Saturday, November 2, 2013

Mitigating Against the Zero

On or around October 31, Leyden teachers may have noticed a strange grading phenomenon:
students' grades mysteriously went up. Some slightly, some more profoundly. The reason for this is that I goofed up. I'll explain.

You may remember our grading codes as:

E (Excused)
The assignment is permanently excused. The student does not need to make up the assignment.
P (Pending)
The student is expected to make up the assignment, and it is temporarily counted as “excused”. Thus, the pending assignment is not adversely affecting the student’s grade.
M (Missing)
The student is expected to make up the assignment, but it currently counts as a zero in the gradebook. The student could incur a grading penalty when the assignment is turned in.
0 (Zero)
The assignment cannot be made up.

We ask that teachers not leave any grades blank in the gradebook, as it does not give any information to students, parents, case managers, or other stakeholders about the status of the assignment. It's not perfect and it certainly doesn't give complete information, but it's better than nothing.

When students' grades suddenly spiked on 10/31, all the "M" grades in the system were not being calculated as a "0." Rather, they were being calculated as "50%". That's still a failing grade for the assignment, but not as deadly to the student's overall grade as a zero. Anyway, I was experimenting and I left M = 50% on too long. I apologize for any confusion. Everything is as it was. By the way, the date is a coincidence- it wasn't a Halloween prank. I just goofed.

However, here's why I was experimenting in the first place. For some time, I have been very concerned with the extremely detrimental impact of the zero on students' grades. Naturally, if a student does not turn in an assignment, the student's grade will be impacted negatively.
Unfortunately, when you use a 100- point scale (as when we use percentages), a "0" is not mathematically accurate.

On a typical percentage-based 90-80-70-60 system like ours, the intervals between an A and a B, a B and a C, a C and a D are all 10%. However, when a student does not turn something in, we have nothing to go on and it seems our only choice is to assign the zero. In that case, the interval between an D and the F is actually 60%. It drags down the grade disproportionately compared to all other scores.

Therefore, I believe that a zero has a more negative impact than is warranted, and the punishment does not fit the crime. One of my favorite educators, Doug Reeves, writes about this more eloquently and forcefully than I ever could in The Case Against the Zero. Along with Robert Marzano and many others, Reeves advocates for a 4-3-2-1-0 based system, rather than grading on a 100 point scale. Reeves writes,

"To insist on the use of a zero on a 100-point scale is to assert that work that is not turned in deserves a penalty that is many times more severe than that assessed for work that is done wretchedly and is worth a D. Readers were asked earlier how many points would be awarded to a student who failed to turn in work on a grading scale of 4, 3, 2, 1, 0, but I’ll bet not a single person arrived at the answer 'minus 6.'"

The point is, on a 4-3-2-1-0 the interval between a "0" and a "1" is the same as the interval between all the other grades. A "0" would have a detrimental effect on a student's grade, but not catastrophic. Also, the thought that a slew of zeros that drag the grade into the teens or single digits somehow motivates students to complete their work is not supported by research. In fact, it may have the opposite effect and cause the kid to shut down.

And in case you're thinking I'm coddling students by suggesting we "dummy down" the grading scale and go easier on these scofflaws who don't turn in work, think about this: we use these types of grading scales all the time in other contexts and don't have any problem with it. Here are a few examples:

  • GPA has been calculated this way for decades, and is widely accepted by colleges, universities, and employers. Again: A= 4, B= 3, C=2, D=1, F=0. (And again, an F does not equal negative 6.) 
  • Advanced Placement grading is on a point system. Short answer questions are not assessed using on a strict percentage value. Rather, they are given a score based on 4-3-2-1, and the overall test is given a score of 5-4-3-2-1. These are the exams given to our top students, and accepted by top universities as evidence of student knowledge. 
  • Our teacher evaluation system is based on a 4-3-2-1 system. There are many, many parallels to evaluating teachers fairly using this system (as we all want) and evaluating student progress fairly, but that's another blog post. 

As much as I would like to discuss going to a 4-3-2-1 grading system, the trouble is that most electronic grading packages (like ours) are fixed on a 100-point percentage scale. It would take tremendous fitting-of-round-pegs-into square-holes to actually type in a "4" and have it mean an "A," for example. In the end it might be more confusing to students, parents, and ourselves. Until we have a grading system that gives us the option of actually using a real 4-3-2-1 system, and we've had time to really discuss the idea as a staff, we will work with what we have.

However, if this idea intrigues you and you want to give it a little try, here is why I temporarily changed "M" to 50%: In order to simulate a 4-3-2-1 system, the intervals between A to B, B to C, and so on must be equal.  From A to B is 10%, B to C is 10%, C to D is 10%,  and D to F (even for work that's not turned in) must then also be 10%.

That is, 4-3-2-1-0 is mathematically equivalent to 90-80-70-60-50.

Therefore, to partially simulate such a grading system, I temporarily changed all the "0's" (stored as M's) to 50% to see what would happen. Yes I know it's not a perfect simulation because there are lots of other grades out there lower than 50%, and zeroes not entered as "M's". I just wanted to see what would happen if we simulated a 4-3-2-1 system in some small way, mitigating against the deadly impact of the zero on a 100-point scale. As you may have seen, student grades jumped. Some students whose overall percentages were in the teens were suddenly within striking range of passing.

I know, I know: it's unsettling to think of giving a student half credit for nothing. I'm a former math teacher, and it's taken me a long time and several blows to the head to get to this point in my thinking. (Math teachers: I kid because I love). However, I don't think of it as "half credit" for nothing. It's just simulating a more mathematically accurate and fair 4-3-2-1 rubric based system. I'm sure I will have some interesting conversations with many of you over this issue, and that's great.

The Conclusion (finally)!
If this makes sense to you, and you would like to help "make the case against the zero," we have created a new grading code that calculates any assignment as "50%" by default. In other words, if a student does not turn in an assignment you may use the following code:

NS = "Not Submitted". This calculates the assignment as a 50%. 

(By the way, I'm not sure I completely like the code "NS", but it's a pretty complex idea I'm trying to get across here. So far this blog post is around 1,200 words, and "NS" is the best I could do with two letters)

Updated Codes for use in the eSchool gradebook

E (Excused)
The assignment is permanently excused. The student does not need to make up the assignment.
P (Pending)
The student is expected to make up the assignment, and it is temporarily counted as “excused”. Thus, the pending assignment is not adversely affecting the student’s grade.
NS (Not Submitted)
The student is expected to make up the assignment, and it is calculated as a 50%. Thus, the assignment is negatively impacting the student’s grade, but not as severely as a zero.
M (Missing)
The student is expected to make up the assignment, but it currently counts as a zero in the gradebook. The student could incur a grading penalty when the assignment is turned in.
0 (Zero)
The assignment cannot be made up.

You can still use "M" = Missing (counts as a 0), "E" = Excused, or P= Pending (counts as excused). The use of the "NS" is not a mandate. However, I would encourage you to think about this issue and consider using the NS and see how it impacts student grades. Of course, the goal is for students to complete all assignments- that should never be in question. Yet, I think it's time to consider the impact zeros have on our students, and the impact of how we assess students overall.

By the way, thanks to all the teachers I've talked to in the last couple of weeks who have contributed to this discussion and helped shape this argument. You know who you are, but I won't call you out by name. :-)

Some other useful links on grading and zeroes:

Doug Reeves: The Case Against the Zero. Among other articles from Reeves, you can read Leading to Change-Effective Grading Practices.
Thomas Guskey: Zero Alternatives (Guskey is one if the  "go-to" guys in terms of grading and assessment)
Ken O'Connor: Making the Grades (O'Connor is also a heavy hitter with grading)
Alfie Kohn: From Grading to De-grading (Ditto with Alfie Kohn, but he's a bit more radical than Reeves, Guskey and O'Connor)
Jeffery A. Erickson: A Call to Action: Transforming Grading Practices and Grading Practices: The Third Rail
Joe Bower: Giving a student a zero teaches them a lesson (But not the lesson you might think)


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  2. We all talked about this when we read "15 Ways to Fix Grades" -- which should really be called "5 1/2 Good Ideas and 9 1/2 Ways to Throw the Baby Out With the Bath Water."
    While it's nice to go over the math, I teach economics. Economics says that people respond fairly predictably to incentives. A student who has his/her grade "devasted" by a zero has a pretty powerful incentive to *make up the work.* That's the behavior I want from them. If you reduce that incentive ("hey, making this up really won't help my grade that much -- I already have a 50%"), then you reduce the desired behavior (going back and actually *doing* the work).
    If I get a $50 parking ticket, there's no way in the world that I have caused $50 worth of harm to my community by parking where I shouldn't. Yet I'm charged $50. That's *not* a "mathematically accurate" assessment of my action; it's not even intended to be. It's a (dis)incentive, to make me not want to do it again.
    People's behavior can be shaped by incentive structures. Give a kid half-credit for doing nothing ... and you'll get a whole lot more doing nothing.

    1. OK, but there's actually no evidence that disincentives really work overall in the context of grading. Maybe with parking tickets..... :-)

    2. Wow, really? Thoughtful responses are requested, a thoughtful response is given -- and all I can get is a tossed-off one-liner consisting of a single dismissive wave of the hand claiming "no evidence"? Well, I can see that the concept of disincentives is clearly understood.
      I believe that the studies you may be alluding to (yes, I have read some of them, too) are about the assignment of a permanent zero for missed work, a position I was clearly not advocating, but strangely appears to be actually encouraged by the "0" grid in the blog above.
      I collect over a hundred data points every single semester of missed work being turned in that corresponds nearly exactly to one of two things: a) a fairly steady trickle of students who have recently looked up their grades and noticed that it fell below a level with which they are comfortable, or b) the swift-moving river of students of all sorts at the times when grade reports are approaching. In both cases, the students readily understand that zeroes are the culprit and they take action accordingly. And throwing them a 50% for doing nothing would significantly prolong their crossing at least the first threshold, if not both. Exactly how many actual data points from classrooms might constitute "evidence" that wouldn't be pooh-poohed?

  3. I can understand Tom's position on this grading category. Many colleagues will likely agree that drawing out excellence from our students requires the highest of expectations and related consequences for making poor academic choices. However, while an expensive parking ticket is intended to discourage the wrong behavior from citizens most of us know a handful of individuals who have a glove box full of such tickets. It would seem that the presentation of the negative and sometimes extreme financial fine does not appropriately motivate all citizens to do the right thing. Special needs students are a segment of our student population who’ve been receiving tickets for years. They see no way to pay their debt and will often shut down and simply give up trying to save their money in order to settle their account. Students with IEP’s sometimes have the benefit of course modifications that take into account the student’s diminished ability to complete homework on their own, or perhaps an inability to attend to tasks for reasonable periods of time. Often times in such cases a student might be graded differently than their classroom peers on homework, or provided with fewer questions than other students on small assessments. While modifications and accommodations are designed to offset legitimate deficits, they can also coincidentally serve to encourage the student who struggles academically to continue the apply themselves.

    While special needs students receive appropriate modifications and accommodations to facilitate their achievement the general education student has access to Rti interventions that to some degree can be used to provide coincidental encouragement to the struggling student. The NS grade category can assist students who are on the cusp of making connections with education to do the right thing, and perhaps recognize that they can achieve (or pay their tickets) if they continue to apply themselves.

    I often reflect on being and having been a parent, teacher, coach, and mentor. I frequently tell my students and my children that I readily expect them to make mistakes, and that my role is to help prevent them from making mistakes that could be devastating for their futures. I think the NS grade can help us to more honestly grade and encourage students to do the right thing instead of punishing them for making mistakes (or doing the wrong thing).

  4. Part 1:
    Although I understand the philosophy behind the "no zero" grading, I'm going to have to side with Tom on this one (Aux armes, les citoyens! - inside joke). I have a few issues with instituting a no zero policy within a grading system that can't be changed from the 100 point system. First of all, Tom is completely correct about a loss of motivation to make up work. Our students are very savvy. If nothing ever counts for less than 50%, they will know that it really won't take much to just get a D in a class and unfortunately, we have a lot of students who are happy with a D. I'm not happy with a D and I don't think anyone should be happy with a D, (do you want an employee working for you who got all Ds?), so unless we make anything under a 70% a failing grade, then giving a 50% for doing nothing just doesn't make sense.

    Secondly, there are kids who take tests and get lower than a 50% on them. Is it fair that a kid who never takes the test gets a 50%? For my homework grades in the lower levels, my students can get either a 5, 3, or 0. Why should a kid who does absolutely nothing get credit for doing something? This is what is going to be very hard for teachers to stomach. I just don't think the math makes sense in this case (just as I still do not think that getting rid of the 40-40-20 grading was the right thing to do for student motivation, if we're going to go down that road).

    Third, I really don't like the idea of giving the NS as an option because you have the potential of having Teacher A of a course never giving a zero and teacher B of that same course giving zeros. Teacher A's grades will be far more inflated than Teacher B's grades, even if Teacher B is providing the same quality of instruction as Teacher A, the same homework assignments, and the same assessments. It will look as if Teacher B is a worse teacher just based on grades. You're putting the onus of student pass rates on the teachers and NOT on the students. This is unfair and is the worst form of social promotion. Either we all give zeros or nobody gives zeros, and not after a very open, extensive discussion that includes the faculty.

  5. Part 2:
    In the end, the problem is not whether or not teachers give zeros. It's about the traditional system of grading that we have that has rather arbitrarily assigned grades to only the upper 40% of a grading system of 100 points. In France, they grade on a 20 point scale where getting a 10/20 is what we might consider a "C". If we want to talk about honesty in grading, let's look at the grading system as a whole instead of basically faulting teachers for failing students. I understand that in the end, universities want rankings and GPAs and such, but that only works for our higher-level students who are competing for spots in top-tier universities.

    This brings me to my belief that we're not serving all of our students by trying to fit them all into the same system. Whatever happened to a true trade-school education that happened at the high school level? We can talk all we want about "college & career readiness" but there is a big difference between the math one teaches to a kid who is going to go to MIT and the math one teaches to a kid who will become a plumber or bricklayer. Why aren't we working with local trade unions to start apprenticeships in the high school and having math and science courses that help our students get into VERY good, well-paying skilled jobs? Even I am able to admit that they all don't need to be able to read Voltaire, even though it would be nice. ;)

    I really wonder at the true motivation for a no-zero grading policy. Is this just about honesty in grading or about pass rates? At what point are we just going to stop challenging our students out of fear of anyone failing and receiving a poor evaluation? No business in the Leyden community will want to hire graduates who don't understand the consequences for not doing their work, because I don't know of any businesses (other than the mafia-run toll-booths) that pay employees for not doing their work.

    1. May I add something from a completely different perspective: I live in the Netherlands and have three kids going to school at a Jenaplan school ( I myself am heading a team of scientists working for a large American multinational. So, I am not a teacher, but I have great respect for those who try their best to prepare our kids for the future...

      If someone is >really< serious about getting kids ready for jobs (either college or plumber), I believe we should start grading students on a second dimension - something that is increasingly done at companies: don't just tell them how good / bad it is >what< they have done, but teach (grade?) them the huge relevance of >how< they work.

      I know this is challenging in a classical (high) school setting, but I am regularly confronted with bright people who score very badly on the HOW axis. And given the choice between someone who is not that bright on the WHAT axis but is very strong on the HOW axis (communication, motivation, ...), I am favoring that one.

      In this context I learned at nice Dutch saying "gelijk hebben en gelijk krijgen". It means something like: there is a difference between being right (the WHAT) and being able to convince people of your opinion that something is right (the HOW).

      And another connection is with Mikkel's arguments in favor of ACE goals over SMART goals: SMART goals link exclusively to the WHAT while ACE goals emphasize the relevance of the HOW!

      And now I will be lurking in the shadows again and let you continue your discussion... ;-)

  6. Lisa and Tom have very real points. When the district moved to reduce grading categories from something like fifteen or twenty to the few that we use now, there was an effort to standardize how we address grading. However, at the same time that this refinement was implemented departments were given the latitude to determine percentage values for each category independently. So it would seem that the effort to standardize grading, so students know what to expect from one class to the next was contradicted by the flexibility provided to departments in assigning grade weight percentages to grade categories. Additionally, it became necessary for several subject areas to squeeze their tasks into the what they feel are the most appropriate categories provided (ie: labs, essays, etc...).

    I think we want to ask ourselves some questions about what we are attempting accomplish as a district. Are we looking to institutionally provide teachers with added flexibility in their grading methods as a policy, or are we merely asking teachers to consider the significant impact of zero grades on a student's grade point average? Even without the NS category teachers have the ability to enter scores of 0-49 into their grading if they choose to do so. That being said, do we really need the NS grade category?

    After reading Lisa's post I started to wonder about something. Tentatively we are stating that the NS grade means "The student is expected to make up the assignment, and it is calculated as a 50%. Thus, the assignment is negatively impacting the student’s grade, but not as severely as a zero." The NS grade has a distinct meaning. Moving forward what is the meaning of a grade of zero, 13%, or 32%?

    Just some thoughts...

  7. The argument in favor of a zero-free grade book has only ever made sense to me in regard to assignments that are summative and holistically graded. If that is the case, then the new “NS” category really just replicates the AP grading scale. Here’s one thought: to argue against the NS category is sort of like saying that the “0” in the AP scale is not low enough-- as though we should start students at a negative number and then have them work their way back to the 1. This seems strange to me. A “1” (or D) should reflect something marginally better than not doing the work at all. When a student earns a D on a paper in my class, generally speaking he has barely addressed the question, scarcely demonstrated the stated outcomes, and largely ignored the conventions of grammar and mechanics. That should not be calculated as earning 60% of all possible points. That should be calculated as 10% better than incompletion.
    Regarding the inconsistency issue, this concerns me greatly. I do not want to be in the position of being largely out of step with my colleagues who are teaching the same course. On the other hand, what is our other option at this point? I do not think from this blog that anyone wants this to be mandated. The only other option would be to ignore current research and about grading reform. That doesn't seem right either.

  8. Grading is subjective. Even objective tests become subjective when we consider how each of us uses weighted categories in our grade book. The number of total assignments in a grade book makes grades subjective too. By nature, grading is inconsistent. No-zero grading is an attempt to make grading as fair as possible. It will always be subjective – this is an attempt at fairness. The NS category raises a lot of questions. What are we grading? Should we only grade summative assessments that measure mastery of skills only? How many total grades should we have? Should we revisit the current categories and grade weights?

    This issue also raises questions about attitude or approach. Do we want to give students every opportunity to practice a skill, or do we offer limited opportunities and punish them for not trying? I want to encourage grit – to develop the soft skills of responsibility and hard work, but I don’t think these things are mutually exclusive. Can I understand the inequity of a “no zero” policy, institute it, and still develop students’ grit?

    I want to work in an environment that encourages its members to question current practice and reflect and experiment with possible solutions. This is not a Leyden-specific policy change to boost passing rates. This is coming to us from a larger conversation. Education is an art – it changes. Here’s a change for us to consider. I do not want to dive in without thinking about consequences, but I also do not want to reject it simply because it changes too much about my current practices. If zero penalties do not motivate students, and if zero penalties are unfair, I want to consider solutions. I should have a chance to try these solutions and refine my practices based on trial and error. No one is not saying we must all do this now – it’s opening the conversation and saying, if this interests you, try it. I understand the inconsistencies in some of us trying it and others not. But if Leyden is willing to support that in the interest of trying different solutions, I’m in.

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  10. Call me crazy, but last time I checked, a percentage represented a part/whole. If no part of the whole is completed (0/100), then the percentage is 0%, not 50%, which represents "half" of the whole. This concept of "0" is not new - it was first used in arithmetic in India about 650 AD. Even modern day calculators take 0 divided by any number, and return an answer of 0...

    This can result in grade inflation at its worst.

    How long will it take students to figure out that they are better off not handing in an assignment than actually doing one and/or turning it in late?!? I bet it's less time than it takes them to figure out a way to use Facebook and Twitter on their Chromebooks during class.

    As far as these other comparisons, several of them are somewhat inaccurate:

    "GPA has been calculated this way for decades, and is widely accepted by colleges, universities, and employers." This is true.

    "Advanced Placement grading is on a point system. Short answer questions are not assessed using on a strict percentage value. Rather, they are given a score based on 4-3-2-1, and the overall test is given a score of 5-4-3-2-1." This perception assumes that the students sit for the test and attempt to answer some of the questions. It is possible for a student to earn 0 points on an essay. Also, a student who comes to the test, fills out the name/info but does not answer any questions receives a "Blank/Non-Graded/0" score - not a 1. This info was verified by the College Board. In addition, the 5-1 scoring system actually reflects a mostly normal distribution of scores, so for us to go to that system would mean "grading on a curve," which, depending on the performance, would mean that some students who've mastered 80-90+% of the material would receive 3s (the equivalent of a C).

    "Our teacher evaluation system is based on a 4-3-2-1 system." Yes, but once again it assumes that the teacher has actually been observed/evaluated (like a student who has turned in an assignment). A teacher who was not observed or one who is on leave (the equivalent of a "missing" assignment) will not be rated on the system. In an extreme case, if a teacher abandoned the job and did not show up to work, he/she would be terminated, not given the same rating as someone who performed poorly in the classroom.

    I know this seems like I am splitting hairs - which I am; however, while I respect Mikkel and Doug Reeve's opinions, I still believe that making 0% equivalent to 50% is rewarding students for doing nothing and is wrong.

    My question to people worrying about failures: How many of these failures may have been reduced if students took advantage of the tremendous number of opportunities offered to them - Period 0, Period 11, ACCESS, checking OpenClass, actually taking material home, raising their hands to ask questions, doing work in Freshman/Guided Study, not spending their study hall time on YouTube or GoogleChat?

  11. I have come to the conclusion that this debate centers around how accurately does a zero portray a student's learning. If that is the gist of this, then please consider this idea. Under the current system students have been both punished by zeroes and also have had their grades inflated by "check for completion" assignments. Both of those practices do not reflect what a student has learned. If we can agree that some sort of assessment determines that, then the emphasis of the student's grade should be those assessments.
    For example, in US History we have have small assessments (formatives) and large assessments (summatives).
    I suggest that we either eliminate entering any grades that are not summative assessments, or make that weight percentage so small, that a zero, or a even 50% won't affect the grade, yet can be used, by both parents and teachers, to track the students' progress, or lack thereof. This way, a student who does nothing, still has to pass the large assessment. Also, this category there would be no minimum, as what you earn as a grade is what you get.
    This would eliminate the "something for nothing", the devastating effect of the zero, and truly reflect what a student has learned. However, it also eliminates the possibility of helping kids with extra credit, and a few fluff points to get them over the threshold. Problem solved.......sort of........

    1. I completely agree-- I think this makes a ton of sense. Yes, yes yes. Eliminate formative grades or make their weight negligible at best. I posted before that I think the NS option really only works for summative assessments that are holistically graded, but I would also add that I think it works best in a "lean" gradebook without a lot of superfluous points.