academic achievements than some other faculties?

    This argument will go on forever and there just isn’t a perfect solution for this. Hence, I still believe that under normal circumstances, the grades we get are more often a relative reflective of our peers.

    Therefore, I would like to pose this question to the floor, is it better to opt for a major that you know consist of lower competition to standout than opt for a major that you are interested in?

    I am still following my interest in finance but somehow I feel that this “bell-curve” isn’t helping. At a certain level, the bell-curve should be scraped. And I do hope that that level will be when the administration realizes that equally excellent work is being penalized just for the sake of the bell curve.

    I would like to thank Prof Tan for opening this blog, it does help clarify a lot of doubts about the system. Happy Chinese New Year everyone!

  25. In working life, here is what I think appraisal works.
    There are some smiliarities.

    1) “First, the class size must be large enough, preferably above 30. For smaller classes, Professors are given discretion on an appropriate grade distribution because small sets of data may not be normally distributed.”

    Quite true. I once worked in an office with more than 30 people. If you made mistakes, it’s not that obvious.

    Once you worked in an office with only 3 people, every cough and fart is annoying because it is so small.

    2) Second, we are not looking for a perfect fit, i.e., we usually ignore small deviations.

    Quite true in working life. Small deviations like spelling mistakes in your report should not matter much.
    As long as you do your work, you should not get into trouble.

    But then again, Depends on boss. If boss is really micromanage, your flaws can be easily seen when you are under the microscope.

    3) Third, if Professors have strong reasons to deviate from the recommended grade distribution, we are usually amenable to acceding to their requests.

    True. In working life, if one boss is very difficult to work with, sometimes, the bigger boss may also moderate it a bit.

    4) Fourth, we sometimes also look at the CAP profiles of a class, and tweak the grade distributions appropriately. For example, if many students with high CAP choose a particular course, it will not be fair to apply the recommended grade distribution to this class.

    True. My friend works in EDB and it is a high scholar until everyone is competitive.

  26. In working life, some organisations also kept their appraisal and promotion system confidential and we as salaried workers can’t challenge or question the system because we can be seen as insubordinate of behaviour…. But as fee paying student, at least you can be more vocal about it but I strongly hope that you don’t carry this ‘questioning’ attitude at work… Most bosses don’t like subordinates who challenge their authority or clash with them directly…. I got a Grade B in my appraisal but I heard that 80 per cent of us got C grade in ranking and I also did not voice out.

  27. My appraisal was Grade B consistently for about 3 years. In the last final year, I committed a grave error in my work on 11 March 2010 and was sacked. After lawsuit and pleading, I finally got my Certificate of Service, my conduct was listed as “Satisfactory” so it was more or less a Grade D. Therefore, there are no absolute standards in this world.

    1. The questioning attitude is accepted in some organisations and discouraged in others. It depends on the primary purpose of the organisation; organisations based on research and innovation tend to be more flexible, open and transparent. To others, stability is more important. Flexibility and stability are directly contradictory.

      Also, small organisations tend to value feedback, large organisations tend to value stability.

      From the short amount of information you wrote you were almost definitely employed in the military, nearly nobody else uses the term “ranking”. And the military is ESPECIALLY inflexible, due to its function. If not, a really military-styled organisation.

      I believe that them putting the Satisfactory there is in a way partially justified as you have also acknowledged that a grave error was conducted. That said, the reduction should have been in the performance area, instead of conduct, but then the military’s the military.

      Ultimately, not all of the jobs out there are like the situation we have in NUS, and not all are like the military either. The student/worker would do well to observe the culture at the workplace and adapt accordingly, at least until we are actually able to do something to change it to a form that we prefer.

      —–

      Where I was, ranking data was highly classified, the number of us who were privy to the information usually was restricted to the few who process the ranking, and those who perform the appraisal in the first place. It is strange that you got to know your appraisal, if indeed you were in the military.

      They don’t usually want people to know how they were rated because it causes unhappiness.

  28. Edmund, I think your analogy is flawed. Unlike employees for a company, students are in fact the university’s customers. We are *paying* lots of money for this education.

    The least the university can do, is to set a transparent process in assigning grades. I have taken or taught courses in at least 3 universities overseas, none of them operate in this way that NUS does.


  29. Samuel:

    Therefore, I would like to pose this question to the floor, is it better to opt for a major that you know consist of lower competition to standout than opt for a major that you are interested in?
    I would say that opting for major you are interested in is better. No point graduating first class honors in a major you dislike, only to suffer burnout and switch career after ten years..
    Terence Tao once said of mathematics, “If you don’t enjoy it, you won’t have the stamina to keep at it.”

    Unless you have two equal passions, then why not, you should opt for the one with lower competition. It would be more practical and no loss is suffered. Like Robert Frost said, “Two roads diverged in a wood, and I— I took the one less traveled by, And that has made all the difference. ”

  30. I realise the current bell curve system isn’t completely fair in the case of GEMs and SS modules. An SDE student should generally find a SSD module easier than a Computing student would. A YST student could probably sleep through Science of Music and get an A+.

    Bell curves assume normal distribution, but there is no accounting for weighting a difficulty. A student who has spent all of her JC life and 3 years of her university life on a major, who then takes a GEM for that major, has an unbeatable lead on someone who is taking it for the purpose of GEMs itself – to learn stuff that are outside their usual field.

    Similarly, using LSM1401 Fundamentals of Biochemistry as an example, students from different majors taking a module under the same module code has a major issue. If I recall correctly, we had Engineering, Chem and Pharmacy students all taking it together and marked ostensibly under the same bell curve.

    Given the completely different entry requirements to the majors, and the resultant divergence in abilities in different subjects between people of the three majors, marking all of them together will inevitably skew the curve to award the As more to people of the Pharmacy cohort than to our fellow students, especially those of Eng. This is quite easily accountable by the fact that H2 Biology, which is a compulsory requirement for Pharmacy students, has covered more than half of the LSM1401 syllabus, so to us it’s a simple repetition. Not to mention that to even enter the major in the first place, the majority of us already aced H2 Biology. To the Eng cohort, they needed to have taken both Chemistry and Physics, and thus the majority of them will not have any H2 Biology background.

    This would unfairly sabotage the Eng students taking it relative to their peers because the A percentage of the bell curve has effectively been removed from them already.

    It’s just used for illustration’s sake as a concrete example, but I doubt LSM1401 is the only module of its type which people from multiple majors need to take.

    I would believe the bell curve system to be justified when we are dealing with modules with the following characteristics:

    1. The students taking it have a similar background level of knowledge in the subject.
    2. The students taking it are going to be competing with each other for the majority of jobs. The Civil Service doesn’t count since they employ everyone, I mean specialised jobs here.

    If the requirements are not fulfilled someone will probably end up being unfairly penalised by the system. A multiple bell curve system might work for the LSM1401 scenario, but the complexity involved in GEMs and SS modules would ensure that there will always be some inherent Mickey Mouse Module creation going on.

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