What's the best way to scale grades?

It happens. An exam question is not clear, or more challenging than intended. The exam is marked by an over-zealous TA. Or perhaps the students haven't studied as hard as they should have.

As a result, the students' grades are, in some sense, too low - they do not accurately convey the students' level of ability or understanding of the material, or are lower than grades given to comparable students with similar levels of knowledge elsewhere in the university.

So the professor scales the grades.

But there are at least three ways of scaling grades, each one of which has different distributional implications.

Suppose the class average before scaling is 65, and the professor wants to achieve a post-scaling class average of 75. 

One way of scaling the grades is just to add 10 percentage points to every student's grade. It has the advantage of simplicity. But a constant amount added to each student's grade represents a greater percentage increase for low-scoring students than for high-scoring students, as some simple examples show:

Grade before scaling    Grade after scaling    Percentage increase    

40/100 (F)                        50/100 (D-)               25%  

50/100 (D-)                        60/100 (C-)            20%  

79/100 (B+)                        89/100 (A)             13% 

Giving all students 10 marks is a "progressive" change in the grade distribution - it is a greater percentage for students at the bottom than students at the top. It's an option I find most appealing when all of the students in a class have been attending regularly and working hard.

An alternative approach to scaling is to increase all students' grades by the same percentage. An increase in the average grade from 65 to 75 represents - for that average student - a 15 percent increase. This approach is especially easy to implement if one has had the forethought to make the exams out of 115 ("Look, I got 75, I'm doing really well, what a great prof..."). 75/115 is easily scaled to 75 percent.

But compare the impact of a 15 percent increase with a 10 percentage point across-the-board increase:

 Grade before scaling    Grade after scaling    Percentage increase

40/100 (F)                        46/100 (F)                15%  

50/100 (D-)                        57.5/100 (D+)          15%  

79/100 (B+)                        91/100 (A+)             15% 

This proportional grading scheme gives all students the same percentage increase - but now grades change much more at the top end of the distribution than the bottom end of the distribution. This method of scaling is attractive when there are very few students with scores above, say, 80 or 85 before the transformation is applied, but a fairly large number of students in the 70 to 80 range, so more variation is needed at the top part of the distribution. 

There is a third, less obvious, way of scaling grades. A grade of 65 can be pulled up to a grade of 75 using the transformation final grade=initial grade+(100-initial grade)*[(35-25)/35]. For example, 65+(35)*(10/35)=75. Applying this transformation to each grade:

Grade before scaling    Grade after scaling    Percentage increase

40/100 (F)                        57/100 (D+)                  42%  

50/100 (D-)                        64/100 (C)                  28%  

79/100 (B+)                        85/100 (A)                  8% 

This would be a useful transformation if the exams had been marked by someone who gave out too low marks for wrong answers. For example, I'd say that in the less advanced undergrad econ courses, a clearly labelled more-or-less relevant diagram is usually worth between 3/10 and 6/10, even without any intelligible/correct analysis. But a TA will sometimes think 'this isn't the right answer' and give 0/10 or 2/10. That's when this last transformation would come in handy.  

So there's no single best way to scale grades - it depends what one is trying to achieve. As the diagram below shows, each method of scaling has a different impact on the overall distribution of grades. The first method leaves the variance of the distribution unchanged, the second method increases it, the third method decreases it. For any given class, the optimal scaling method will depend upon the desired variance of grades, as well as the desired mean.

Comments

[Jonathan]

I once had a professor curve by newgrade=oldgrade^(1.025) or so.

[RSJ]

A good reason to avoid grades on tests. You can give grades for the course.

One of my best teachers at first didn't assign grades to tests, but would write some comments next to your answer, such as "Oops", with an arrow to the offending work section, or "I like this Lemma". Then he would talk about things. Even though there was no grade, the feedback was excellent, because you knew what you did wrong.

Some of the students started complaining, so the next time he did all the usual stuff, but then applied stickers. A smiley face was good, and a frowny face was bad. He was trying to tell us not to be like dogs barking for scores, but to understand what we were doing. I don't remember what grade I got in that in class, but I do remember the class. Then there was another class in which the professor gave told us a problem, and said that if anyone solved it, they would get bonus points. After a while, I brought in my work, he looked it over and agreed that it was a good solution. As I was leaving, I asked him about the bonus points, and he took a post-it note, wrote "bonus!" on it, and handed it to me.

I'm not sure that would work anymore. Nowadays students bring lawyers with them, and you have the helicopter parents. When I was a TA, I remember a girl weeping in my office because she got a B. She was trembling, but I was trying to explain to her that it was just a letter, and that even with the B, she still had an outside shot at happiness. Then another student got his test back with a C-, and he was exuberant. It was as if I had handed him a trophy.

[Frances Woolley]

RSJ: "A good reason to avoid grades on tests. You can give grades for the course." The advantage for students of having early accurate feedback is that they can drop courses in which they are unlikely to get a good grade and reallocate their effort to the courses where the marginal productivity of that effort is highest.

"Then another student got his test back with a C-, and he was exuberant." I remember reading somewhere that silver medalists were among the least happy Olympic contestants. Bronze medalists just felt lucky to be on the podium, gold medalists felt they had won everything, but silver medalists always thought - "what if..." and agonized about how they might just have done a little bit better. That B student is your typical silver medalist.

I've got to say I don't have much sympathy for your prof who wrote "bonus" on the post-it note. The reality students face is that the job market is pretty brutal. Medical school, law school and grad school are perceived as being the best route to a decent life style. So marks matter. They really do. It's a tough world out there.

[brendon]

I have to agree with Frances. I had a professor once tell us that in the job market, "Grades are your only currency" and it really stuck with me.

[RSJ]

France, I don't remember an employer ever asking for an exam score -- other than standardized tests, of course. But perhaps they do that in Canada? Who knows. Usually they only ask for a diploma, and grad schools want a transcript, even though in many fields the standardized tests carry more weight.

But on the transcript, it all averages out. You will sometimes just miss the grade and other times you'll squeak by, but the law of large numbers will be in your favor, it will converge to a decent approximation of how good of a student you were, even if you failed to strategically drop all the classes in which you suspected you might not get a good grade.

And that is the only reason why you would need a grade on a test. Of course you need feedback about what you are doing right and wrong, but feedback is not a number. Giving good feedback is hard work.

It's not clear to me that you would want to encourage students to engage in this type of strategic dropping.

I would think a university would want to discourage it. They should take all the classes they need to take. Moreover they will know if they are doing well or not if you are giving them feedback. The only thing they wont know is whether they are just a bit above or below some cut-off. But again, that's not important if they are taking 50 classes.

[Wendy]

I think every prof/lecturer in all disciplines should read this. It offers three methdologies for scaling scores that can be presented as reasonably fair when the student and/or his/her parents or lawyer show up to argue.

My method was more arbitrary. Students had a grade for (at the time experimental) online WEBCT participation, that didn't count toward their final grade (too controversial to be graded on this at the time). Except, the deal was I'd use it when students were borderline between marks (such as a 79%, C+ vs an 80% B-); students who participated in WEBCT got bumped up.

[RSJ]

Sorry for the typo, Frances. Should have used preview.

[Patrick]

Yeah, It's a tough world. And a good place to learn how to deal with it is in school. Sometimes people judging you aren't fair (e.g your TA), sometimes the bar is set above what you can achieve (hard question), sometimes you fail if you don't exert enough effort (partying and didn't study enough). Presumably it all comes out in the wash - for every zealous TA you'll get a softy. For every question that was a little too hard, one will be a little too easy.

There was no scaling at McGill in either engineering or Comp Sci when I was there. And personally, one of the most valuable things I learned out of the whole torturous experience (esp. engineering) was how to persevere when faced with adversity and my own mediocrity. It SUCKS slogging through something that you don't enjoy and aren't good at. And it sucks more when it makes you feel stupid. And it totally sucks when it makes you worry that you'll end-up flipping burgers. But despite all that, if it's important, you do it anyway. By definition not everyone is a rockstar, so learn to deal with it.

Their future boss (someone like me) isn't going to scale their performance goals, or make their job any easier. And if they start bawling or pounding the desk about how they ought to get their bonus anyway, they'll just end-up being fired or marginalized as unstable.

I'm feeling more and more like an old curmudgeon.

[Mark_dowling]

The example reads pleasantly because the prof is increasing grades and who doesn't want to help him/her do that except grade inflation vigilantes?

So you do an exam, you go home feeling pleased and expecting a grade based on your answers and on sample papers or other guidelines and then get a grade lower than you expect because the Prof arbitrarily decides the exam or the marking was *too easy*? Where's the moral hazard for the Prof/TA here?

Let's not blame the students for irrational expectations *if their expectations were rational*. If they are going to be in effect graded on a curve, however that is achieved, say upfront that marks will be subject to both accuracy per the marking scheme but also subsequent "tweaks".

[Frances Woolley]

Patrick - "There was no scaling at McGill" - Other Canadian universities know this, and to some extent take that into account when making graduate school admission decisions. The question is: how to do this? McGill B = Noname University A? But then what about the really smart, hard working students at Noname U? If Noname University A = McGill B, then there is no way that a strong Noname U student could conceivably, ever, rank above a McGill student. Lots of smart students end up going to their home town university for financial reasons, and the home town university isn't always a "top 5" or whatever university.

I agree that there is something really satisfying about knowing that there are standards and striving to meet them - if everything is scaled then, by implication, all that matters is a student's ranking relative to other students. And what is the educational experience all about?

Wendy, I use these kind of incentive schemes too.

RSJ: "Giving good feedback is hard work." Agreed. But students have been proven to learn from it (subject for another blog post).

"It's not clear to me that you would want to encourage students to engage in this type of strategic dropping." This raises philosophical issues about the nature of education. A "Fail" grade shows that a student has tried and failed to complete a course. Why is this of any relevance? In a pure human capital view of the world, what matters is what a student has learnt - not what a student has failed to learn. (Of course, I don't actually believe in a pure human capital view of the world, but it's interesting to think about).

"But on the transcript, it all averages out." - Much depends upon how strictly a given university enforces grading norms (e.g. "no more than 25% As"). In the absence of grading norms, I suspect that a student who was able to strategically avoid hard markers/opt for easy markers would end up with a significantly higher GPA than a student who did not do so. Sites like www.ratemyprofessors.ca are good for finding hard/easy markers.

[Frances Woolley]

Mark: "So you do an exam, you go home feeling pleased and expecting a grade based on your answers and on sample papers or other guidelines and then get a grade lower than you expect because the Prof arbitrarily decides the exam or the marking was *too easy*? Where's the moral hazard for the Prof/TA here?"

I don't think I've ever had to scale my grades down, but I do know of one or two situations when it's happened.

Suppose the prof sets an extremely easy exam. The distribution is min=80, max=100, mean=90.

There's a really compressed distribution, and much of the variance in that distribution is probably stemming from careless errors, marks taken off for slip ups, things not being explained quite right, etc.

It's then really hard to adjust the grades in any way that will produce a distribution that gives high grades to the students with an excellent grasp of the material, and low grades to the students with a poor grasp of the material.

That's why I would always rather give a harder exam and scale up - as long as the variance is coming from differences in the students' knowledge of the material, you can come up with a good assessment.

[Jack]

I sometimes wonder why z-scores have not been adopted, other than the obvious reason that they are more difficult for the layperson to interpret than are grades. The standard criticism is in a small course, one might have a strong cohort one year and a weak cohort the next. But I don't find that convincing. How likely is it really to occur?

[Patrick]

Frances: Don't know ... maybe interview them, or give an entrance exam? It's not something I've thought about because even if they took my McGill C and made it B, they'd rightly still toss my application in the rubbish bin anyway ;)

There are two aspects to this. If you are doing grad school entrance, grades are more relevant because you want to know how good the applicant is at being a student. In the labour market, we don't really care how good the applicant is at being a student, we care about how well they'll be able to do a given job. So when hiring new grads (bachelor degrees), we don't look at grades. And I never had an employer ask for grades. Proof of degree - yes. But never grades. On the other hand, I've done many full and even multi-day interviews.

And come to think of it, it would be an interesting interview question to ask a new grad "Have you ever been blind sided by an exam that was way to hard? How did you handle it?"...

BTW, if my experience was/is still typical, I would advise prospective undergrads to go to Noname U over BigEgoUndergradsAreWorms U any day. I turned down a very nice offer from Noname U in a bucolic southeastern QC town not far from home town, and have regretted it ever since. As in jeans, name brand recognition doesn't imply a good fit.

[Frances Woolley]

Jack: "I sometimes wonder why z-scores have not been adopted" - if I recall correctly, Queen's and University of Toronto give class average scores as well as individual scores, which to some extent gets at this issue.

[Frances Woolley]

And some old British-style transcripts give the student's rank rather than, or as well as, a percentage grade.

[Min]

There is also grading on the curve, with a certain percentage of A's, a certain percentage of B's, etc.

My high school used a variant of the first method, adding points to make the top grade 100. One problem with that is illustrated by the result when my high school English teacher graded over all of her classes and out of 160 students, gave only one A.

[Sina Motamedi]

The moral of story is that professors should put a lot of time/thought/effort into writing "fair" exams that meet distributional requirements without scaling.

[Karen Moustafa Leonard, Ph.D.]

Grading is an interesting topic to me. Do you give the students the instructions on how to make an A and then back off when they achieve your expectations? Or do you give students instructions on how to make a C and then anything better is an A or B? I find rubrics help a lot.

[Wendy]

On RSJ's comment regarding employers really not caring what grade you got. You're right, undergrad students need to hear this. We just hired a commerce Co-op student. In the hiring process on their resumes all of the applicants told us what percentage they earned in various semi-relevant courses. Some were shocked when we told them in the interview that we didn't care who among the applicants received 87% vs 89% vs 75% in a given course--the fact that their profs recommended them as co-op / interns was good enough for us.

We were actually evaluating writing and communications skills as much as anything.

[Min]

When I was in college there was a lot of discussion about grades and grading. It seems to be a perennial topic. :) I did not have much of an opinion, but when I got out into the world and taught adults, I was glad that I did not have to give grades. I felt that they would have been more hindrance than help. You can grade on the curve, but if 7% of my students failed, I would take that as a sign that I had failed.

[Frances Woolley]

Karen "I find rubrics help"
Sina "writing 'fair' exams"

I only learned what a rubric was by reading the ones that my children were given in school - and I bet I'm not alone. As for writing fair exams - well, I don't know if I'm there yet either. I'm not convinced that subjecting profs to extensive training in pedagogy would make matters better - sometimes the latest in fashionable pedagogical techniques cause more problems than they solve - but sometimes it is really helpful just to talk to other people about what they do, read other people's exams, get a sense of other people's expectations.

Wendy "We were actually evaluating writing and communications skills as much as anything."

This is what I tell students "Imagine that you're an employer with a big pile of, say, 100 resumes. You're looking for some simple rules to narrow that pile from 100 resumes down to 10 or 5 resumes. One simple rule is "throw out every resume containing a spelling mistake, it shows that the person doesn't take care." An employer will use that rule because it makes the pile smaller, so makes his or her life simpler."

[Anonymus civil servant]

It's been my experience as well that grades per se don't matter at all on the labour market. However, having a degree from a prestigious university does matter (words like LSE or Harvard look very good on a cv...). And grades matter to get the scholarships that will get you to that prestigious university. Grades also matter to get into the contingented programs that lead to high-paying jobs. So grades do matter on the labour market, but for what they provide access to rather than for an employer to choose between candidates. At that stage writing skills are indeed much much more important.

When I was in CEGEP, z-scores were used by Quebec university to select candidates. IIRC the z-scores appeared next to the average score on my transcript. Of course that was 20+ years ago, not sure they're still used. But as someone involved in giving out scholarship, I bless universities who do provide group averages on transcripts!

[Alex Lougheed]

In many of my undergraduate math courses, professors deliberately chose the most arbitrary scaling functions. Sure, each resulted in the desired mean and variance, and were monotonic, but why involve logarithms? The formulas got more complicated once you factored in that one's class grade was based on nested max() and min() functions.

UBC also posts averages on transcripts now. Median is probably a better measure. And percentile is probably an even better measure than that. (i.e. z-scores).

[Chris S]

One thing that should be checked, though, is to make sure that the distribution makes sense. Decades back, our entire program got mixed up with a situation that put two major tests on the same day. We were "writing tests" for 4.5 hours out of a 5 hours stretch -- in two completely different disciplines (chemistry and calculus). However, this was just our program - most calculus students were only writing the calculus test. (Yes - we did request a schedule change. It was denied.)

As a result, the calculus distribution was strongly bimodal, with an average of 45%. The prof and department decided to use method A - simply add 5 marks to everyone.

But becaause of that bimodal distribution, the result seems to favour only the department. All the students below 50% were typically below 45% as well. So - anybody who failed before the adjustment also failed after it. And anyone who passed before still passed after. The only beneficiary seemed to be the department, who no longer had a "test with an average mark of 45%" on the record books.

Needless to say, we weren't happy or impressed.

[KV]

Whether to scale or how to scale probably isn't just a blanket answer. The oddest marking I had ever had was from a physics professor (amazing professor, by the way) who would tell us ahead of time that the 120 marks exam would be marked out of only a 100 because he didn't want to give part marks to people who were guessing.

Nah, I'm kidding, the oddest marking I ever had was in high school by an english teacher who would give poetry or name of birds and such as marks.

[Frances Woolley]

Chris S - that seems like a classic case where the last type of transformation is called for. Interesting.

Alex - well, I'm very fond of the use of max formulas myself, as they solve all sorts of administrative problems.

"why involve logarithms" - you don't really have to ask, do you?

[RSJ]

Anonymous Civil Servant,

The argument is not that grades don't matter, but that grades assigned to individual homework scores and exams are a distraction.

While you are taking the class, what you really need is feedback about what you did wrong or right, not feedback about how well you are doing relative to others in that class.

The latter de-emphasizes learning and emphasizes relative performance. But the only relative performance that counts for the total number of classes taken. There is random noise in relative performance in each individual class taken. So you are emphasizing random noise.

I *think* it leads to poorer educational outcomes.

Imagine if all students are *only* given informational feedback, but not ranking feedback while they are taking the class. After they complete the class, they get a grade which is based on their rank. But only after they can do nothing to influence that grade. While they are in the class, they receive no numerical or ranking feedback, they only receive comments explaining what they did right and what they did wrong.

In that context, do you think they would learn more or less? I think they would be motivated to learn more, and I think a lot of the effort expanded at optimizing the noise will be re-directed into learning.

[Andrew F]

I enjoyed one course where you started the semester with a negative grade (with a component that had a max score of zero and min of around -5 to -10%). I'm not sure what the point of this was other than to scale grades down. Perhaps it was designed to motivate students to try harder for that component due to loss aversion?

[AC]

Can someone explain the formula for the third method?

[Chris J]

Frances - this post was popular. In a smaller class a prof can read the exams and understand the level of knowledge in the student and give an appropriate grade. But I did hear of one interesting curve when a prof (unintentionally) hammered the students on a final: take the square root and multiply by ten.

0 -> 0 and 100-> 100 so no pesky illegitimate grades result.
Significant bunching to the top: a 36 becomes a weak pass and a 49 a low B.

[Frances Woolley]

AC: third method: finalgrade = originalgrade + (100 - originalgrade)*constant

where constant=(desired increase in mean)/(100-original mean)

For a student at the mean, it just ends up adding the desired increase in mean; for students above that, it adds less, for students below, it adds more.

Chris J - another fascinating scaling method.

RSJ - some Ontario high schools are now using methods very similar to what you describe - a student will get "3" "3+" 4-" "4" "4+" "4++" with 4++=perfect=100%. It works as long as there is no need to make subtle distinctions between students. But if a teacher is looking at a series of grades that are 4, 4+, 4++, 4+, what does he or she award as the final letter grade? Yes, it will be somewhere between 90 and 100, but where? When the difference between a 93 and a 94 is thousands of dollars in scholarship funding or admission into a competitive undergraduate program that's a pretty hard call to make on a series of 4s and 4+s.

Of course the current Ontario high school system is designed so that the lowest mark any answer (other than a blank sheet of paper) can get is 1-, which amounts to a D-, making it impossible to fail.

[Frances Woolley]

RSJ - continuing on the high school system - and students are smart enough to realize that the net impact of the system is that students can't fail, and also work out that this was the intent of the system. So they regard it with the same sort of cynicism that students have had about high school for generations.

[Jonathan Powers]

Grades have two main uses: (1) social and (2) pedagogical. Both are important, but it's very clear that the main social use of grades--as a socially visible and efficacious mark which sets apart the "smart" kids from the not-so-smart ones--is predicated upon the sound functioning of the main pedagogical use--as a form of critical feedback that lets a student know relatively how s/he's performing. Grade inflation is driven by the democratization of the university and the concomitant rise of the social importance of grades. Since a university-level education is now regarded as a sine qua non for a decent job, and since universities use high-school grades as an admissions test (i.e., to make invidious distinctions between students), it's no surprise that enormous pressure is placed on teachers to give higher marks. Similarly, since university students now presume (rather unimaginatively, in my opinion) that a graduate degree is the key to social success, and since graduate schools look at university grades as an admissions test, university students correctly adduce that good grades are key to their social success. And since grades are presented with little context, enormous pressure can be brought to bear on teachers, since it hardly matters how a student gets good grades. The succesful wheedler can expect a level of social success (status and salary) equivalent to that of the class genius.

With that in mind, the crucial context that makes it possible to put grades to any use is deep knowledge of the relative expectations that presumably animate the teacher's instruction. I always think of this context as having three layers: (1) the student's performance vis-à-vis his/her peers in this particular course (during this semester, with these students); (2) the student's performance vis-à-vis other cohorts taking more of less the same course (i.e., compared to all students who've taken this course with me); (3) the student's performance vis-à-vis the universe of students who have ever taken, are now taking, or will take a course more or less equivalent to this one, in any institution and with any instructor. Comparing students only among their immediate peers can give a false impression of their performance, since cohorts and classes can and do differ in relative strength. Some groups should skew higher or lower, because the groups are stronger or weaker than other groups. I find this kind of contextualizing to be very difficult, and while algorithms can be helpful as a method, they are no substitute for the judgment that decides which of them to use or whether to use them at all.

RSJ's thought experiment in which students are given feedback but no grades actually exists at several institutions in the US. Hampshire College, for example, provides no grades: at the end of each course, the teacher and the student both draft a 300-400 word narrative discussing the student's performance. These narratives form the body of the student's "transcript." I took two courses at Hampshire, and I found the students to be engaged, engaging, and highly motivated. (Since I attended a different school, which did give grades, my teachers gave me a grade, but I can tell you that the narratives they wrote are far more precious to me. I still have them.)

I think what RSJ was trying to do (she can correct me if I'm wrong) is to highlight the distinction between the social and pedagogical uses of grades. A better thought experiment for that might be to imagine a university that gives grades, but does not publish them. Students are told what grades they have received, but the records are then destroyed, so that no one can "prove" anything. The students' transcripts are simply the lists of the courses they've taken. Anyone could say he'd gotten an A, but only he and his teacher know for sure, and no on can prove anything. Wouldn't teachers and students then simply regard the grades are a rather autistic and reductive form of feedback? Would giving grades be worth the trouble? Would teaching per se be easier or harder? Relative performance would still need to be graded, in the strict sense of the word, but since the social value of the grade has been eliminated, the only value left is its pedagogical value. So what IS the pedagogical value of a grade?

[Determinant]

Totally. I went through Engineering, I had the same gruelling experience, but I kept at partly because I actually did want to be there. I was told by another student in another faculty in rez one night that was I was unusual because I was in engineering because I really did want to be there, not because my family forced me to take it for their aggrandizement and pecuniary gain.

Yet I'm making career choices that will take me away from engineering and I've given up the profession partly because it is filled with so many people that put money first. It has really destroyed engineering as a profession.

[Patrick]

Determinant: I dunno about that. These days, engineering is really not a good choice if you're looking to have a really high income. Too easy to send the jobs to places with lower wages. And considering that a good engineering program can range from grueling to downright brutal even for smart kids, it seems to me that there are better and easier choices for the gold diggers.

I've done some hiring recently, and I don't see too many non-immigrants applying for electrical engineering jobs or software jobs. I gather all the non-immigrants want to be accountants, lawyers (neither of which can be offshored) or go to biz skool. A biz skool finance major with a math minor is probably going to get you a very nice wage. A B.Eng will get you 4-5 years of apprenticeship just to get your ring, and you top out low six figures unless you're entrepreneurial and lucky. Sky's the limit for finance.

[Determinant]

I've dealt with some racism directed towards me in interviews due to the fact that well, I'm not an immigrant and I'm not related to one for a few generations.

These days a B.Eng will get you nowhere. Companies don't do many apprenticeships anymore. Too costly. They just sign contracts for term work and expect the experts to be there.

The fact that investment has been impacted by the recession is plain for me to see.

Hehe, I was a visible minority in my electrical engineering program. I daresay there was a cultural difference between how Culture A viewed education, its goals and the appropriate course of study for a young person and how Culture B viewed education.

Culture A viewed money and prosperity as the only goal of education and didn't really care if you wanted to be there, it was what the family expected of you. Culture B took a broader view and expected you to want to be there, else how could you expect someone to do a good job? Culture B was also far more amenable to careers based on the Humanities, Business and Social Science.

Culture A students also had a reputation among Culture B students for cheating, copying and other shortcut practices without giving it a second thought.

[RSJ]

Frances,

It's about the type and timing of feedback. I am arguing that when you are learning, you should only get educational feedback. Ex-post, you can get a grade. But the grade will be a _relative_ feedback that distills what you did into a number that ranks your position among the other classmates, whereas the educational feedback is not relative and is multi-dimensional.

By the way, this is my experience in the business world. When you are working, you get specific feedback, but you do not get a "grade". Once a year, there is a performance review and you get a grade -- literally "1" - "5" that plays a role in promotions and bonuses. However, imagine if, after each task, you were to get a grade: "that marketing slide was a 2.3!".

First, it would be insulting, but second, it would distract from the task at hand. If you could make the marketing slide better, then you should be told how it could be made better, not whether it is a 2.3. Nevertheless you do a grade for the year's performance, but the grade is assigned after you can do nothing about it. While you are "earning" the grade, you are given only feedback directly relevant to maximizing your absolute performance.

But for some reason schools do not work this way. They insist on giving real-time relative performance information for each unit of work delivered. Every test and homework assignment needs a "score", when all the students only need to be told which tasks they succeeded at and which tasks they failed at. Then you get all the haggling "I should have gotten a 9.5! instead of an 8.5!", whereas all the discussion should be about how to best do the work. After the class is over, you can fail them all if you want -- this discussion has nothing to do with whether there are grades assigned for performance ex-post, or how tough those grades are.

There is, however, one case where firms do give out "grades" in real-tme -- when their goal is to pit employees against each other, for example in sales.

By the way, if you do this, you have more freedom in assigning grades. For example, imagine a cooking school class that teaches how to bake deserts (I'm hungry at the moment). There are four deserts, and each desert can be poor, average, or good. You can give an A to someone who gets "good" at all 4 deserts. A "B" can be those who are able to make all deserts at least average, and two out of four deserts are good. Etc. It would impossible to mimic that type of a grading system by assigning numerical scores to each desert and then adding them up according to a curve. While the class is being taught, all you need to tell the students is how to improve their deserts. After the class ends, you give them a grade. A less trivial example would be to assume that each of the deserts used some combination of three techniques, and you decide to give an A to students who master all three techniques, a B to students who are adequate at all three and master two of them, etc. Again, you would not be able to mimic this by giving a score for each cake. Feedback in that case would a discussion of the techniques as well as the overall tastiness of the cake.

[Determinant]

Speaking of grades, in my faculty it was a point of pride among students to have received every point on the grade scale. 1-12 was great, 0-12 was even better. I earned the latter.

Every single point on the scale!

[Frances Woolley]

I just received this interesting paper via email:
http://http-server.carleton.ca/~karmstro/papers/GS-IA'.pdf

It sets out a number of criteria that a scaling formula should satisfy, discusses the most commonly used scaling methods, and proposes an alternative.

[Frances Woolley]

RSJ - "While the class is being taught, all you need to tell the students is how to improve their deserts. After the class ends, you give them a grade."

I agree with you that it is vitally important to tell students how to improve their work. To have clear expectations and let people know whether or not they are fulfilling those expectations.

Yet at the same time, students face a time allocation problem - they're often working 10, 20, 30 or more hours a week, and taking a full course load on top of that. School is, for many, a means to an end - a degree, admission into a graduate program, a marketable credential. They need to know how much effort they're going to have to put in to achieve the desired grade.

"You got 65% on the midterm, 80% on the assignments and will need a minimum of 40% on the final to pass the course, 55% for a C-" tells them the information they need to decide how much effort to put into studying for the final exam.

They don't want to know how to make perfect pastry. They want to learn a good enough recipe for pastry: 1 cup flour, 1/3 cup shortening, a and a pinch of salt, zapped in the food processor, moistened with a couple of tablespoons of water, rolled out between two sheets of wax paper. Not superlative pastry, but good enough for a basic pie. Especially something like pecan pie that does well with a crispy crust.