Grading System

by rrusczyk, Feb 20, 2009, 7:25 PM

A teacher an AoPS Community member asked me a very interesting question a few days ago -- what grading system do I prefer? He was lamenting the standard 20 question, 5 points per question (and I'll let him comment here if he wants to elaborate -- he had other valid complaints, as well).

I have some complaints about the typical system used in middle and high school, mainly centering on the way it dampens intellectual adventurism by setting the top standard at 95%, and thereby forcing the material to be easy enough that students can regularly hit it. I liked the system I saw in college (and in math contests), where the top tier would be shooting at the 75% range, and these were 'A's', and they were not terribly common.

Outside of these thoughts, I haven't thought much about effective grading schemes, and I'm curious to hear from people about what they think.

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14 Comments

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The grading policy used by most standard high schools is very flawed (at least, here in MD). I can usually manipulate my grades for my benefit without even having to do every assignment. I can even fail certain assignments on purposely and have an easier method of achieving that "A" for the final semester or quarter grade.

(Just as a note, here in MD, each 10% represents a grade letter. So a 90%-100% represents an A, 80-89 is a B, etc. There also might be curves involved if the general students are failing. In my AP Chemistry class, an 85% is the cutoff for an A.)

From what I've seen, alot of math teachers use a points system where the final grade is the number of points you accumulate out of the number of points possible (which should be rather large - like 500, 750, or even in the thousands). Tests/quizzes are usually worth 100 each, classworks and such are worth 50, and homework can range from anywhere from 5-10. The main disadvantage for this system is that the low-valued assignments such as homeworks or even classworks can be disregarded. What this means is that I can miss a homework grade now and then and it can do absolutely nothing to my final grade, given that I ace the high-valued assignments - such as tests and quizzes. The advantage of this system? Assignments that test the students' knowledge (such as tests) are valued much more - and their final grade will reflect their overall understanding of the curriculum, even if they had not completed each and every assignment.

My sixth and eighth grade math teachers used a double-weighted points system, where each section of classwork, homework, and tests occupy a percentage of your final, calculated grade. Usually, my school district has a policy where classwork equates to 50% of your final grade, and teachers may decide how much tests and homeworks are going to be. (Say for the sake of an example, tests are 30% and homeworks are 20%). The double-weighted side comes in when each section (classwork, homework, and tests) is weighted individually. For example, one test could be worth more than the other (100 points, as opposed to 50). And therefore, the average section score was calculated, and multiplied by the percentages, and then summed to give you your final grade. Unfortunately for the student, he/she will have to excel in ALL parts of the class, and maintaining a high average on every assignment. It is exploited however, because you can on purposely fail some assignments (say classworks). This will skew your average classwork grade down, making your overall grade lower. However, because your average classwork grade is low, your future classwork grades need only be marginally higher, and your overall grade will usually go up. Of course, this requires very careful calculations and I never do this (well only in AP chemistry) nor do I recommend students to try this. Always try your best.

by n0vad3m0n, Feb 20, 2009, 9:10 PM

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7h3.D3mon.117 wrote:
The main disadvantage for this system is that the low-valued assignments such as homeworks or even classworks can be disregarded.

I don't consider this a disadvantage.

I believe in some countries, grades are determined solely by performance on the final exam.

by chess64, Feb 20, 2009, 9:32 PM

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Where I live, too, 90% is an A. I think in France, they use a method where 10 points out of 20 are considered passing, 15 or so is doing well, and scores of 19 and 20 are almost never given.

But any grading system allows teachers considerable play. For instance, the honors precalculus teacher at our school (an ARML coach) gives a hard class, by school standards. Many of the students (if not most or almost all) would probably fail if she graded without a curve. But she gives a very generous curve---you can earn up to 112 or so out of 100 on tests and quizzes, the lowest quiz grade is dropped, there are daily questions which are curved, etc. Few people get 90% of the questions right on tests, but many people each semester earn As (90%) and everybody else who makes a good effort earns a B (80%).

All in all, I think that the difficulty of the course is more in the hands of the teacher than the hands of a grading system, because the teachers can always transform their ideas of As, Bs, and Cs to fit the system's.

by Boy Soprano II, Feb 20, 2009, 10:07 PM

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Sadly, I think that grading on a curve (which I'm all for) is actively discouraged in many schools, and even where it isn't, it's hard to get a teacher to switch to that after they've been so thoroughly trained (by their school experience, or even by explicit training) to have clear standards for students to hit for their score. But I do agree with your general point that the difficulty of content is largely (but not entirely) orthogonal to the grading system.

by rrusczyk, Feb 20, 2009, 11:17 PM

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Actually, I think grades are completely useless and unnecessary. They're supposed to be a measure of how much you understand, but how accurate are they?
True, people usually study more and try harder to learn the material before a test than they normally would, but about a month later, most people don't remember a lot, so it doesn't really matter, does it?
If someone really wants to learn, she/he will. Otherwise, there's not much you can do about it in any case.
At my school, grades are just something people fret over, because
(a) If you have poor grades, it won't exactly aid you in getting to college. Even if you're in middle school(since colleges don't look at grades there, to the extent of my limited knowledge), if you've got poor grades chances are you won't get to a magnet school(if your region has one.)
(b) They're concerned about what their parents will say. And of course, parents care about their childrens' grades because low grades usually demonstrate that their child is dumb/not making enough effort.
So(at least my school), people don't really care about what they learn and understand, but rather what they get on their report card or test paper or homework assignment.
Furthermore, I find the whole grade thing quite hypocritical. On the first day of school, when the teachers talk about the class and what will be covered and the textbook and so on, they always get to the grade system and spend about 30 minutes discussing it.
For instance, my science teacher uses the point system that 7h3.d3mon.117 mentioned, and I recall her saying, "The point system is better, because it will make your grade a little higher."
Excuse me if I'm wrong, but I thought grades were supposed to reflect how much you understand. But everything at school seems to be a mad dash to "make your grade a little higher".
Another example is how teachers specially hand out study guides, and there are actually whole classes devoted to test taking skills, test preparation skills, et cetera. What happened to seeing how much you *know*, not how much you can memorize in a certain period of time.
In my science class last year, the tests were quite hard, not because the material was particularly difficult, but because it was based so much on what the textbook says. An example of a question is "Name a few materials and classify them acids or bases." The question was fine, I guess, but the thing was that the only answer that would be accepted was if you wrote down everything that was in this table in the textbook, which I found extremely ridiculous.
After receiving a bunch of complaints, the teacher relented and allowed students to use notes during the tests - but only handwritten ones. My hand still hurts when I think about the countless hours I spent copying out the textbook, sidebars and all.

by isabella2296, Feb 20, 2009, 11:48 PM

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Grades no longer demonstrate the amount of knowledge one accumulates through school. This is clearly evident with the evolution of elite education since the early 16th century, and with public education, the amount of knowledge one knows doesn't even matter. All that matters is getting good grades (through whatever means necessary), getting into a good grad school, and getting that name on the dipoloma. Who cares if you know more math than half the professional body? All that matters is how good of a diploma you can wave at your potential employer's face.

by n0vad3m0n, Feb 21, 2009, 12:11 AM

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The posts so far have been from students. I've taught introductory calculus as a TA, and had final grade responsibility for a summer section.

The scale I used? I announced in advance approximate weightings for different parts of the course, with the tests dominating. I did not announce what the standards would be for converting into final grades; that I chose at the end, when I could see the actual point totals I was working with. If I had chosen standards in advance, the midterm I gave which turned out way too hard would have been a disaster. As it is, I fudged scores on it upwards before incorporating them into the final totals.
I don't think of it as "grading on a curve", and the extreme version of that fails badly in a class of less than 20. My top student wound up at 84%, and I gave an A-equivalent for that (3.8 on a numerical scale). The bottom students were around 50%, and got low passing grades (OK, I gave one failing grade to a student who stopped showing up but never officially dropped).

On test formats: the challenge for a high school teacher is to write something that you can stand grading 150 copies of. While all-or-nothing questions aren't ideal, they do save grading time.

by jmerry, Feb 21, 2009, 12:22 AM

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Um... the purpose of grades is to objectively measure a student's success in a class. Perhaps I'm just terribly unimaginative, but fundamentally, I don't believe there's any other grading system different from just plain-old ___ out of 100.

by leoxnlin, Feb 21, 2009, 3:36 AM

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Quote:
If someone really wants to learn, she/he will. Otherwise, there's not much you can do about it in any case.
Isabella2296 makes a really good point in saying this, a point that I have been thinking about for some time. Why do schools insist on tests and measures and rubrics? All they do is irk the students that really want to learn, and drive students who are not as motivated to learn away from that subject completely.

If the student wants to learn, which is something that a good teacher can always tell, then he/she will. However, there is something you can do about a student who doesn't want to learn. Most of the stuff taught in school really is quite interesting, but schools make it quite unpalatable. Here's how schools drive away unmotivated students from learning:

The school creates this equation in many students' heads: learning = boring rote memorization of test questions (and canned answers) + memorization of everything that the textbook says (or creating a hand copy of the textbook :wink: ). By repeatedly testing students on answers, not concepts, schools can convince students that learning is indeed about the answers, about what goes in the blank, instead about how and why certain concepts hold.

If schools (and state administrators) would only stop caring so much about testing students to see where students are (just ask the teacher, the person who obviously spends the most time with the student at school, about that student!) and start caring about providing open-ended opportunities for motivated students and allow unmotivated students to explore topics and rediscover that learning is in fact not equal to tests, quizzes, and grades.

Speaking of grades, there is an obsession with grades at some schools in my area. One of my friends reported that there was a mutual understanding between the teacher and the students that grades were more important than learning, and that, at the end of the day, grades were all that matters. I'm not saying that's false, I'm just pointing out that that shouldn't be.

My school, for instance, would never dare let me study AoPS books or take an AoPS class as an official course because that's not the norm. They cannot ensure that their version of math learning, that is, memorization of "negative b plus or minus the square root of b squared minus four a c all over two a" etc. is being emphasized. (thankfully, it's not) After all, it is clearly harder for schools to test students on understanding than on memorization. But schools testing for memorization aren't testing for learning.

To summarize, this problem all boils down to credentials. Students want good grades to impress employers, schools want high (and overly rigorous and precise) standards to impress boards of education, boards want schools that score high on standardized tests to impress the government, and so on. What happened to learning?

Edit: P.S. I'm not saying that all schools do this, I'm just saying that all too many do.

by ThinkFlow, Feb 21, 2009, 4:21 PM

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Most of what I would say has already been said, so I'll just make comments.

Among my teachers attitudes towards grading, I must prefer my physics teachers'. He never assigns problems for a grade, nor does he give quizzes. Our only grades are tests and lab work (which is our only hw). He emphasizes understanding and retention from the beginning. He never gives a study guide for tests (which is a stupid tradition, teaching and learning for a test won't promote actual learning) and never teaches to it. We take each test a second time, but work in groups and with resources (groups by first time score, so that every group is at around the same level of understanding) - thus, there becomes an incentive and opportunity to learn the material even if we do badly the first time. That's addresses one problem I see in schools in regards to testing, once a test is over, there is no point gradewise to retain the material, or even learn the material once the grade is set. The only time he ever bumped a test grade was the first test we took. And it's one of the only classes I actually enjoy, because we actually learn things in it.

My school also has a policy where every class must give a final exam at semester's end, which is absurd considering classes like PE and most art classes.

Another thing that is absurd is how a lot of many friends can get worked up about how they scored "a 97% while X scored only 95%", and yet, hypocritically, I'll do the same on occasion. Or about class rank and number of AP classes and standardized test scores.

by pianoforte, Feb 22, 2009, 7:34 AM

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I agree with pianoforte. My AP Biology teacher used that grading system, where tests and labs only made up your grade. That class for me, wasn't about grades anymore - it was actually about understanding and acing the AP final at the end. Although I got a B for the year, I really didn't have any regrets. That type of grading system really does focus on what a student knows about the material. So that B was a result of my slacking off, and not because of assignments that were weighted.

by n0vad3m0n, Feb 22, 2009, 3:49 PM

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I agree that curves should be used in the classroom, however I also agree that schools and teachers are steering clear from using them. My biggest problem with grading is the fact that final exams are worth such a high percentage. Whether cumulative or not, if the student performs poorly on the final but does well on the other course tests, its not fair that they should suffer by receiving a bad grade because of one test. They obviously performed well throughout the entire semester and should be rewarded for doing so.

by jwdapkev, Feb 23, 2009, 4:27 PM

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I also think that there is way too little teacher involvement in the learning and grade process in many classes. Since the teacher is the one who spends the most time with that student and is also the one who really knows how a student is doing based on class responses and homework. Given this, why are many teachers so removed from the grading process?

At my school, all teachers use a grading program. Here's how it works: The teacher enters in the possible score (an arbitrary point value to facilitate weighting) in the program, then enter each student's score. The system then quickly calculates a simple percentage based on those values and assigns a student an A, B, C, D, or U based on a linear scale. 90 and above is an A, 80 and above is a B, etc. As a result, a teacher has no control over a student's grades; everything is handled by machine.

Another example of cutting teachers out of the student evaluation process is standardized testing. It seems almost as if state administrators feel that teachers are untrustworthy. If teachers are certified (which is the job of the certification process), they should be able to confidently tell state administrators which students are exceptional, which are average, and which are behind. Instead, states and school districts place an unwarranted emphasis on one-shot high-stake standardized testing that drives fear into students' hearts. Which is a better use of the students' time, the teachers' time, and taxpayer money: a two-hour interview with the teacher regarding student progress and targeted allocation of additional resources or a week's worth of boring, mind-numbing testing that messes up teachers' plans, stresses students, and costs a lot to administer?

Are teachers being cut out from grading? I'd like to hear others' opinions as well.

by ThinkFlow, Feb 23, 2009, 9:58 PM

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FOUND THIS HERE : http://news.yahoo.com/s/csm/20090210/ts_csm/agradeless

This is very similar to ALCUMUS!


By Amanda Paulson
Westminster, Colo. – School districts across the US are trying to improve student performance and low test scores. But few have taken as radical an approach as Adams 50.
For starters, when the elementary and middle-school students come back next fall, there won't be any grade levels – or traditional grades, for that matter. And those are only the most visible changes in a district that, striving to reverse dismal test scores and a soaring dropout rate, is opting for a wholesale reinvention of itself, rather than the incremental reforms usually favored by administrators.
The 10,000-student district in the metropolitan Denver area is at the forefront of a new "standards-based" educational approach that has achieved success in individual schools and in some small districts in Alaska, but has yet to be put to the test on such a large scale in an urban district.
"There was a sense of urgency to attend to what wasn't happening for kids here," says Roberta Selleck, district superintendent, explaining why she decided to go with a drastic approach. "When you see the stats for the whole school district over time, we realized we are disconnecting [from] our kids."
The change that's getting by far the most attention is the decision to do away with traditional grade levels – for kids younger than eighth grade, this first year, though the district plans to phase in the reform through high school a year at a time. Ultimately, there will be 10 multiage levels, rather than 12 grades, and students might be in different levels depending on the subject. They'll move up only as they demonstrate mastery of the material.
But Dr. Selleck and others are quick to emphasize that that's only one piece of a radically different, more student-centered, approach to learning – and that it's not the same as tracking, the currently out-of-favor system of grouping students by ability.
Students help craft own lesson plans
The district is training teachers to involve students in the lesson plan in a far greater way than before – the students articulate their goals and develop things such as a code of conduct as a classroom. And when children fall short of understanding the material, they keep working at it. The only "acceptable" score to move on to the next lesson is the equivalent of a "B" in normal grading – hopefully showing proficiency and giving kids a better foundation as they move on to more advanced concepts. Advocates sometimes describe it as flipping the traditional system around so that time, rather than mastery of material, is the variable.
While the idea of "standards-based education," as it's often known, has been around for a while, the only public district where it's been tried for any length of time is in Alaska, where the Chugach district – whose 250 students are scattered over 22,000 square miles – went from the lowest performing district in the state to Alaska's highest-performing quartile in five years in the 1990s, a shift the former superintendent, Richard DeLorenzo, attributes to the new philosophy.
"We saw how radical a reinvention needs to happen," says Mr. DeLorenzo, who is serving as a consultant to Adams 50 and is now the founder of the Re-Inventing Schools Coalition, which is seeking to spread the model.
In Adams 50, the challenges aren't quite so severe as they were in Chugach, which had only had one college graduate come out of its schools in the 20 years before DeLorenzo implemented the reforms. But the district, which has a 58 percent graduation rate, has been on an academic watch list for several years now, and has seen a drastically shifting student population in which percentages of minorities, non-English speakers, and low-income kids have shot up.
Selleck decided the district needed a massive transformation, and got the OK from the state. This year, the district is beginning to phase in the changes before all the schools switch to the new, gradeless system next year. One elementary school is serving as a pilot program, and many of the 300 or so teachers who have undergone training from DeLorenzo are implementing a modified approach in their classrooms – albeit still in traditional grade levels.
In Nikolaus Namba's first-grade classroom, that means that his students have worked over the year to create – and refine – a classroom code of conduct (which includes items such as "don't hit people" and "we will not play with hair" written in childish handwriting on Post-it notes mounted in the front of the class) and goals of the week. Students use what Mr. Namba calls "power voting" with the Post-its to get a voice in these and other classroom decisions – hoping, ultimately, to give them a greater sense of independence and ownership of their learning.
Namba says it's been somewhat tough to implement the new approach halfway – still in a traditional first-grade classroom with all ability levels and learning speeds mixed in – but he says that even a few months into the year, he's come to appreciate it.
"We have discussions about what is a good student, and what does a good teacher look like," he says, noting that it's easier now to talk to students about work that comes up short, for instance, of where they thought they were, and says that everyone is aware of each specific thing they need to learn.
On one recent day, that included a quiz on telling time. Namba has the student who received the only perfect score help some of the others. "Cristian knows how to tell time," he says. "He's available to help others."
Next year, Namba hopes to really dive into the reforms, and is looking forward to being able to work with students all at a similar level. "The goal is that they'll accomplish things faster," he says. Moving up without truly understanding what they learn "is what creates the cracks in the foundation later on."
But if Namba and other teachers who have bought into the idea in a big way have high hopes for the future, there are also significant complications.
Scheduling is a big one. It's also unclear what will happen if large numbers of kids arrive in high school still unable to demonstrate proficiency in certain subjects, like math, and a bottleneck gets created. Since no student can move forward without a "B" equivalent, it's also essentially impossible for students to have lower than a 3.0 GPA, which could be a challenge to explain to colleges.
'Video-game' approach to grade levels
Still, Selleck says most parents she talks to are enthusiastic, and the district is doing an enormous amount of outreach and education to explain the changes to them. (She often uses a video game analogy: Students are engaged, take as much or as little time as they need to at each level, and can't move on to the next level until they've mastered the one before it).
Arisbeth, an articulate fifth-grader at F.M. Day school whose teacher is already incorporating some of the reforms, says she's looking forward to the changes. "You'll be working with other kids where you're working on the same thing," she explains. Already, she adds, "Our voices are being heard more."

by paulancka, Mar 3, 2009, 4:44 AM

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