Grading Techniques: Final Answer vs. Work Done

[Alkatran]

I'll start by saying that I'm not a teacher, and I've had a lot of problems with how my teachers mark.

Do you think that a question should be graded on the work done? The final answer? The ingenuity? etc etc...

I personnaly think that the final answer should be worth a minimal amount, the main thing to analyse is the work. If a student makes a mistake on step 1 but uses the answers they found from Step 1 correctly through step 10, do they really deserve a 0? Why would you give someone who had it right until step 9 more points?

A good example of this is actually from one of my geography tests. We had to draw a population graph. At the very top of my page I wrote:
F(x) = x/20 000 (where 20 000 is the total population)
What did I get on the question? 0. Because I was supposed to divide men by the male population and women by the female. ONE mistake made it so the rest of the (correct) work, such as the layout of the graph, the age groups, etc. Wrong. If I had merged 2 age groups I would have had 19/20.

I also think ingenuity is worth marking, but not extensively. If a student can find a shortcut around a large problem, way to go. But if the problem says you have to do it one way, don't do it.

I could go on, but I want to hear what others think first.

 

[chroot]

Generally, work should be graded with as high a granularity as is feasible. You can break any problem down into a set of sub-problems -- did the student use the right formula? did the student manipulate that formula properly? did the student make any arithmetic mistakes? each of which should be given its own grade. In that way, a student who does exactly 56.5% of a problem's work should be given exactly 56.5% of the problem's points.

The difficulty is that the teacher or TA often just doesn't have the time to grade to this level of granularity. They simply mark entire questions correct or incorrect based on their final answers to save time. While this is essentially the same as rounding a student's score down, as long as it's done consistently to every student it won't make a difference. Few college professors assign final semester grades by raw percentages anyway.

- Warren

 

[e(ho0n3]

I guess it all depends on the teacher. Some are more strict than others. There are some very strict teachers who will mark an answer wrong if the answer is not simplified. For example, say the anwer to a question is 4 and you decided to leave the answer as 2 + 2. A very strict teacher will probably mark this as wrong. On the other hand, an easy-going teacher might mark it correct. As I said, it depends on the teacher.

In standardized tests, you either get the correct answer or you don't, regardless of the work you did (whether you cheated, did it on your own, etc.), so it is best to get the correct answer above anything else. I suggest you be more careful next time.

 

[shmoe]

When it comes to grading, universally unfair is fair.

Finite man hours to mark makes very detailed marking schemes difficult sometimes. This is why multiple guess questions appear on tests. It would be great if every student could be given an oral exam, which is one of the best ways to see if they know their stuff, but this is impossible for most courses.

I wouldn't give any bonus points for ingenuity and finding a clever way to solve a problem. This has it's own reward of saving time, giving the clever student more time to check over the rest of the test. I have a fondness for questions that have a short "back door" for the bright ones but that can be done the long way by anyone who was awake for more that 52% of the lectures.

 

[mathwonk]

I agree grading is determined by available energy and time. I have spent many hundreds, maybe thousands of hours, grading tests in my life and writing out detailed comments on every one. The result is a huge collection of hundreds of tests with hand written comments that no one has even had the curiosity to come pick up and look at.

As long as the student is only interested in the final number on a test and not why they got it wrong, or how they could improve, it is hard to ask the teacher to behave differently.

Still, like Don Quixote, I continue to write out comments that no one will ever read on hundreds more tests every year.

Indeed Don Quixote is my favorite model for a teacher, riding out on his nag, optimistic as ever in the mroning, and riding back home in the evening, beaten and bedraggled. But he never gives up his ideals, just because they are seldom realized.

The whole point in being a good student, is to get over the attitude of arguing about your grade. A teacher pretty much assumes a student who is arguing about his grade is a poor student, missing the point of learning. In the opposite direction a student who does not care about his grade may be given the benefit of the doubt by the teacher as a student who has finally gotten the point of learning.

Grades are a fantasy, they do not mean anything. they are numbers. I once became frustrated with a flawed grading scheme and just gave a whole class A's. Everyone assumed he/she deserved the grade and not one person thought it was a mistake, or an experiment, or that anything was amiss, nor questioned it in any way.

Let me give you an extreme example, which however is literally true. I washed out of grad school the first time, after passing the prelim exams, because of inattention and other worldly distractions.

Then later I decided to go back to grad school and entered another school. When I got there, the first day I asked to sign up for prelims. They were flabbergasted, as all their own students were frightened to death of prelims and avoided scheduling them as long as possible, and here i was asking to take them.

So they began to inquire of me: Why do you want to take them? I said well, don't they determine whether I am qualified to try for this degree? If not, maybe I should be doing something else with my life.

Then they really flipped out. "well, wait a minute. are you sure you need to take them? haven't you maybe taken them somewhere else?"

I said well yes I have taken them at my previous school. "Did you pass?" yes.

"Oh! OK, then you do not need to take them here!"

So without even checking the truthfulness of my statement they ushered me over to the professor in charge of prelims and he stamped my form "passed".

Later when I saw the prelims at that school, I noticed to my extreme relief that they were much harder than the ones I had passed, and I was quite unsure of being able to pass them.


The point is that tests and grades are only for the chickenhearted. Sorry, that's the truth. Any real strong student has nothing to fear from them. So get that attitude, communicate it to your teacher, learn the material, more important take an interest in learning the material, and you will never have anything to fear from tests or grades.

 

[Alkatran]

So, since the time to correct a test is limited, you're saying you should design the test to complement logic and ingenuity? (Mathwonk's example is a good one, I think I'd like him as a teacher) Or putting problems that require a slight amount of logical though.

I can tell you one thing, I read all the comments on my tests.

 

[vsage]

That's an admirable outlook, Mathwonk. I always read my teachers' comments: I'm not THAT arrogant to think I don't need to. Being a first year college student in say 6 days I can't say I can relate to what's being said here as I'm just getting my first taste of college anonymity. The only college classes I took before were two math classes: multivariable calc and differential equations and both teachers gave partial credit. For the first time though my conscience was being tried in the latter class because of the copious amounts of partial credit given, I was able to ace the class but I miserably failed at a competition in differential equations for the math club with a 40%, which was good for other high school kids but I had actually taken the course and still only scored marginally better. Right now I can't really recall anything from the last half of the book besides laplace transforms. Anything past superposition is a blur. Did I really deserve an A? I don't think so, but I feel like I was cheated by the ease of the class and cheated by myself in accepting the credit.

 

[robert Ihnot]

I guess it all depends on the teacher. Some are more strict than others. There are some very strict teachers who will mark an answer wrong if the answer is not simplified. For example, say the anwer to a question is 4 and you decided to leave the answer as 2 + 2. A very strict teacher will probably mark this as wrong. On the other hand, an easy-going teacher might mark it correct. As I said, it depends on the teacher.

In standardized tests, you either get the correct answer or you don't, regardless of the work you did (whether you cheated, did it on your own, etc.), so it is best to get the correct answer above anything else. I suggest you be more careful next time.

You got to take into consideration standarized tests, since your instructor may have little leaway in how he grades. The department may want to keep the power to itself being afraid that one instructor will grade differently than another. This means that only the answer counts, and students get to thinking that only the grade counts.

 

[Alkatran]

You got to take into consideration standarized tests, since your instructor may have little leaway in how he grades. The department may want to keep the power to itself being afraid that one instructor will grade differently than another. This means that only the answer counts, and students get to thinking that only the grade counts.

If there is one thing I hate, it's someone who has more "test skill" then me scoring higher. You know, someone who always knows exactly how much the teacher wants, how they want it, etc. I'm always caught on foolish little things (you didn't show the imaginary roots! (fair enough), you didn't put enough work (by the end of the year I was doing problems TWICE))

 

[BobG]

Testing is an imperfect system where each method has quite a few plusses and minuses.

Grading a test where partial credit is given always means extra time is required to grade the test. However, if extra time is given to constructing the test key, the amount of extra time to grade the test can be held to a minimum.

Typically, the 'right' way to solve the problem is used on the key. Any differences from the norm are handled case by case by the instructor. Since some errors are a lot more common than others, a teacher can get fairly quick at recognizing where the problem's going, but they spent half the grading period learning the common errors and what to look for.

A little extra time spent figuring out where the most likely errors are going to occur ahead of time allows the key to reflect the different possibilities (i.e. error 'A' committed on first step, follow column 'A' to check steps b, c, d, etc). This would probably only be worth the effort if the test was going to be used term after term.

A little bit of this type of analysis is done by professional curriculum developers. If the school is buying its books, lesson plans, and tests from a service, you'll notice the distractors on multiple choice tests always have very plausible answers (i.e. - an error on this step results in an answer that matches choice b, an error on this step matches choice c, etc.). That may seem a little unfair, but doing that is seen as preferable to giving away the farm with distractors that make wrong answers obvious.

Personally, in an academic environment, I see no problem with tipping off the student that they've made the wrong choice. You account for that by putting a strict time limit on the test. Silly mistakes get corrected, but there's not enough time to just randomly try different methods until you finally get an answer that matches one of the choices.

Any way you go, writing your own tests can be a pain. I've usually had to trend multiple choice tests, not just by right or wrong, but by which wrong distractors are chosen and by who's missing the questions (it's always embarassing if all the guys getting 60% get the problem right while the guys getting 90% are missing the question). I've had trends that were unsolvable no matter how much emphasis you put on it in class only to wind up resolving it by moving the question as little as one spot on the test (sometimes, the person taking a test can get channeled along a certain train of thought by a series of questions and has problems breaking out of that when the questions suddenly switch to a new topic).

 

[BobG]

If there is one thing I hate, it's someone who has more "test skill" then me scoring higher. You know, someone who always knows exactly how much the teacher wants, how they want it, etc. I'm always caught on foolish little things (you didn't show the imaginary roots! (fair enough), you didn't put enough work (by the end of the year I was doing problems TWICE))

'Test skill' is a valuable skill to have. A long enough test and I've always been able to add a few points by finding the answer to question #23 in question #46, or at least knowing that choice 'd' of question #13 couldn't be correct or question #19 would make no sense, etc.

My all time favorite triumph was a literature class where we had to read about 6 to 8 short stories. There'd be true/false questions and multiple choice questions on each story, plus there would be one essay question on one of the stories. Inevitably, there'd be at least one story that you just knew wasn't worth reading just from the introductory blurb. And what are the chances of that being the story the essay question would come from? I guess pretty good if you make a habit of doing that. Sure enough, there came the time where I had to write my essay from 4 multiple choice questions and 3 true/false questions.

Managed a 'C'. But, boy, you should have seen the comments the teacher wrote on the test. She had no idea where I was pulling some of this stuff from. I was laughing when I read some of the comments, thinking, "Why are you getting on my case? It was your true/false question! ... Doh! I guess that means I missed that question on the test, too." Obviously, she never thought to go back and read the test while she was grading my essay. Instead, her final comments were almost a veiled offer to get me help if I needed it (psychologolical treatments, electro-shock, drug rehab?)

 

[Alkatran]

'Test skill' is a valuable skill to have. A long enough test and I've always been able to add a few points by finding the answer to question #23 in question #46, or at least knowing that choice 'd' of question #13 couldn't be correct or question #19 would make no sense, etc.

That wasn't the test skill I meant. That is the ability to exploit teachers' mistakes. I've seen a lot of them, ESPECIALLY on fill-in-the-blank tests some teachers like to give. A good example is when they put "Are", and only a few of the answers are plural. And yes, I've seen a few occasions where an answer is given in a question. But in physics this is almost always true (Hmmm I have meters and seconds, and I'm looking for speed... the units of speed is meters/second... HMMMMMM)

The test skill I'm talking about is the ability to understand what a teacher wants. Seeing the question in the context of "What are they looking for?", which can potentially change the method you use, and which steps you show. Some teachers want to see ALL the work while others really don't care much.


On another note, my last physics teacher (in grade 12) had the nasty habit of putting a few true/false questions on tests that we hadn't even learned! Things that weren't in the book, and which were NOT EVEN HINTED AT. For example, we had a true/false: Does a neutron have more mass than a proton? Now we hadn't even touched neutrons, and definitely hadn't learned the mass of a proton (we knew that of an electron), but alas...
Another example: "Esque la Teree est bombee sur les poles?" translates very roughly to: Is the Earth wider along the poles? Now realize I had no idea what the verb "bombee" meant. Nor did the rest of the class.

 

[Moonbear]

The most important thing in writing, giving, and grading tests is giving the students clear instructions of what is important to the grading. If the final answer is worth all the points and there won't be any partial credit, students should know this...for those who can find some shortcuts or who can do the math in their head, they needn't waste time writing it all out if it won't count for anything. On the other hand, if you are going to give partial credit, then the students need to know this too so they write out their work to get any possible credit they deserve.

I'm not fond of giving credit for creativity. Sometimes that just means dumb-luck that your shortcut worked for the given example. I don't teach math courses, so I don't know if there are cases where that would make more sense.

One of the problems I run into in grading is the essay question. I like to give one or two of those on exams to really give those who really understand the material fully a chance to shine, but the tough ones to grade are the ones where the students ramble on for 3 pages for something that should have been a 4 sentence answer in hopes that they'll say something worth giving credit for. I've known people to take very different approaches to grading those. I tend to use the essay as a measure of whether the student actually understands the material or is just regurgitating things they've memorized, so if they can't get to the point fairly quickly, I don't give points. Others will go through and painstakingly read through every sentence and try to "give" the students points. But, I make it clear in my instructions that brevity is important, that the answer shouldn't require more space that provided under the question, and I'm not grading anything written outside of that space.

Much of how a teacher grades depends on what they think is the important lesson in their class. Some may think all the correct work doesn't matter if one mistake gives you a wrong answer (the "real" world works that way...you can't very well explain to the families of those who were killed in a building collapse that it was just a tiny arithmetic error when calculating the stresses on the building supports). Others want to be sure you understand the theory, so grade on the work and reasoning you use to get to your answer.

But yes, sometimes teachers and professors take shortcuts to grading because there are just too many exams to grade in too short a time (especially at the ends of semesters when they give us only 3 days to get grades submitted after the final exam). I was a TA for one prof who gave all essay questions, then didn't have time to grade them, so skimmed each one, sorted them into three piles, lousy, mediocre, good and assigned 0, 3 or 6 points for each of the essays in those three piles, respectively.

 

[Alkatran]

The most important thing in writing, giving, and grading tests is giving the students clear instructions of what is important to the grading. If the final answer is worth all the points and there won't be any partial credit, students should know this...for those who can find some shortcuts or who can do the math in their head, they needn't waste time writing it all out if it won't count for anything. On the other hand, if you are going to give partial credit, then the students need to know this too so they write out their work to get any possible credit they deserve.

Completely agree. This reduces some of the "random chance" affecting too many tests.

I'm not fond of giving credit for creativity. Sometimes that just means dumb-luck that your shortcut worked for the given example. I don't teach math courses, so I don't know if there are cases where that would make more sense.

In math, the chance of some random shortcut working is near nill. Usually a 'trick' comes from an insight into the problem.

One of the problems I run into in grading is the essay question. I like to give one or two of those on exams to really give those who really understand the material fully a chance to shine, but the tough ones to grade are the ones where the students ramble on for 3 pages for something that should have been a 4 sentence answer in hopes that they'll say something worth giving credit for. I've known people to take very different approaches to grading those. I tend to use the essay as a measure of whether the student actually understands the material or is just regurgitating things they've memorized, so if they can't get to the point fairly quickly, I don't give points. Others will go through and painstakingly read through every sentence and try to "give" the students points. But, I make it clear in my instructions that brevity is important, that the answer shouldn't require more space that provided under the question, and I'm not grading anything written outside of that space.

I've heard of people writing like that, only trying to hit on 'keywords'. I have had a teacher who graded ENTIRELY on keywords, in fact her tests were almost entirely revolving around the memorisation of terms. 50% for definitions, the rest on questions where the keywords matter. :(

Much of how a teacher grades depends on what they think is the important lesson in their class. Some may think all the correct work doesn't matter if one mistake gives you a wrong answer (the "real" world works that way...you can't very well explain to the families of those who were killed in a building collapse that it was just a tiny arithmetic error when calculating the stresses on the building supports). Others want to be sure you understand the theory, so grade on the work and reasoning you use to get to your answer.

You don't fail a test if you get under 100%, why should the questions be any different? You get one chance to be wrong in your life, don't ruin it!

 

[Moonbear]

Completely agree. This reduces some of the "random chance" affecting too many tests.

It's really easy to write a test, and really hard to write a good test. When you have students who are losing points because they aren't sure what the question is rather than how to find the answer, then it's a bad test.

When I was first learning to teach, I had a very good mentor who was very wise when it came to teaching, even if he was a little nutty. He taught me that the best way to write a test is to go into a lecture knowing what two or three main points you want to get across for that day, make those points well, then go home and write two or three questions based on that material while it's fresh in your mind what you taught, emphasized, and actually covered in the class, including the questions students asked. This way you aren't left trying to recall if you actually got around to covering a particular topic in a lecture you gave a month ago.

For the course I taught with him, I wrote the quizzes and he wrote the major exams. He went through every one of my quizzes and checked that the questions were unambiguous. This is very helpful, to have someone else who knows the subject read your questions to see if they understand the instructions.

I also learned to be flexible in my grading if I did let a question slip through that was worded in a way that you could interpret it in more than one way...this would become apparent when many students all answered the same wrong way. If a question was missed by a large number of the students, then I would evaluate if the question was a bad question, if the material wasn't covered adequately, or if it was just a tough question and only the top students would get it right. This can be hard to determine, and generally didn't make any difference in the grades to just drop the question from the scoring, but did make a difference in keeping the students happy so they'd keep learning. I'd then go over the answers to any particularly challenging questions (some were intentionally written to be more challenging, so only a few would get them right...this helps sort out the A students from the B students).

You don't fail a test if you get under 100%, why should the questions be any different? You get one chance to be wrong in your life, don't ruin it!

I agree. I believe in partial credit and write my tests with that in mind. I think how you get to the answer is important. I'm also careful to make sure the point value of a question reflects the number of components that go into getting the full answer so that I can easily break it down for partial credit (i.e., writing down the formula is 1 pt, understanding the variables and using the correct numbers in the formula is 1 pt, using the correct units is 1 pt, solving the equation is 1 pt).

However, when all else fails and a question winds up ambiguous anyway, there is one good test-taking skill you can readily employ...raise your hand and ask for clarification. If the problem really is with the question and not your knowledge, you should be able to explain to your teacher why the problem is confusing and the two different ways you could answer it to find out which the question is actually asking for. I know I've always preferred it if my students ask this during the exam when I have the opportunity to announce a clarification to the entire class rather than have to hear them whine about it being unfair later (and yes, some really do whine about it).

 

[Alkatran]

I also learned to be flexible in my grading if I did let a question slip through that was worded in a way that you could interpret it in more than one way...this would become apparent when many students all answered the same wrong way. If a question was missed by a large number of the students, then I would evaluate if the question was a bad question, if the material wasn't covered adequately, or if it was just a tough question and only the top students would get it right. This can be hard to determine, and generally didn't make any difference in the grades to just drop the question from the scoring, but did make a difference in keeping the students happy so they'd keep learning.

That is the one thing I've never seen. I wish I had and hope I will.

Funny story: I had a question resembling this one:
Where is the electrical field force (terms are wrong, I learned this in french) equal to 0 between charge A and charge B? (continue on with specifics on A and B)
I lost points because I placed charge A to the right of charge B. (the teacher assumed we would assume A was to the left)

 

[Moonbear]

That is the one thing I've never seen. I wish I had and hope I will.

Funny story: I had a question resembling this one:
Where is the electrical field force (terms are wrong, I learned this in french) equal to 0 between charge A and charge B? (continue on with specifics on A and B)
I lost points because I placed charge A to the right of charge B. (the teacher assumed we would assume A was to the left)

That's borderline insanity with grading. Unless something in the question made it make a difference, well, I'm sorry you have such unreasonable instructors.

 

[Alkatran]

That's borderline insanity with grading. Unless something in the question made it make a difference, well, I'm sorry you have such unreasonable instructors.

This teacher would have any test corrected within 30 minutes of receiving it. I mean the entire GROUP of tests. I got my exam mark back the same DAY!

By the end of the year I was very very cautious with this teacher. I made sure I wrote dx/dy(x^n ) = nx^(n-1) at the start of any derivative problem, etc...