Guiding Principles For Assessment

I’m back off a five-day trip attending my fiancée’s graduation in Los Angeles. I’m back, wishing I had more May, and wondering what you do here:

A student wanders dazed into your class on [x, where x is some second semester date] with a failing grade, wondering if passing is even possible.

Under typical assessment – comprehensive, tight-fisted, chapter-based stuff – if [x] is anything later than Cinco de Mayo, the student is screwed. And so are you. Because if you tell that student no, sorry, friend, we’ll see you next year, that kid has no other purpose in your class except self-amusement, which will almost certainly conflict with your purpose. Enjoy the seventh circle of classroom management hell.

I don’t know how to fully control for synthesis. I don’t know how to fully control for rote memorization. I don’t know how to fully integrate this into the humanities.

But if my career spun a wacky, cinematic 180° and I found myself teaching (eg.) English comp, I’d build my assessment strategy around three unshakable convictions, convictions which conventional assessment fails at most turns, convictions which aren’t exclusive to mathematics.

  1. It doesn’t matter when you learn it, so long as you learn it. A student’s grade should reflect her current understanding of the course, not last month’s, not her understanding when it was convenient for me to assess her. Keep a loose grip on your students’ grades.
  2. My assessment policy needs to direct my remediation of your skills. My comprehensive test on “Twelfth Night” won’t do much for us two months down the road when you come in looking to patch yourself up. Assign separate scores to “Twelfth Night Themes,” “Twelfth Night Vocabulary,” and “Twelfth Night [whatever else it is you English teachers do],” scores which can be targeted and remediated individually.
  3. My assessment policy needs to incentivize your own remediation. How many students will put in the effort to remediate their skills if the reward isn’t tangible and immediate? Traditionally, what do you have? The promise that your studying here at lunch is really gonna pay off on the next test? Which is in three weeks. The student’s like, awesome, glad I came in.

That’s everything.

I can’t fully answer the question “how does this work in [x, where x is some course which isn’t math]?” but I promise you that if I was drafted into the service of [x], I’d fight with as much creativity as I could muster to keep those principles intact.

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. While I can’t help but notice the subject you opted to consider in this wild premise of yours (“English composition” — silly business that!), there is something in your post that really hits home for me in just the last few days as the transition from teaching year to summer break has kicked off.


    I hate grade books. I hate the #’s that supposedly determine better than my own observations whether a kid has learned and lived up to my expectations or not. And I hate that a short-hand letter grade at semester’s/year’s end will say
    something that often has little bearing one what I really know about this kid.

    That being said, I do wear big-boy pants when I go to school every day, and I’ve made some peace with the reality that teachers must hit send on their grade calculations at key points throughout the year.

    I’m also fortunate enough to work in a school that gets it on a larger level, a level geared towards teachers being given the opportunity to apply their professional discretion at the last minute when it comes to turning grades into the school’s senior grading system at year’s end.

    One of the final bits-o-advice our school’s leadership team gave we teacher types 2 weeks ago as we prepared to administer our comprehensive semester exams and to finalize the students GPA was:

    “Always know you can over-ride what the computer’s grade calculation is. Truly evaluate the student’s overall growth and knowledge; do not just hit ‘send’ on the computer’s grading score because that’s what the assignment grades technically added up to.

    Do what is right..”

    The unspoken caveat at my school is that we always have the opportunity to raise the grade tally if we truly believe the kid has learned beyond what a missed quiz penalty might imply weeks earlier, et al, but we should be hyper-hesitant to drop a grade at the last minute if we hadn’t already dealt with that issue earlier in the year F2F when the kid could have done something about it in real time.

    This opportunity hit home for me with one young woman (who hit that 1,000 foot reality cliff you hint at above) just 3 days before the year’s grades were to be locked down forever, in a way that will remain a steady memory and professional signpost for me as long as I teach.


    The final biggie assignment of the year was the annotated bibliography research paper on Othello. In short, the kids had to spend 4+ weeks ‘living’ with various literary critics, throwing their own 2cents in on one of the great English plays of all time, finally wrapping it up in an extensive document of analytical observations and personal reactions.

    This is not — in other words — one of those assignments you can afford to get less than a “C” on, let alone not doif you want to pass this course. At a college-prep independent school like mine, this is akin to chopping off a limb at the student-view, not some esoteric teachery thing.

    The “this is huge!” and “anything later than 3 days past the due date is going to be a zero, a zero that cannot be recovered in most situations” messages were repeated over and over again, almost as often as the “you’re going to really crush this assignment once you tell Coleridge a thing or two about his feelings on Iago, so don’t be gentle with the old Romantic poet just because he’s published a few things along the way” chant I echoed over and over.

    Well, life happens. Kids are kids. And stress does funky things to kids and life.

    On turn-back-the-assignment day, I suddenly realized that there was no graded paper for this student. Wondering why it took me this long to figure that out is to be saved for another day, but I was left with major Q’s running through my head that were leaning towards something less than desirable:

    Had I lost it? Left it at Starbucks during a weekend grading frenzy? My own dogs eaten it in an ironic twist?

    Or…[gulp]…had one of my kiddos NOT turned in this epic-mother-of-a-paper in spite of all of the crazy warnings and obvious atomic bomb on the grade book consequences they knew about?

    While running up a set of stairs that morning when I saw this student, I asked her:

    “Hey, can you fire me off a copy of your paper by email tonight? I must have misplaced it and know you did it since you did so well on the rough draft, so if you can get me that copy tonight, I’ll grade it and hand it back tomorrow.”

    No problemo was her response. For 4 straight days, no problemo was her answer along with a myriad of odd details to explain why it would be in the ‘next’ day instead.

    On the final Friday before grades were to be submitted to my admin team, I called her mother since it had still not been turned in no matter how many friendly nudges I gave the girl over a 4 day period. Said something to the mother along the lines of:

    “Wondering if you and I can team up to help her get this into me so she will get a grade that approximates her efforts even though we seem to have a ‘strange’ set of circumstances’ happening here, circumstances that could make a teacher wonder if the paper was actually written at all…which is strange because she received an ‘A’ on her formal rough draft that was turned in 2 weeks prior.”

    Mom said, no problemo.

    Fast forward 3 hours.


    Student (and her mom) knock on the faculty lounge door, asking to see me. Tears on student’s face. Mother steps back 2 feet, a bit delicate and angry all at once. Add embarrassment, too.


    Tears. Tears. Tears. Lip shaking. “Mr. Long, I lied to you. The paper was never done.”


    “I know. I actually knew several days ago. I just wanted to see if I was patient enough if you’d come tell me the truth. Today was that day. Guess we have a foundation to start working from now that we have the truth on the table, especially with your mom standing right behind you…”


    “I never turned it in. I don’t know why I didn’t do that, because it was almost finished and I loved the play and I’ve really grown as a writer this year and you gave us so much time to do this…but I froze or something. And I hate that I lied to you.”


    “OK, we have a challenge in front of us, don’t we? But its a challenge we can pull off, or better yet…you can pull off.

    Grade or no grade — because I am not sure at this moment, to be honest, what I do about an assignment of this magnitude being 2 weeks late, well past the zero/incomplete line that was an option at day 3 — I do know that the only way for you to pass this class and get full credit for the semester is to get it done in the next 2.5 days before I hit send on my grades.

    And grade or no grade, this is bigger than that. This is one of those life moments — with your mom and I watching — where you’re gonna have to dig deep and find out what you’re made of as a person, a moment where you’re going to learn a lot about your inner character and willingness to get over the embarrassment of owning up to something really tough like this and just remind yourself that your brain and imagination are capable of amazing things even when you’re up against the wall and feel like it might not be worth doing.

    And ultimately, this isn’t about the grade or your mom/I watching; this is about you, you looking in the mirror in a few days, you turning in this assignment because it was worth reading, because you have the brain and imagination to convince a reader to care about your opinions, because one way or another you’re gonna dig deep and find a completed paper in you…and you’re going to complete it at a level you’re proud of — grade or no grade — and for once this year, you’re not going to have one single thing hanging over your head. The desk will be cleared off. And you’re going to know what you’re really capable of doing.

    Me, I’ll figure out the grading side of things. That’s my responsibility.

    You, however, are the writer. And at this moment, that’s all that matters. I look forward to being your paper’s audience on Monday when you hand it to me. Truly do.

    Fast forward 3 days.

    The paper, completed in all ways I needed it to be written, came to me. Done. 100% done. A ‘B+’ level, one of her strongest pieces of writing the entire year, actually.


    As for your post, Dan, you’re spot on with what you said:

    “A student’s grade should reflect her current understanding of the course, not last month’s, not her understanding when it was convenient for me to assess her.”

    100% agree with you.

    Even if hate tallying grades and what they often say, there are times where the only thing we can morally do as teaching professionals is over-ride the computer and give our kids one fighting shot to live up to their greatest potential, even if the clock is ticking down and if it challenges us to re-write out entire grading process on the fly.

    Thanks for the chance to chew on this a bit this morning. The kid was worth it. Period.

  2. Dan, as a future administrator, how can we get other teachers on board with this thinking? These three principles alone cause students to take ownership of their own learning, instead of thinking themselves as victims of rigid and inflexible expectations. To me, that is what the heart and soul of education is all about. Digested at the students’ pace, rather than force fed.

  3. I’m always torn on this issue. I completely understand the English example and I think it makes sense. Although it does bring to mind the question of “when do we teach kids deadlines?” The IRS will not be very forgiving if you don’t come to an understanding of your taxes by April 15th (or at least file for an extension).

    Also I don’t think the example holds very well with math. If a student doesn’t learn right triangles by the deadline I create in class for the test, they will have lots of trouble with the following chapter because it builds on their knowledge of right triangles. For courses like math and science where the content is constantly building on previous material won’t the student get behind a very large snowball of things they don’t understand?

  4. Dan, I buy the three principles totally. They are brilliantly simple and appropriate, pushing all the right incentives to boot. I’m struggling with how to take this to the next level…

    If your assessment is totally flexible then it drives a lesson delivery method too (IMO). What I would like to do is devise a delivery system that can: a) deliver at an appropriate pace to get through the material b) provide individualized curriculum c)allow fast kids to go faster d)allow slow kids to go slower.

    I’m in the draft stages of something that looks like this:

    Monday – skills day; catch up on prerequisite skills
    Tuesday – new concept intro for the week; about the ‘whys’
    Wednesday – draft day; practice the concept
    Thursday – final rewrite; practice moves to formal solution output of word problems
    Friday – measurement; (your) concept quiz of the week.

    I want a structure that allows plenty of time for ‘equalization’ where kids can seek their own level and find, in the process, appropriate materials to grab and run with.

    What does your week look like?

  5. jg – Say for whatever reason, a student is really, really trying and just can’t grasp which side of a right triangle is “opposite” and which is “adjacent”. Of course they are going to struggle in the next section/with the next idea. Lets say it is “applications of right triangle trig” then “law of sines”. The kid is still struggling, they just can’t see it. Then in the midst of the “law of sines” unit, the student gets it. They can now do each of these types of problems. It may be a few weeks later than the rest of the class, but they get it. Isn’t that the end goal?

  6. Interesting article Dan. I teach at a school where a large percentage of the students are less than motivated. I see this working well to some point with them.

    My question is this, and it kind of goes along the lines of what jg said above. I believe most students are procrastinators (God knows I was). If they know that it’s what they know at the end of the year that really matters, then what motivation is there for the student to work consistently throughout the year??

    Test time for me is the time where most of my students say “gosh, I better buckle down and make sure I know this stuff.” Do your kids still say that to themselves using your assessment method?? or do they say “gosh, I don’t have time to study this stuff now, but luckily it doesn’t matter since I can just do it later without it hurting me.”

    Do you see my point? What I’d be worried with is a bit of a slippery slope where they continue to push off actually learning the material until it comes to a point where they can’t survive in the current material because they haven’t learned the past material. I’m sure that perhaps you might run into this sort of issue, what do you do to fix it?

  7. @Christian, I think we’re talking about different things. It seems you’re referencing every teacher’s mandate to avoid a hardline stance w/r/t grading and take a more fluid view of a student’s understanding.

    What I’ve tried to do is take the subjectivity out of that kind of judgment call. A student who wants to achieve advanced understanding and a higher grade can but not because, subjectively, I’ve made an exception. The exception is the rule, in this case.

    @Rick, tough hypothetical. I don’t know how administrators get anybody to do anything. I reckon it’d start as a new-school-year resolution (like “we’re gonna beat back tardies this year”), presented to the department heads and the site council to get them on board and then, with their endorsement, to the staff.

    @JG, @Anthony, @Anybody Else Concerned That Students Will Slack If They Can Retake Concepts At The End Of The Year, they don’t. There are intrinsic and extrinsic motivators that won’t let them.

    Intrinsically, no one wants to feel dumb. If you lay down a straight, clear path to knowledge, nine students out of ten will take it, especially if their peers are already halfway down the trail.

    Extrinsically, if a student doesn’t know a concept, I fill in a 0 in the gradebook for that skill, a 0 which I’ll happily and quickly update later, but which sinks their grade and promotes student initiative.

    And Jackie has the ethic down exactly. I’m not here to prepare them to punch the clock ten years from now. I’m here to see them achieve, at whichever point in the semester that may be.

    @Paul B, basically I suck at the differentiated, in-class remediation aspect of this plan. I can get anyone to come come in for five minutes at lunch or after school but I haven’t built this into my day-to-day well at all.

  8. Dan, I’m not talking taking this concept over by force, I’m just asking how do we sell it to the masses and get the majority won over? There are always the foot draggers and the nay sayers out there, so let’s forget about them for now. I have to believe there is a contingent of math teachers out there who are willing to look at this from another angle. It’s that population I can see you reaching with all of this.

  9. Rick, as a future administrator, how do you sell any concept to the full faculty? As an elementary principal, I encounter the same foot-dragging with almost all new ideas. It’s one thing to be able to peer model this belief as a classroom colleague. Your skill at identifying the formal and informal leaders in your building and bringing them on-board before trying to move the nay-sayers is a slightly different, but ultimately related, skill just like motivating the struggling learner in your classroom. The motivations may be different, but I am finding myself using Dan’s philosophy with my staff just as I would when I was a high school English teacher. Now just don’t ask how I go from high school English to elementary principal. :)

  10. TheInfamousJ

    June 7, 2008 - 8:20 pm -

    “For courses like math and science where the content is constantly building on previous material won’t the student get behind a very large snowball of things they don’t understand?”

    This is my concern. I have over 52 skills to teach my students in a semester of 90 minute periods. This sets an artificial and rigorous schedule, assuming that each skill (most of which build in some way on another) take equal time to teach. Which is not true.

    If it takes you a lot of time to figure out how to balance equations, so that the transition to moles, molarity, stoichiometry, gas laws, etc. takes less time then so much more the better.

    If balancing equations is the start of what I like to call “the great slow down” where it takes one day to learn to write an unbalanced equation, two days to learn to balance, three days to learn about moles, four to learn stoichoimetry, you are already six days behind schedule.

    And after all, each topic is harder. That’s why we call it scaffolding.

    What I do as a stop-gap measure is to send home a letter informing a parent that a critical skill has not been mastered to the level that it can be built on, along with additional practice work, and offering my services as a private tutor. Not that I can say anything positive about the results. I had one student catch back up and finish off the year strong. Most did test corrections. None took me up on the tutoring offer, though a few got their own private tutors, during the last week of class.

  11. InfamousJ:

    Good points. Here’s how I wrap my head around this…

    Kids are making snowballs anyway in a traditional setting. The difference is that in the traditional setting there is no way to ever ‘melt’ it. Once kids get behind and their grades get locked in they know it. There is no incentive to pull yourself up by your bootstraps so behavior goes down along with the grades.

    Worse, you won’t know it with any great certainty and neither will the kids until some big test blows up and you get a huge amount of failures. I like the ability to constantly track mastery as a way to adjust the scaffolding before you get to that point.

  12. Here’s how I see this integrated with a ‘delivery’ system. I like to hand kids a challenge that pushes them into a bit of a discomfort zone. Before they’re put there I deliver a lesson and a formative assessment. The lesson covers the necessary ‘tools’ they’ll need to succeed at the challenge. I’m not giving away solutions here, just prerequisite dots and definitions they’ll need. The formative assessment tells us that they are equipped for the challenge. This can be quick and informal; discussion, some sample work, maybe a problem or two worked out and then discussed.

    The formative assessment is key because it’s the early warning system that tells me whether or not a snowball is growing. When they’re let loose on the challenge they connect the dots of the lesson. A concept quiz tests their synthesis. If they ace the quiz (twice) they’ve mastered the concept.

    The process takes about a week and I build in Mondays for melting snowballs discovered in my formative assessments.

  13. The structure of grading is one area that can impact student success, and which can be influenced by the leadership team and administration.

    The biggest culprit is the use of “average” grading with the use of the zero for missing, late, or incomplete assignments. I’ve heard that one about the IRS not being forgiving, but I think it’s usually quoted by people who have not been late on taxes. It’s not as if the IRS takes all your money on April 16, which is sometimes the effect of a “day late” equals a zero rule.

    The structure of assignments can be a problem too. For example, the huge project with no check points along the way that counts for 50% of the grade. Doesn’t the reading, the research, and the thought required of earning an “A” on a rough draft constitute a major portion of the effort.

    The impact of the “0” has been well documented. How I usually demonstrate it is to compare two standard averaging grading methods: the 100% scale (with below 60% = F) and the 4-point scale with A=4, B=3, C=2, etc. For three assignments–two perfect papers, 100%, A; and one not done, F, 0% — I use the average method. Averaging the the 100% scale grades results in a 67% which is a D+. Averaging using the 4-point scale results in a 2.7 which is usually a B- or C+.

    Same work, two accepted methods. One which was commonly used prior to the prevalence of computer grade book programs, and the other that many–maybe most–computer grade book programs use. Change this system of using 100% averaging with zero grades in a school, and you’ve taken one step toward improved learning and reporting.

  14. I suppose that I’m old school in my ideas as a teacher Joel (though I am just 23). I give 0’s for assignments that are missing. I am fully aware of the impact that 0 has on that student’s grades and I am content with that outcome. I would rather a student perform horrendously on an assignment and turn in a lousy assignment than none at all. I usually will not assign a grade lower than a 50 for anything that is turned in (within reason, don’t put a bunch of crap on a paper and turn it in, and expect me to take it). If a kid gets 100 on two tests and doesn’t take the other one, then I want them to have a 67. They didn’t do one-third of the material and thus when I say they know 67% of the material then I’m quite content with that.

    I guess that goes back to the question of what is the purpose of public education. If we believe that public education is to prepare a student for the work world, then I have absolutely no problems with my averaging grades with 0’s. I tell students sometimes that nobody cares how much they know in the real world… we only care how much you do… and even if you knew how to do the assignment, but you didn’t DO it… you’ve failed in my book.

    I should add that I permit every student to retake tests they’ve performed poorly on. I accept all late assignments. I may subtract points from them for being late… I may not. It depends on the situation (or the class). My lower level classes of kids who are most likely not college bound are permitted to turn in any assignment late with no penalty. They’re permitted to take any test over again with no penalty. However, I do not excuse 0’s. If you don’t do something, then it will hurt your grade. My higher level classes, such as Calculus, I don’t have the same policies. If it’s late, then I may not accept it… I will subtract points from it.

    Point being, I hear you Joel about the averaging 0’s with 100’s… but I am quite happy with that practice. (of course my policy of allowing retakes and retakes and retakes… and accepting late work leaves no excuse, besides laziness, for a 0 ever being assigned to begin with).

  15. Thanks for the reply. One thing. Giving zero grades is not “old school” it’s what happened–usually without any awareness of the inherent unfairness–since the implementation of the computer grade book.

    When I started teaching in 1975 that was “old school”–mostly we didn’t use 100% scales–we used 4-point scales: letter grades on assignments.

    Thanks again for the great post. You might try converting your grades to the 4-point scale before using the zero for a different view– “old school” — of giving a zero grade.

  16. I am one who stopped giving zeros this year. After a great workshop and a lot of research, I came to understand that one) it is unfair to a student to calculate grades from A-D above the 60-65% range, then allow F’s to be as low as zero. The gap is 35-40 points, definitely an impossible chasm to jump. Two)failing at 65 or 60% is the same as failing at zero. An F is an F; one just does a better job of obliterating evidence of mastery from before.

    I also began using a mastery grading system this year, which allowed me to assess students on their skills at the time and specifically pinpoint what they may be lacking. I used a 1-5 scale, then translated it into the school’s letter grade system at report time. It allowed student’s to perfom better for me and see for themselves what skills needed more work. Letter grades are used as a comparison against other students; don’t we all consider a C to be “average”? One can only be average in comparison to another. I prefer to see what skills my students excel or miss based upon their own learning, not the learning of the entire class.

  17. I understand the merits of both the 4 point grade scale and the utilizing of 0’s as part of their grade (the only 0’s in my gradebook are from kids who refuse to make up tests they’ve missed or refuse to make up work).

    Here’s the traditional argument for the 4 point grade scale: A kid has 3 assignments. He gets a 100 on 2 of them, and doesn’t do the other one… he ends up with a 67, which is an F (in my school’s grade scale). Is that fair?

    I can see that reasoning. One 0 is very hard to come back from (of course I combat this by saying they can retake and make up any test… no matter how late).

    Here’s my issue with the 4 point grade scale. I give 8 assignments. The kid doesn’t do (or does horrendous) on 7 of them. He gets an A on the 8th (which perhaps was a bit easier of an assignment). I average these grades 4 + 0 + 0 + …. and I get a 0.5, which we round up to a D. Did that kid deserve to pass? Did he really know the material?

    Or, even the 65% versus a 0% argument from jf… I can do the same argument of 7 missing assignments (or very poor ones) and one good one gets a kid a passing grade.

    I’m not sure if there’s any easy answer to grading questions like this… when it comes right down to it, I look at my grades at the end of the 9-weeks and I make sure what I subjectively feel the kid should get matches up with the numbers… it usually does.

    I do like the idea of grading using the mastery method that Dan (and jf) suggest. I was intrigued by the idea and that’s how I found this blog to begin with.

    Again, I’m struggling with what amount of knowledge a student has that they can pass with. If I use a 5 point mastery system (with 1 being the lowest). A student can “master” one of these topics with a 5 and be clueless about everything else and might pass. How is this problem addressed?

    jf, I assume using the mastery method of assessment you’ve run into this. What do you do about it? Do you ever find yourself assigning a grade of a D to a student who really has no clue of what’s going on??

    I’m enjoying the discussion on grading and methods of assessment. It seems very often in education we force ourselves into an either/or dilemna where we can choose one or the other and both methods have drawbacks. Anyone have a hybrid of the two that they use that can combine the best of both worlds?

  18. Isn’t it true that some of the agony you go through over grades is simply due to unclear objectives from the grading system itself (above your pay grade). For example, what is the meaning of an F in your school district? Does it imply repeat of the subject? After all, if it was important enough to make kids take it and the end result is that they did not succeed, then shouldn’t a repeat be automatic?

    In my school district retention is anything but automatic. You can fail half your kids in a core subject like math and only 1 or 2 will be retained. Retention is far more likely if those kids also had some other issue, like really bad attendance.

    I think nobody has the stones to say, “These are the concepts that must be mastered and if they are not you will be placed into a remediation (which by the way probably doesn’t exist either)”. If administrators made this kind of objective, grading would make a whole lot more sense. Hell, it shouldn’t even be a ‘grade’. It should be a mastery report, right?

  19. At the risk of hijacking a thread, I think traditional grading systems are the offspring of the traditional grade grouping that is pervasive in public education.

    If kids were allowed to track at their own speed in a system designed to accomodate such a ‘radical’ concept, then your whole perspective on grades shifts to more of a report that says “Here is where your child is (on this continuum). Here is the normal distribution for peers. Here is the standard deviation.”

    When you bring your infant to the pediatrician and she/he is below norms, the doctor doesn’t say, “Well Mr. B, your child got an F on weight, but he did real well on length where he reached a B-, and that smile, well that got him an A+ on citizenship.”

    Oh, and by the way, such a report could tell the story of exactly what that kid is ready for next in subsequent teaching the child receives (notice I didn’t say next teacher or next grade).

  20. The problem I found was that my school system averages together all the grades to produce one final outcome on the report. So, if I assessed mastery on 12 standards in one nine weeks, the school report would only show the average of those scores. I would much prefer a report that showed each standard assessed and the mastery of each individual standard. That way, a student can “fail” (I call it “Not there yet”) some standards, yet show Mastery or Good Understanding on others.

    Yes, I have had students have better letter grades than I would have given once I have put my information into the school system. However, this seems to be the fault of the school system which is still archaically based on letters. If I could truly report the standards and the mastery level, skill assessment would be much more clear.

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