A Percent by Any Other Name

I don’t like assigning grades. I tell my students that I don’t “give” them grades, but that they “earn” them. However it is still one of my least favorite parts of being a teacher. I don’t mind assessing their work as it lets me know what they understand and what they (yet) don’t.

Yet I wonder, how do I effectively communicate all that a student has (or has not) learned by a percent? By a letter? Is there really a difference between the students who ends up with a 79.2% and the student who has a 80.2%? Lately I’ve been wondering if my grading is too harsh, then the next moment wondering if it is too forgiving.

From what I’ve been reading, it appears I’m not alone with these thoughts. Jen is wondering if her grading is too lenient. Pissed off Teacher was told not to give partial credit (and then was given a different message ). I think this tweet from Kelly sums up my thoughts pretty well.

As I prepare to grade my seniors’ test on quadratics, these issues are weighing heavily. I want them to be able to correctly solve the problem. I also don’t want to penalize those that make a silly arithmetic mistake. Yet, how much partial credit is deserved? Does a student who makes “silly” mistake after mistake on every question “deserve” to pass? What if they have been coming in for help consistently and still just don’t get it, do they deserve to fail?

Well, the exams are graded. Some of the cherubs rocked. Some made strange mistakes. Most fell somewhere in the middle (which shouldn’t surprise me, but somehow, it does – every time).

The average for both classes was 75.5, the median was 83.6. I really don’t know how to interpret this. Does this mean the majority of them are getting it? That my grading is too easy? That too many aren’t getting it? What scores would make me happy? I just don’t know.

The first box-and-whisker plot below shows the combined averages of both classes. The second is for my 4th period section, the third my 8th period.


One thing I do know, I’ve gotta figure out what is going on in 8th period. I really don’t think having math the last period of the day is the best idea for a lot of these kids. I just really don’t know what else to do about it.

In the long run, I’m still wondering what this all really means. What is/are the purpose(s) of grades? To report achievement? To reward? To punish? To guide instruction?

Nope, I don’t like this part of teaching at all.

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11 Responses to A Percent by Any Other Name

  1. kwhobbes says:

    The purpose of assessment should be to assist teachers and students to see what work needs to be done. Ultimately, it is used to reward and punish. As for reporting achievement, we can do that in so many other ways other than grades. I’m really questioning our whole system. Should we not be starting at with a positive instead of a negative. For example, instead of starting at 0 and working up, students should be assumed to know the concept that you taught – 100. For each error, you move away from 100. Simple mistakes, for example in math a simple mistake in adding should not be counted against the student since it is not part of the concept that is being studied. Students have already passed addition. You focus on the concept and whether a student understands and can apply their knowledge.
    If, as teachers, we are as good as we say, then all of our students should have learned 100 % of what we have presented. If someone is missing something, then it is up to us to figure out what part of the 100% we did not get them to learn. Ultimately, our job is to get 100% of the students to know and understand 100 % of what we teach. I’m not sure why we constantly work from a deficit model. I hear too many times teachers who “brag” about how many students don’t make their classes. Sad, very sad.
    The purpose of grades is mostly up for debate. We want to report what students know and what we, as teachers, need to improve in our teaching in order to improve student success. Too often, it’s a threat to try to get students to “toe the line” and comply with teacher demands. Because of our deficit model of marking, there are many students who are unsuccessful in our system.
    An even greater question is “What is the purpose of school?” That might help us determine why we have grades.

  2. Robert says:

    The purpose of grades is to compare student understanding of a concept against professionally-constructed standards. They are not intended to reward, punish, evoke emotional responses, pass judgment on the worth of the person being graded, or any such thing. Grades are information; they let the student know where they stand in relation to an objective standard; and how the student and teacher use that information is something outside the purview of grades as such.

    And so it’s very important that teachers build up their whole assessment scheme in a class so that the grade really reflects a well-rounded view of what constitutes quality work in whatever context they are in. It sometimes takes years to hone such a scheme to accuracy. In the meanwhile we’ll always err on the side of too much leniency or not enough, or not assessing everything in the right balance. That’s why we should strive for objectivity but not be afraid to fudge things every so often.

    “What if they have been coming in for help consistently and still just don’t get it, do they deserve to fail?”

    I think the word “deserve” here is unnecessarily emotional and personal. The point here is not what the student “deserves”. The point is whether the student’s work measures up to your standards. If it doesn’t, consistently, then the student gets a failing grade. If it does, the student passes. We are not grading on effort or desire; we are dispassionately looking at the student’s work and judging it for what it is. The moment we or the student make it personal, things go downhill.

    Call all that a gross oversimplification of grades if you like, but I’ve found once I explain to students what this grading thing is all about, the less they feel like it’s me vs. them and more like I’m helping them get ready to better themselves in a very difficult and competitive world.

    This doesn’t change the fact that I dislike grades and loathe grading.

  3. Ben Chun says:

    Yeah, what Robert said! The only thing I want to add is that different grades mean different things, and that can be tricky too. There’s a mark on a paper, a score on a test, a 6-week progress report, a quarter report card, and a semester grade. The one that ends up on their transcript has a lot of power in the long term. The ones that we give day to day can have a lot of power in the short term. I think the only way to get comfortable with the final mark is to be confident that it reflects what the student has demonstrated they can do, and that you’ve done everything you can to help and motivate them toward that goal. The more I think about this, the more I think Dan Meyer has it figured out. You’ve read his “How Math Must Assess” essay, right?

  4. H. says:

    Amen, Jackie. Sometimes I wish there just were some great external exam, so that it was more clear to the students that it was us together against the big test.

    And as far as Dan’s system goes, I’m using a modified version of it, and it amounts to only 35 or 40% of the students’ grade (I reintroduced cumulative tests into the equation instead of letting these concept-wise assessments count 70% because my Department Head suggested that would be better). This part of the grade is the one part that I feel okay about – this grade component does say something meaningful about where the students are, and the data from these assessments are very useful for planning purposes, too. And since the student has so many opportunities to repeat the test and improve, a low grade is useful feedback, not a crushing verdict of what the student “deserves”.

    As for Robert’s entry – if the situation permits, that’s great. There are cases where you take over a class that is so far behind, that grading them on mastery of relevant standards will certainly cause more than three fourths of the class to sink as a stone. Students who are consistently failing before the end of the first quarter tend to just stop working. It is possible to use the rhetoric of “high expectations” to send a class into complete defeatism and defensiveness – if they have not been held to similar standards before you have to find a way to make effort and coming for help pay off in order for the students to learn anything at all.

  5. Robert says:

    H., I agree. Context is important here. Still, though, if I am teaching a college-level calculus class and I get a bunch of students who are miserably unprepared for it, then I’m going to go way out of my way to help them get caught up — but if I do all that I can and still 3/4 of them are failing, then 3/4 of them fail.

    The crucial thing is what teachers and profs do to bridge the gap between appropriately high standards and student preparation which may not be up to par. (And I should mention that I teach college, and this often looks much differently here than it does in K-12.)

  6. Jackie says:

    Kwhobbes – as to “What is the purpose of school?” if that were clearly defined (and of course, agreed upon) grading would be much easier. Can ya work on that? 🙂

    As for the “simple” error not being counted against them – part of me agrees, and part of me doesn’t. If a student makes an arithmetic error which leads to a result which isn’t logical in the context of the problem, said result should clue the student that he/she made a mistake. Not catching the mistake, tells me that the student doesn’t understand the concept and/or that the student isn’t thinking about what they’re doing.

    Yet, I generally don’t work from a deficit model – a simple mistake early in the process doesn’t mean that a student receives zero credit for the problem. It is the series of mistakes in one problem that causes concern.

    100% is always my goal – which is why I’m always dismayed when it isn’t met.

    Robert – I agree “deserve” was an emotionally loaded word (it was one of those long-dark-teatime-of-the-soul weekends). However, some of the messages I receive imply that effort should be considered and that students should be graded based upon the amount of improvement that is made. If I failed 3/4 of my class, I’m not sure what would happen (actually, I have to report the number of D/F grades on a weekly basis. I now have to attend a meeting with admin. due to the numbers I reported 1st quarter, so I’m pretty sure what the response would be). Yet, I’m also given the message to make sure I’m preparing them for standardized testing and post-secondary work. This has left me a tad bit confused.

    Ben & H – Of course I’ve read Dan’s works on grading. However, as a first year teacher, I didn’t feel I could totally change the system walking in the door, so I took the advice given to me (for the most part). However, I told my classes today that we’d be having more frequent “quick quizzes” to check various concepts. By the way, I do offer my students the opportunity to retake tests/quizzes – if they meet with me to go over the concepts first. Some are taking me up on this, some aren’t.

    Thanks for all of the feedback.

  7. mathmom says:

    As far as I’m concerned, an A in a math course goes beyond “getting the concept” to executing it accurately at least most of the time. Part of it is what Jackie says about many “careless” errors being detectable in the nonsensical answers they cause, but even when they don’t, there is more to math than just “getting it” — IMO you also have to be able to “do it”. I would give partial credit to a correct approach with careless errors in it, but not full credit.

    I would like to imagine that grades are a dispassionate measure of a student’s mastery of the subject. Effort that does not result in improvement would not be “rewarded”.

    And yet I don’t think this is what most grades really do mean. Part of the grade may be assigned for class participation, which may be somewhat orthogonal to comprehension and mastery. Sometimes grades are given for organization of binders (!) again IMO somewhat orthogonal.

    Ideally the “reward” for effort would be improvement. I don’t think you can pass a student who tries but just never gets it. What does that do for them when they try to take a follow-up class? I guess the question is different for a student for whom this may well be their last math course ever, but still, a passing grade is supposed to indicate, IMO, a certain mastery of the subject.

  8. Jackie says:

    I agree that a passing grade is supposed to indicate a certain level of mastery. Considering that was does a grade of a “D” really mean? I have quite a few students who have earned a “D” in every math course they’ve taken. Not surprisingly, their foundations are, erh, shaky.

    Today most of my seniors were shocked that I expected them to know that 4x^2 + 5y^2=10 was an ellipse. They thought it was unrealistic that I expected them to remember the conic sections from Algebra II.

  9. mathmom says:

    That is a good question about what a “D” really means. What does a “C” mean — average — but what does “average” mean in a mastery-based subject like mathematics?

    I tend to think qualitatively about what the grades mean (i.e. “A” means you get it, all of it, and rarely make errors in carrying it out), but of course the grades are quantitative. When tested, the student got a certain percentage of the questions right. (Or, rather, a percentage of the points available, since there are points for more than just final answers.)

    So… do you have to “get it” to get 65% of the points overall in the course? I’d have like to think that if you can get a 65% average, you did have to “get” most of the concepts and have some idea how to use them.

    Does it mean you’ll remember over the summer and be able to apply it in your next math class? Probably not.

    I think, depending how long it’s been since AlgII for those seniors, and how much play conic sections get in Algebra II, it may well be unrealistic for you to expect them to remember without any review…

  10. Jackie says:

    Yeah, I kinda realized that a review is needed. I really thought they’d recognize it as a conic section though. Apparently I was wrong – it has been an interesting process for me (learning what they’ve really learned).

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