Basically this is a test grading system that can be very quickly graded.  It applies mostly to problems type courses.  I used it for all the engineering classes I taught.  I loved it and the students did too.

The students get more points for correct work and lose less for mistakes.  It all evens out in the end because you grade on a curve anyway.  The students can skip one of the four problems and still get a 90 if they do everything else perfect.  Their best problem is worth 40% of the grade and their worst only 10%.

This system promotes accuracy and completeness, it's better to finish one problem then it is to start 3.  Just like in the real world, one finished and useable bridge is much better than 3 partially finished bridges.    

I developed it because one semester I taught the largest engineering class ever taught at KSU.  It was Engineering Economics.  The semester before the class was not offered due to a faculty shortage, normally there were 2 or three sections with 40 or so students per section.  So this semester I had two semesters worth of students all combined into one giant lecture.  I agreed to teach it, I enjoy a challenge.  The class was so large we had to find a larger lecture hall than what was available in the engineering buildings.  It was an auditorium. The class was a disaster due to classroom layout, the blackboards were far too small, too far away from the students along with many other problems.  There were over 240 students in the class.  This test method was really the only good thing to come out of that semester.

Basically the system involves four problems.  The problems have to be such that they involve many (maybe 10 or so) steps or decisions to come up with a final numerical answer.  A typical engineering design course fits this mold very well.   I often would have 2 part problems, part A that basically asked do you have any idea what's going on and then part B that is more involved.

These problems are graded on a 4 level system.  

Perfect  ----  Almost perfect  ---  More than 1/2 right  ---  Less than half right

The marks I use to represent these 4 levels are  3,2,1,0  This is all that is recorded in the grade book and on the test sheet handed back to the student.  You do have to quickly mark up the test with  a couple circles, x's, check marks, and/or lines to show what was there and what was not correct.   I always grade in ink and draw a line across the paper at the end of the students work.  The important thing is that you don't have to spend the time to fully understand the students work in order to do this grading.   I require the students to write the final answer in ink and box it. Finding it is faster and easier when bolded like that and you know what they think is the answer.  Often the correct answer might be on the paper, they may have worked the problem 2 ways, but they chose the incorrect one as their answer.   They are required to have all the work, the answer boxed, in ink with correct number and units to be perfect.  Almost perfect (2) is rarely given on the first grading, a 1 (more then half right) is marked and it is left for the student to rework the problem after the test is returned, (that's the next 50 point test) discover their mistake and then argue (not much argument here) for the almost perfect grade.  Almost perfect is one stupid math error, no theory errors.  

The retake test (50 points) is a take home, same problems, due one week later, work with anybody, even come in and ask me, get it right test.  Basically learn what you didn't learn exercise.  If you got a 105 on the first test just hand it back in.  If a student missed a test due to illness, they take the make up at the end of the semester, but they still hand in the retake for the test they missed.  This retake is the best part of this system in my opinion, most of the time students never learn from their mistakes.  They take a test, get it back, look at the grade and then stuff it away in the notebook. 

More then half right, is just as easy and quick to grade.  You ask yourself, "Does it appear that they in the correct ball park?"  Less than half right, sometimes takes a judgement and a little more time, they have missed many important steps. they get nothing for this.  Normally it takes 10 seconds or less to grade a problem.  Basically you check the answer, quickly scan the method, make a couple marks and write a number 3,1 or 0.  Their answer in ink reduces the students ability to change mistakes after the fact to argue for a 2 and a couple marks on the paper reduces the ability to add material later and upgrade a 0 to a 1.  There have been times I have photocopied all works earning a zero and caught a couple students cheating like that.  I offer them a chance to drop the class before I push for expulsion from the university.  They've been caught red handed, hopefully they learn something from the experience.  

This zero credit for less than half right forces the students to concentrate on the problems that they know how to work and not just try to put something on the paper to try and get some partial credit for stuff they know little about.  It takes a long time to figure out how to grade that using the old method.  Hard decisions, is it worth 3 points or 4 out of 25, etc.  That's what makes it take so long to grade the old way.   If they are clueless, with this method it's best to leave it blank, punt that one and try another.  

My tests are closed book, I also allow the student to bring in one 9.5x11 hand written crib sheet, front and back, even edges, LOL.  No photocopies, they have to spend the time writing and organizing this.  It's a good study aid to make them at least open the book and copy the formulas.  With open book tests I found the poorer students often waste too much time thumbing through the text trying to find a similar example problem.  This hand written paper (cheat sheet) eliminates the advantage a student might have with an expensive programable calculator over one that could not afford such luxury. 

This system results with 4 numbers as the grade recorded in your record book and also on the returned test, like 1331 or 0321  This is then turned into a score with the following set of rules.  You never do this conversion, all you do is record the 4 numbers.  The computer does the conversion when it calculates and prints students grades and class averages.  The students learn the conversion very quickly and are quite satisfied with a 4 number record of test performance.

The students best problem is worth 40, 35, 30, 0 for a grade of 3, 2, 1, or 0

2nd best   30, 25, 20, 0  for  grades of 3, 2, 1, 0

3rd best    20, 15, 10, 0  for grades of 3, 2, 1, 0

worst        10, 5, 5, 0    for grades of 3, 2, 1, 0 

There also is extra credit given for no 0's,  +10 points for no 0's no's 3's, +5 points for no 0's some 3's.  This seems backwards but they've already got their extra credit if they have a 3 and got 40 points for one problem.

I developed, modified and tested this system by using old pregraded tests I had in my files. Before the beginning of the semester I tried this system and many other similar schemes and compared them to old way of 25 points per problem with partial credit given for the amount of work completed correctly.  This is the sliding scale that works well for me and my style of giving partial credit for partial completeness.  I would imagine or at least hope my style is very similar to most teachers, but there are some very harsh graders out there that wouldn't like this system. I suspect their harshness might be due to not wanting to devote the time it took to do a good job of grading and even they might like this system.  Using this method I can grade 40 student tests in under an hour, where the old fashion way took 6 to 8 hours.  Very rarely would there be a score in the range from 60-100% that  varied by more than 5% out of a 100. This fast method normally gave the students on the average 2-3% higher grades.  Again grading on the curve takes care of that, you just make the test 2 or 3% harder.  The tests that scored below 60% using the old system quite often would get 30% or 0% using this system.  That is one of the best features of this system, it sends a very strong signal to those students. 

I always offer to grade the test the normal method if the student desires it after the fact.  I try to be very fair when doing that, and I do that with the student watching and explain my decisions on points given or deducted.  Normally the fast method ends up being a couple points higher, but if the old method gives them a better score, that's what goes into the grade book.  I use a letter to replace the first problem score and then follow that with the test score. My computer program system recognizes this as normal percentage score and replaces it automatically.

I also offer a makeup test at the end of the semester to replace a missed or low score test.  It can't replace a retake.  Previously excused absences are handled with an "equivalent" old or modified test taken in the office at a convenient time.   Test differences (slight problem difficulty ratings) don't matter as much with this grading system. 

TRY IT, YOU'LL LIKE IT 

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