Is grading on a scale a flawed method for evaluating student performance?

[bluemoonKY]

I have always thought that grading on a scale is stupid. When a teacher/professor grades tests based on a scale, the teacher grades each student based on their performance compared to other students. This is a stupid way to do things because it can both cause some students who know the curriculum well to fail a class, and it can cause students who don't know the curriculum to pass a class (or even potentially get an A in a class!). If everyone in, say, a calculus class knows how to solve all types of calculus problems on the tests compentently, the teacher/professor should pass everyone in the class. If nobody in a calculus class knows how to solve calculus problems on the tests at an adequate level, the teacher/professor should fail everyone in the class.

Many times in my life I have heard people say that teachers/professors should grade rigorously and fail incompetent students for two primary (and related) reasons: 1) passing incompetent students harms the reputation of the school or college and 2) if you pass incompetent students, it will result in incompetent /workers in the real world. I agree with both of these reasons. However, if teachers/professors grade the way I'm saying they should grade, there is no danger of teachers/professors passing incompetent students harming the reputation or the school or causing incompetent workers in the real world caused by the teachers' grading.

Let's take the situation of students majoring in aeronautical engineering at a university taking a calculus class. I've heard people use as an example the idea that teachers/professors should not pass incompetent calculus students because " it will result in planes falling out of the sky and crashing." These people are (correctly) implying that the engineers' ability to design planes that won't fall out of the sky and crash is predicated to an extent on the engineers' calculus skills. If everyone in the calculus class in our example ( including the aeronautical engineering majors) is competent at solving all types of calculus problems, and the professor thus passes everyone in the class, then this will not result in planes falling out of the sky due to incompetent calculus students being given passing grades because everyone in the class is competent at solving calculus problems. Conversely, if everyone in the same class (including the aeronautical engineering majors) were very incompetent and awful at solving calculus problems and the professor graded on a scale and gave the least worst calculus student (who is still VERY incompentent) a grade of A and that least worst calculus student is an aeronautical engineering the major, then the professors' grading on a scale could result in planes falling out of the sky and crashing due to the incompetent student receiving a grade on a scale of an A.

 

[Borek]

You are completely ignoring the main reason behind the idea of the grading to scale. Can you at least explain what it is, so that we know your opposition doesn't come from ignorance?

 

[bluemoonKY]

If you asked teachers/professors who grade on a scale why they grade on a scale, they would probably say something like they think that there should be as many A's and B's as there are D's and F's (and vice-versa). But the real (off the record) reason that teachers usually grade on a scale is because the students are so incompetent that if the teacher didn't grade on a scale, the teacher/professor would end up failing just about the entire class. Probably another (less common) reason that some teachers might grade on a scale is to prevent grade inflation. However, both reasons are stupid reasons to grade on a scale for the reasons I said in the original post.

 

[berkeman]

By "grading on a scale", you mean grading on a curve, right?

https://en.wikipedia.org/wiki/Grading_on_a_curve

 

[Borek]

But the real (off the record) reason

And you know that from... ?

 

[micromass]

I have always thought that grading on a scale is stupid.

I agree. It's stupid. I try never to curve the grades or to grade on a scale. But this requires a lot more effort in designing exams and tests. You'll need to design an exam which is hard enough to make sure incompetent students fail, but easy enough so competent students don't fail. This is a tricky balance which is quite hard to achieve.

 

[bluemoonKY]

Berkeman, yes, grading on a scale = grading on a curve. I've seen and heard teachers/professors use both of them, but they both mean the same thing.

 

[bluemoonKY]

Borek, I know that the real (off the record) reason teachers grade on a scale is so that the teacher doesn't have to fail the entire class from my years of observation at both public schools and in college. I think the reason micromass gave could be another reason, especially in upper level college courses. In public school, the reason micromass gave makes less sense to me because the range of student abilities is/was so large.

 

[bluemoonKY]

I agree. It's stupid. I try never to curve the grades or to grade on a scale. But this requires a lot more effort in designing exams and tests. You'll need to design an exam which is hard enough to make sure incompetent students fail, but easy enough so competent students don't fail. This is a tricky balance which is quite hard to achieve.

micromass, based on the *extremely* wide range of abilities I observed in most of the classes I attended when I was in school, I wouldn't have thought it would be that difficult to design an exam that would ensure that incompetents fail and competent students pass, but you would know better than I would since you are a teacher.

 

[micromass]

micromass, based on the *extremely* wide range of abilities I observed in most of the classes I attended when I was in school, I wouldn't have thought it would be that difficult to design an exam that would ensure that incompetents fail and competent students pass, but you would know better than I would since you are a teacher.

Sure, I know it sounds weird. But believe, designing good exams is difficult. The very first exams I designed were much too difficult. They took way too long to solve and required some ingenious techniques which are very much obvious to me, but not to students of that level. I think every teacher should grade on a curve the first few years until he knows the abilities of the students more.

 

[bluemoonKY]

micromass, are you a public school teacher (K-12) or a college professor?

 

[Borek]

For the record: I don't care about grading approach, I just hate skewed/partial arguments no matter which way the go

And micro hit the nail on the head. It is like with taking photographs. If you choose wrong parameters and you end with either over- or underdeveloped pictures, then the only way of saving is to modify the histogram. That's what grading on the curve does.

 

[micromass]

micromass, are you a public school teacher (K-12) or a college professor?

I did both.

 

[Mondayman]

I have quite a few friends in engineering at my university, and they have a saying, "Ride the Curve". They have even gone as far as to design a T-shirt that has a stick man riding a surfboard along a normal distribution. While the shirt is funny, it is a little disturbing to hear that in some of their classes the average grades hover around 30-40%. But I wouldn't know if this is the instructors intention or the fault of the students.

 

[bluemoonKY]

I can see how a teacher would need to grade on a curve to separate incompetents from competents in courses that are subjective like history. But in a math course, I don't see why a teacher would need to grade on a curve. Why can't mathematics teachers/professors just use their mathematics textbooks as a source for the problems on the course and just change the coefficients? Mathematics textbooks usually feature a math problems in a range of difficulties.

 

[micromass]

I can see how a teacher would need to grade on a curve to separate incompetents from competents in courses that are subjective like history. But in a math course, I don't see why a teacher would need to grade on a curve. Why can't mathematics teachers/professors just use their mathematics textbooks as a source for the problems on the course and just change the coefficients? Mathematics textbooks usually feature a math problems in a range of difficulties.

Good question and I'm glad you're asking this. First of all, this holds for rather computational courses like calculus only, not for more advanced math courses.
Second, how many problems should you give? Let's say the exam lasts two hours. How do you make sure the exam is not too long or too short. If the exam is too long, everybody will get bad grades even though they don't deserve it. It is very tricky to make an exam with the right amount of problems.

 

[bluemoonKY]

For the record: I don't care about grading approach, I just hate skewed/partial arguments no matter which way the go

And micro hit the nail on the head. It is like with taking photographs. If you choose wrong parameters and you end with either over- or underdeveloped pictures, then the only way of saving is to modify the histogram. That's what grading on the curve does.

I still don't see why it's difficult to choose the right parameters in mathematics. I mean, if a teacher is teaching calculus II, why would it be difficult to choose the right parameters? There are limits to the amount of fudging that can be done with the course content. The teacher must teach integration by parts, integration by partial fractions, integration by substitution, parabolas, and sequences and series. The teacher must include problems on tests requiring integration by parts, integration by partial fractions, integration by substitution, parabolas, and solving for whether or not different types of power series and other types of series converge or not. If all the students can solve all the types of calculus problems that I just listed, they are all competent. If none of the students can solve any of the types of calculus problems I just listed, they are all incompetent. If the students can solve the different types of calculus problems I just listed to different degrees, the students are individually as competent or incompetent to the degree to which they can solve the different types of calculus problems I just listed, not competent or incompetent based on how well they do in comparison to each other.

 

[bluemoonKY]

Good question and I'm glad you're asking this. First of all, this holds for rather computational courses like calculus only, not for more advanced math courses.
Second, how many problems should you give?

You should err on the side of giving them more than enough time.

Let's say the exam lasts two hours. How do you make sure the exam is not too long or too short. If the exam is too long, everybody will get bad grades even though they don't deserve it. It is very tricky to make an exam with the right amount of problems.

If the exam last 2 hours, you should give the amount of problems that you think that they should be able to do in an hour.

 

[micromass]

You should err on the side of giving them more than enough time.

If the exam last 2 hours, you should give the amount of problems that you think that they should be able to do in an hour.

So then some people will be able to solve it completely while being too slow.

 

[bluemoonKY]

Micromass, since when was speed supposed to be a determining factor on someone's grade on a course on anything other than keyboarding? I always thought that when teachers give math tests, the math tests are strictly supposed to test whether or not the student knows the course content, not the time it takes the student to answer it.

 

[micromass]

Micromass, since when was speed supposed to be a determining factor on someone's grade on a course on anything other than keyboarding? I always thought that when teachers give math tests, the math tests are strictly supposed to test whether or not the student knows the course content, not the time it takes the student to answer it.

You don't think speed should somehow be a determining factor? I'm not saying everybody should be super fact problem solvers, but if you need to take 2 hours for solving $x^2 - x +1=0$, then you should fail the course even if you do find it after 2 hours.

 

[bluemoonKY]

I think that it wouldn't be that difficult for a teacher to determine what would be a reasonable amount of time to solve mathematics problems. I don't think it's any reason for a teacher to need to grade on a curve.

 

[micromass]

I think that it wouldn't be that difficult for a teacher to determine what would be a reasonable amount of time to solve mathematics problems.

It is that difficult. I have made errors in judging this multiple times.

 

[jtbell]

I wouldn't have thought it would be that difficult to design an exam that would ensure that incompetents fail and competent students pass,

I second micro's comment. It's hard, at least at first. The first intro physics exam that I wrote 33 years ago was a disaster. With time, you get a feel for how your students will do on different questions. Also, certain types of questions are very difficult to design and chose effectively according to difficulty: true/false and multiple choice. For those questions, grading is binary, you either get it right or you don't. That's why I've always preferred short-exercise questions, because I can adjust partial credit to some extent.

 

[Borek]

The teacher must teach integration by parts

Does it take you exactly the same amount of time to find every integral using integration by parts, or do you find some integrals harder than other?

Have it ever occurred to you that you have spent several hours trying to solve a problem, only to find out it is in fact trivial, you just looked all the time from the wrong side? Have it ever happened to you to fail an exam because of that?

If you think it is all simple and trivial you just lack imagination.

 

[Mark44]

Micromass, since when was speed supposed to be a determining factor on someone's grade on a course on anything other than keyboarding?

In the "real world" there are hard deadlines for when something needs to be delivered. If the product isn't delivered on time, it can make the difference between a company surviving or not. I spent 20 years teaching math, with 18 at the college level, and then worked for 15 years at a well-known software company. The engineers and everyone else involved in the product were expected to get their parts done on time. When that didn't happen, there definitely were consequences.

I always thought that when teachers give math tests, the math tests are strictly supposed to test whether or not the student knows the course content, not the time it takes the student to answer it.

 

[Mark44]

I think that it wouldn't be that difficult for a teacher to determine what would be a reasonable amount of time to solve mathematics problems.

There's a tacit assumption here that all of the students are equally competent and can work at the same rate. That is NOT the case.

I don't think it's any reason for a teacher to need to grade on a curve.

 

[Mark44]

I have always thought that grading on a scale is stupid. When a teacher/professor grades tests based on a scale, the teacher grades each student based on their performance compared to other students. This is a stupid way to do things because it can both cause some students who know the curriculum well to fail a class, and it can cause students who don't know the curriculum to pass a class (or even potentially get an A in a class!).

From your first post in this thread. Your reasoning here is flawed, IMO. The students who know the material being tested on will likely do better than average, and the ones who don't know the material will likely do worse than average. How can you conclude that students who understand the material will fail, and the ones who don't know the material will surpass the others?

I've never heard the expression "grading on a scale." What I've heard forever is "grading on the curve;" i.e., the standard normal curve, or Bell curve (occasionally called the Gaussian). The assumption here is that the sample of students in the class mirrors more or less the normally distributed general population. The abilities of most of them are in the middle, but there are a small number of students at either end of the distribution.

 

[collinsmark]

It really is difficult to assess the appropriate time it takes for students to perform a set of problems. The instructor should take the test himself/herself and time how long it took, and then multiply that by some factor. But what factor? It's really not so simple.

Perhaps it might be best explained with an example.

(No calculators allowed. You must do it by hand.)

Convert the following 10 bit, hexadecimal number to decimal under the following assumptions:

A) The number is in 10 bit, two's compliment format.
B) The number is in 10 bit, unsigned binary format.​

Number: 0x3FE​

That particular problem I can do (Both parts, A and B) in my head in about 20 seconds. Add another 10 seconds to write (or type) the answer onto the paper (or into the computer), and it makes 30 seconds.

Answers:
A) -2
B) 1022

So should I give the students twice that? One minute? I think they might need more. Scale by 4x for 2 minutes? I don't know, it's a tough determination.

It's not that I'm inherently smarter than the students, it's just that I'm way more familiar with the material than the students. That, and this was a particularly easy problem. (Had the number been 0x25A, for example, it would have taken me longer).

What if the student realizes a mistake half way through the problem and has to start over? How to I account for the time it takes for that?

If there are multiple ways to approach the problem should I allow the student time to contemplate the best approach? What if he/she chooses the tougher approach. Should he/she be penalized for that?

It's not an easy thing to gauge.

 

[Drakkith]

In the "real world" there are hard deadlines for when something needs to be delivered. If the product isn't delivered on time, it can make the difference between a company surviving or not. I spent 20 years teaching math, with 18 at the college level, and then worked for 15 years at a well-known software company. The engineers and everyone else involved in the product were expected to get their parts done on time. When that didn't happen, there definitely were consequences.

Sure, but does this really have much to do with the time it takes to finish a test? I don't think a person's on-the-job performance and test taking are that closely related.

 

[berkeman]

In a challenging 2nd year undergraduate physics class that I took, the prof posted the exam results as a histogram, with the boundaries hand-drawn in for the different grades. The histogram always approximated a Bell curve. The exams were a challenge to complete on time, but not overly so. I usually like to have enough time to go back to double-check my answers, and in that class I only sometimes had enough time to do that. I did very well in the class, and seeing the Bell curve of scores helped me to understand how the grades were assigned. The average/peak of the curves were generally around 50/100. That was a great class, IMO, for multiple reasons.

 

[berkeman]

Sure, but does this really have much to do with the time it takes to finish a test? I don't think a person's on-the-job performance and test taking are that closely related.

That's a reasonable question, but yeah, performing under time pressure is an important skill. Even performing on an all-nighter with millions in revenue on the line...

(Don't ask me how I know this...)

 

[lisab]

I dislike grading on a curve, but for a totally different reason than those discussed so far.

I graduated from a program that was 100% curve-graded. It taught me to be tough, and when I graduated I had great self-confidence. It also taught me never, ever share your knowledge with others, because if the tables were turned they would not share with you. In a curve-graded class, it's dog-eat-dog and if you help anyone, you hurt yourself*. My fellow students were stunningly cut-throat.

Once I was working in industry, I quickly realized this is a horrible way to approach the working world. IMHO, this kind of education does not produce a person that is ready for today's team-oriented workplace.

* One exception: if the person you help is 1) behind you on the curve, and 2) the help you give him/her keeps them from dropping the class.

 

[Drakkith]

I graduated from a program that was 100% curve-graded. It taught me to be tough, and when I graduated I had great self-confidence. It also taught me never, ever share your knowledge with others, because if the tables were turned they would not share with you. In a curve-graded class, it's dog-eat-dog and if you help anyone, you hurt yourself*. My fellow students were stunningly cut-throat.

Is this the sort of program where only the top X% of the class graduated?

 

[berkeman]

I dislike grading on a curve, but for a totally different reason than those discussed so far.

I graduated from a program that was 100% curve-graded. It taught me to be tough, and when I graduated I had great self-confidence. It also taught me never, ever share your knowledge with others, because if the tables were turned they would not share with you. In a curve-graded class, it's dog-eat-dog and if you help anyone, you hurt yourself*. My fellow students were stunningly cut-throat.

Once I was working in industry, I quickly realized this is a horrible way to approach the working world. IMHO, this kind of education does not produce a person that is ready for today's team-oriented workplace.

* One exception: if the person you help is 1) behind you on the curve, and 2) the help you give him/her keeps them from dropping the class.

Interesting. At least in my situation, the curve grading didn't hinder me from helping my fellow students. In the physics class that I mentioned, I helped a number of students when I could. There was a giant study session with the prof before the final exam where I asked a question about one of the more advanced questions on the study list, and the prof said "we can get to that later, let's focus on the earlier questions first" I respectfully packed up and left to go study, and I heard other students around me saying "maybe we should go study with him..."