Tuesday, March 9, 2010

Translating to a letter grade

I apologize for not posting anything assessment related in awhile even though this is ostensibly an assessment blog. A post by Edumacation snapped me back into things.

As you know, I separate my different standards into topics. At the end of the trimester I usually end up with 4 to 6 topics. These need to be combined into a single grade for our traditional A-F report card. At the end of the trimester I might have scores that look like this:

Motion Graphing Forces Forces in Fluids
2.5 3.0 4.0 2.0

In my ideal world I could leave those as is. Throw some snazzy bullet graphs and charts onto the report card and send it on home.

I use a method called conjunctive scoring that I learned about in a Marzano book. The basic idea behind conjunctive scoring is that good scores can't make up for bad ones. No averages. This is how my scores are currently translated:

Grade Lowest score At least one
A 3.0 4.0
B 2.5 3
C 2.0
D 1.5
F less than 1.5

So in my above example the student's final grade would be C because their lowest score is a 2.0.

Motion Graphing Forces Forces in Fluids
2.5 3.0 2.5 3.0

This student would finish with a B because her lowest score is a 2.5 and she has at least one 3.

Clearly this is very different. There are no averages so it takes awhile for students to get it. You also really need to set aside time to circle back and allow students to go back and learn something they missed. This also requires a certain amount of balance in your topics. Obviously a killer topic can destroy grades. I would argue that some balance in the topics is something to strive for but there are ways to remedy this. The first year I tried SBG, the Motion topic killed kids because of all the math and because I just threw too much stuff into it. I tried to remedy this by separating out Graphing into a separate topic. That worked to chunk it a little more and helped focus my instruction.

I chose this method precisely because high scores wouldn't make up for lower ones. One of the problems with averaging is that you can accumulate enough points that the rest of the course is irrelevant.We've all had students who realize they're so far into A territory that they can coast the last few weeks of school. I've (hopefully) distilled my many, many standards into a few big ideas. In my view, it's ALL important. I like that a student can have all 4s and one 2 and she'll need to work those last few weeks on that one topic.

If the ultimate purpose of grades is to communicate, then an A should be clearly defined. If an A means a student has mastered or surpassed the standards set for the class, it follows that they should master or surpass every single one.

Side bonuses:
We're in our last week of school before the trimester ends and I always notice it's very focusing for a student to take a look at their concept scores, zero in on the lowest, and start working away at it. It's a lot more nebulous to say, "You need 8% more for a C."

There's also this interesting psychological component. If you look at the first example, she only needs to bring up two scores and she can immediately move from a C to an A. Mentally, students feel this is easier to obtain than needing 14% more or 150 more points to move up two grades. I'm sure it goes back to topic scores being more focusing than percentages.

How did I arrive at that scale?
It came through negotiation. My scale was slightly tougher last year. For example, I allowed only one 2.5 for a B. This year, another teacher is trying standards-based grading and we decided on a common scale. I'm reasonably happy with the new scale. There's an interesting passage in the blog I linked to earlier about what an A or B should mean in comparison to meeting standards. Those are the same arguments we had. We thought of it in terms of our state tests. Anyone with an A or B should be advanced or proficient and a C student should have a reasonably good shot.

What about non-academic scores?
I actually don't use them, but I have no problem with them. Again, ideally you'd want to keep those separate. Most schools have a citizenship grade or something similar, if you redefine that you're all set.
If you can't, you'll need to weight them. You would arrive at a score for your academic topics using the conjunctive method. For non-academic scores, the conjunctive method can be used, but in this case I think averaging is the way to go. Going back to the killer topic idea, imagine your non-academic scores are organization, participation, behavior, and work completion. There's really no reason for any of those to kill the entire non-academic score. For your final grade you take your academic score, let's say 90%, and weight it against your 10% non-academic. There are classes that would have much higher non-academic weights (P.E. comes to mind) but for the most part, keep the academic portion high.

The take home is that it's possible to translate your standards-based scores into a traditional letter grade and I'm reasonably happy with the outcome. If translating to a final grade is holding you back, I think conjunctive scoring is a good solution.


  1. Thanks for this. I really like the theory behind this method of grading, although I'm hearing the arguments right now in my head as I arm myself to start this up at my school next year.

    Related to this post though, my school gives actual numerical grades for the individual marking periods. Any thoughts on how scores could get converted in this system?

    I've not ever been a big fan of giving a numerical percentage for an student's grade. It's so arbitrary in a way. As I scientist myself (physics degree) I understand how error propogates in calculations, and in our current grading system, I'm sad to say that grades on any given assignment probably have an error of at least 5 points (must less for me on tests, but that's probably not true of two different teachers giving the same test). That last sentence alone should convert anyone to your way of doing things.

  2. I did just realize that the blog you linked to addresses the very question I asked, but I would still appreciate any thoughts you may have.

  3. The problem is a fundamental mismatch between a percentage grade and a standards-based grade. Any time you need to translate one to another it's going to be an ugly kludge.

    Before you jump in next year you'll want to take a minute to think about how comfortable you'll be with the messiness that you'll be forced to deal with.

    My administration supports me (well, I was kind of in stealth mode at first but once they saw the difference they were in) and are ok with seeing weird things in my gradebook.

    If you're going to go with percentage grades, 1 = 25%, 2 = 50%, 3 = 75% 4 = 100% is NOT ok.

    I'm assuming you'll need to average your scores and can't manually enter in a final percentage score.

    0 should be 50% or something around there. In my mental translation I would argue that a 2 should be around a C because that would be equivalent to approaching standard or in the system I use, they have mastered the simple concepts.

    The problem next comes with a 3. In the system I use, a 3 represents a student who has mastered ALL of the simple and complex concepts that have been taught. This should be an A. A 4, representing going beyond what you've taught can be the 100%.

    So...looking at what I wrote I'd go with:

    A few percentage points either way might tweak it a little better, but using this you'd end up with:
    3,2,3,3 - 85% (B...for me they'd get a C)
    1.5,1.5,2,2 - 67.5% (D, same as my score)
    Not too bad, but like all averages, it gets ugly when the scores deviate a lot.
    1,1,4,4 - 80% (B..for me that's an F)


  4. Nicely articulated, Jason. Looking forward to using this post as a launching point for a discussion we're having as a formative assessment study group in my building.

    Appreciate your writing, man.

  5. I like this approach, but...

    In your comment, you describe a mapping between grade points and percentages that isn't linear, and your overall approach is to combine grades for each topic in a way that isn't additive. Have you considered multiplication? You'd effectively be grading on a log scale. Not only would this make your system more consistent, but it would be a great opportunity to introduce students to logarithmic reasoning.

    In support of this proposal, 2^(x/4-1) is a pretty good fit for that grade → percentage mapping.

  6. @orawnza My overall approach is outlined in the blog post. The comment was just a suggestion if you were forced to use percentages based on administrator demands. It's a compromise and compromises are always a bit ugly.

    Your formula is enjoyably awesome. I think what Stacy needs though is a number (any number really) that she can manually enter into her gradebook at the end of the grading period. I think she's just looking for a kludge to make her admins happy.

    Some SBG software programs use a power law to calculate the final score for each topic. I don't really like the approach but I think admins are comfortable with a math formula.

    I actually never translate between the two. I'm not a fan of percentages. It loses its ability to communicate. What does it mean to be able to find the speed of a moving object 75% of the time?

  7. "What does it mean to be able to find the speed of a moving object 75% of the time?"

    Doesn't it mean the same thing as being able to find the speed of a moving object at a 2.5 or whatever? What does that communicate?

    This post just blew my mind. I've never head of conjunctive grading or thought about doing it that way. I'm in the admin-want-percentages camp and I like the scale you posted, but the variance in your 1, 1, 4, 4, B vs. F bothers me.

    Do you find that there are students who don't care about having 1's and 2's and don't try to reassess? Or do most reassess and try for 3's and 4's?

    I'm thinking there has to be a way around this. Could I say something like, if you have any 1's that you...well crap, I don't know what I could say. I could offer bonus points to those that have no 1's at all. But what do bonus points have to do with anything. Argghh...

    Um, what if I said for every standard that you score 2 or less on, you will see those problems on the semester final in addition to the normal test. The tests would then be modified for each student but they are still being assessed to see what they know? So then scoring 3's and 4's gets you out of those extra problems because you've already proved you know them? I like this idea but tell me if it's terrible.

  8. How about a different approach than using averages? If our purpose is to evaluate where our students are in their educational journey, why not use Medians instead of Averages? If I test on a particular standard and the student does very well on one evaluation (either knew material very well or easy evaluation) and then did poorly (for whatever reason), and then .... If you use average to report student's progress, then it can be skewed by the highs/lows. If our purpose is to determined where they are, the median will report what they achieve on more than one-half their assignments. This has two benefits: 1) allows students to make up / redo evaluations to demonstrate knowledge (something that your system of taking the lowest grade doesn't appear to account for) and 2) allows the student to take a chance on something new and succeed or fail. If they Fail, and here you won't hear too many educators say, it's OK, just don't fail more than half the time. But wait, a student may say...I can work really hard for one-half the quarter and then take the rest off and fail! Possibly, but they have to make sure they know the total amounts of assignments in the quarter before they do this. If they mis-judge and fall on the failing side of the median, then they get the grade they deserve.

    I tried this many years ago, before I was mandated to use average and total points, and the student motivation and behavior in the classroom was tremendous! I used the usual grading 4pt scale (you can use subdivisions for +/-)to report grades. Since it didn't matter to me (or the school) if the student obtained a 90% A or a 99%A, then I just entered a 4 for that assignment/quiz/test into a spreadsheet and calculated the median. But wait, some assignments require more effort/higher thinking skills (tests, research projects) than others (quizzes, graded homework, etc.). I then weighted each grade by assignment. Tests were worth 3 grades, quizzes/lab reports were 2 grades, homework was worth one grade. So for an "A" test, I entered 4's into 3 columns (title of test column covered 3 data columns). Last column calculated the MEDIAN and Viola! Grade determined on a 4 pt scale so it can be reported on the typical school report card. Students loved it! Parents loved it in that it actually measured learning and not penalizing for ONE "bad test score" and they perceived it as more fair (based upon their experience in schools and being graded), and I loved it because I felt it gave a more accurate measure of the students' performance in the classroom.

    After writing this, I think I will bring up this issue again with my new principal, who seems more willing to use more non-traditional grading/technology/classroom management practices. :-)


  9. @Dan The letter grade gets translated from the Topic Scores only. So first trimester we're talking 4 scores. I prefer conjunctive because it requires a certain level of knowledge for each topic. I don't like median in this case bc of what you state. The "I can drop the lowest score" idea.

    Within topic scores, I don't really rely on any specific measure of central tendency for reasons outlined here:

  10. Jason,
    If you did use skills instead of topics so that you might have 20-30 scores to deal with, how do you think you'd handle reporting the final score? Conjunctive scoring doesn't seem plausible anymore. I know this isn't the case, but maybe your thoughts would help others who might be using skills.

  11. @recycledmaterial Yeah, I think problem with conjunctive scoring with skills is the idea that not all skills are created equal. You've got skills that are of varying depth, while topics basically end up equal difficulty (on class average, not for each student)

    I think I left a comment on this at http://mthmanmusings.blogspot.com/

    A good compromise is to require the power skills while making other ones more or less optional. So if you had 20 skills. You might say 12 are required so for a C you've got to get those 12. If you want an A you've got to master the other 8. A B maybe you can choose 4 of the 8. I'm pretty sure Shawn does some variation on this. I like this as a compromise because you're still guaranteeing a certain level of understanding to reach a certain grade. But it also acknowledges that 1. not all skills are equally important 2. the state curriculum is overloaded and I'd prefer you master a few really strongly instead of a lot at a surface level.