Wednesday, April 21, 2010

False Dichotomies

Do you grade formative assessments or not?

Is it inquiry or an investigation?

GeoGebra or Sketchpad?

Paper of plastic?

Why does it have to be either/or?  I don't care.  Just bag my groceries so I can go to my car.  And hurry up before that guy with the clipboard and stopwatch comes and starts asking questions. 


CalcDave said...

Yeah, well, as mathematicians we want formal, rigorous definitions for things. But, as people (and as the Heap Paradox points out), it's not always easy to pinpoint exactly what we mean.

Teachers at my school are new to the formative concept and they somehow got the idea that the definition of a formative assessment is it is are not graded. I disagree with that statement. There are different levels of formative assessments (as I think you are suggesting here).

There are explorative-formative assessments where we probably don't want the pressure of a grade over a student's head. They should feel free to "do their best" and not be scared to take risks or of making mistakes. But, mentally, at least, we teachers may be somewhat assessing how they do not only to inform our instruction of this topic, but to get a baseline to gauge improvement in the student(s).

Then there can be more checkpoint-formative assessments like mid-unit quizzes that can be graded, but continue to form our instruction and their understanding of what they need to study more.

To me, a formative assessment grade is fine as long as they have an opportunity to prove their growth from that assessment and the growth factor (probably more heavily) into their grade.

David Cox said...

If a student has the opportunity to make up portions of an assessment as they gain new understanding, shouldn't all assessments give them the freedom to "do their best" without the pressure of making mistakes? We have to change that paradigm.

The pressure of the grade is what interests me. Where does that pressure come from? How can we change that?

David Cox said...

Oh, and your first sentence reminded me of somethign. I remember there being some common problems in my number theory and abstract algebra courses in college. The number theory prof was crazy strict about rigor, logic and the form. The algebra prof allowed us to prove in five lines what took us three pages in the NT class. I remember more from my linear algebra class.

Jennifer Borgioli Binis said...

David - Glad I discovered your blog, definitely adding it to my feed. I think I shared with you on Twitter that I really I struggle with the idea of grading formative assessment and have recently come to a point where I'm just not comfortable with it, regardless how the grades are used. My thinking: we all agree formative assessment (the messy assessments that occur during learning, not before and not at the conclusion) are used to help the student self-assess and the teacher to plan. It seems unethical to me to assign a number that will then factored into a grade that will then be used to punish (failure) or reward (passing) when we've already agreed the student is still learning.

To me, it's like putting me in the triathlon in the Olympics but awarding medals based on the swim, even though we still have to bike and run. I may be way behind in the water and will make it up on the road. Knowing that the medal comes while I'm in the water - well, what's the point of running my fastest if you've already judged me?

I am also curious about why there's a need to grade formative assessment. What's the worse that can happen? "Students won't take it seriously" - similar to what Calculus Dave mentioned. But isn't that statement an indictment of the power of grades and the mixed-message impact grading formative assessment could have? "I get that you're still learning, but I'm going to factor your ignorance into your average so you take it more seriously?" The concept of pressure of grades you mentioned.

All of this aside, I absolutely think we should give students feedback on formative assessment. Sometimes that feedback takes a numerical form (i.e. 10/15 correct) but to me, that's not grading.

I'm always eager to hear different perspectives so shout at me if my analogy seems off.

CalcDave said...

Jennifer, I just don't like the idea of being restricted in what I'm allowed to grade or not. I mean, ultimately, everything I see the student do academically should factor into their numerical score at the end of a grading period, right? I don't mean that a poor swim time will hurt their overall grade, but it certainly puts their biking/running times in a good perspective.

I can see your point of not wanting to grade and I totally accept that viewpoint. But, I think it doesn't have to remain ungraded to be a formative assessment. I guess I just see that as the "assessment" part.

Anyhow, yeah, David, I agree about wanting to remove the pressure of grades and changing the system somehow to allow them to make mistakes all the time. But, I think it's human nature that some tasks in certain situations come with pressure. Some people react really well to it and perform better than average in those times, while others have the opposite issue. Maybe it's the whole "training soft skills" issue coming back up again, but I think students sometimes need to learn how they react in those kinds of situations so they can deal with it when they're actually performing their first surgery or meeting their first deadline at the office.

David Cox said...

I think I'd agree with you if I was using a grading system where I averaged my students scores. My gradebook is fluid. By that I mean, I am very specific on my learning targets and any time I assess this target, the student's level of understanding is recorded. I currently have 38 assignments corresponding to the 38 skills I assess in my algebra class. If I give an assessment and the student demonstrates mastery of the concept, why should she have to take another assessment? If the student demonstrates less than proficiency, the score is reported and the student has the opportunity to replace (not average) that grade once proficiency has been demonstrated.

The only way I think your analogy breaks down is in the fact that my students have another shot at the gold each time they reassess.

Matt Townsley said...

I'm still thinking a lot of this "grading formative assessments" thing through as you know, David.

Just some random thoughts running through my mind:
Why do we "grade" the quiz, but not the thumbs up/down activity we do in class...or the expressions we see on students' faces? They're all formative activities (driving future instruction), right? Is it because it's on paper that we think it's okay to grade? Should we grade exit slips, too?

I'm not trying to attack here, just asking some hard questions I've been thinking about related to this topic.

Jennifer Borgioli Binis said...

David - The way you describe your grading system, makes sense. I can make up time I lost when swimming on the road. My hunch, though, is that the majority of teachers haven't reached that level of confidence in their management and sometimes, separating assessments that are graded out of the formative picture can alleviate their stress.

Dave - in terms of definitions, I define assessment as "to collection information about student learning". Evaluation is assigning a value to that information.

There is still a part of me that feels grading changes a student from a learner to a performer - regardless of how those grades are used.

David Cox said...

I see your point regarding pressure. I don't want to arbitrarily add pressure not do I want to turn grades into money. I simply want my grade to reflect what my students know at any point in time.

So can you grade the looks on a student's face? Or the thumbs up/down? Or even the exit slip? Before I answer that let me ask you this Matt, how often are you surprised by a stident's performance on a summative assessment? If your classes are anything like mine, I can predict with pretty high accuracy a student's final grade just by classroom observations and conversations. There was a time when that would have been enough. Our narrative of a student's abilities would have been enough. Today we need evidence. So yeah, I'd love to use those instances you mention to determine a student's mark, but I'm afraid they wouldn't hold up in a parent conference.

"There is still a part of me that feels grading changes a student from a learner to a performer - regardless of how those grades are used."

Exactly! I think that setting grades apart from those authentic assessment opportunities actually contributes to that mentality rather than combats it. If I had my choice, we wouldn't use grades at all. But as long as students see a difference between graded and non graded activities we are going to get questions like, "is this going in our grade" or "how many points is this worth?"

CalcDave said...

I guess I may be thinking about this in the wrong way, maybe? I mean, to me, isn't every assignment formative in some way and summative in another? An exit slip should be the sum of their current knowledge to that point and forms the class for the next day or more. A "chapter test" does the same (or should?). So, I think I agree with the original post here that it doesn't really have to be either/or.

David Cox said...

I mean, to me, isn't every assignment formative in some way and summative in another?

Is this the original way you were thinking or the new way? Cause I agree completely with this.

Matt Townsley said...

I don't think every assignment can be considered formative. Formative assessment should be a planned process (according to the FA guru I heard yesterday from UCLA :) so we as teachers decide ahead of time if the activity/quiz/homework/whatever is going to be formative. We decide if it tells students...
Where am I going? (learning target)
Where am I at? (LT number, lykert scale, comments, whatever)
Where to next? (feedback)

If we don't provide (plan?) an opportunity for students to use the feedback, then it seems like a summative tool.

I'm also wondering about the practice of optional re-takes. When we plan for them to be optional (particularly outside of class), are they really planned at all? If something (a re-take) doesn't come to fruition, then it never happened and might as well not have been planned for.

David will chime in now and say that everything is optional in school. Yes, it is, but when it's outside of class, we're making it it optional.

I think I'm just going around in circles on this topic. Maybe I should just be quiet for a while. :) :)

David Cox said...

So Matt, if I have a targeted assessment covering exactly one skill (where are you going?) with the intention of finding out where my students are and if they demonstrate proficiency of said assessment do they not then know where they are? If a student demonstrates less than proficiency on this assessment does it not show both of us that they need more work on this target? Now the where to next is the question I am interested in.

Do your students receive that kind of feedback after a formative assessment? What is it about your feedback that shows them what to do next? Do you have a list of activities planned based on where their understanding level is? If a student nails the assessment, what do they do next?

I would submit that any skills test with immediate feedback on how the student did is formative. The student knew exactly what the target was, she knew how far from the target she is (if not proficient) and she knows she needs more work. The thing that baffles me is why you wouldn't use the score on such a quiz to show the students level in a more formal way (gradebook).

It makes no sense to me to have a kid take a formative assessment the way you describe it, ace it and then have to do it again just because the previous was "just practice."

The really nice thing about the ExamView tests is that the feedback can be built right into the test. Students can see a step by step process for the problem they just did.

I'm not sure how you can get more formative than that.

Please don't be quiet on this because this is helping shape my thinking.

Karl Fisch said...

I don't have anything substantive to add here (at least not yet), but just wanted to say thanks for continuing to go after these questions. I don't know if it's helping you guys, but it's helping me get my head around this a little better.

Jennifer Borgioli Binis said...

David: I want to address something in your last comment that gets to the heart of my discomfort with grading an assessment that we know (by it's design and our intentionality, as Matt mentioned in the definition of formative assessment) that students have not yet mastered the content.

Grades are not feedback. Grades do not tell a learner "where to next?" - they communicate they value of their work on an arbitrary scale.

You did not state this explicitly but I wanted to bring it up. You asked Matt about giving students feedback and then asked about using that grade. The system you described sounds like one way to capture student learning information. Formative assessment is a large category that encompasses all sorts of messy things - tickets out the door, thumbs up/thumbs down, rough drafts, mind maps - things that cannot be expressed numerically. If we remove the issue of grading from the table, we open the door to a whole bevy of assessment options are traditionally not tapped because they can't be counted.

Consider the following scenario: a student "takes" (a verb that implies test rather then assessment but I digress) an assessment and gets a "good" grade. If grading was off the table, there is room for the teacher and student to review her performance, identify where she can do better and use that reflection on the summative, for all the marbles as it were. Let's say she decides that an 85% is acing it. It's good enough. But with formative feedback from you (or the program you described) she could make the adjustment she needs to really aced it on the summative assessment.

The point of formative assessment is to enable change and improvement through feedback, during the learning process. A number indicates, perhaps subconsciously, that the learning is ready to be summarized, compressed and entered into a grade-book.

A question that I'd like to put out there: who benefits by grading formative assessment? If we say students, my hunch is that we're blurring feedback and grades.

CalcDave said...

Jennifer, I don't think a "grade" has to be numerical. Ultimately, they need to have "mastered" the material. And I can get a sense of that from a thumbs up/down, mindmap, etc. as you say. So, a student gets the feedback they need to progress, but I also get some information on where the student is to inform my ultimate graded assessment of her.

Jennifer Borgioli Binis said...

But how can a grade not be numerical? A bunch of grades = what goes on the report card. How can you arrive at a final number for the report card without using a bunch of other numbers to equal that final number?

So let's say you grade a report and give it a "C". That's still not feedback because it does not tell the learner where to go next.

CalcDave said...

I'm saying you can have both. In your own head, you assess with a "C," but on the paper or conference with the student they read/hear "work on xyz."

I guess my point is that you, as the teacher, should have the ability to use any information from the student to assess their learning and use that to compute a grade for the report card. Also, you (as the teacher) know when it's time for students to explore the concept and take risks and make mistakes without penalty and when it's time for them to really prove their understand as a whole. I don't know that we should get bogged down with labels and say this or that can or cannot be done just because this assessment was meant to be formative.

Matt Townsley said...

David: I am absolutely awful at differentiating up. For those students who get a "4" the first time around, I've got nothing to keep them progressing. "Help another student who doesn't get it" is the subtle message I'm probably sending via the way I setup the "after quiz" activities. I really can't picture a system that helps these students AND the ones that are struggling at the same least in our current secondary setting focused on serving all students. So, I'll admit that I choose to focus instead on the students who still have a learning gap - the students who don't "get it" on the first or second written formative assessment.

The thing that baffles me is why you wouldn't use the score on such a quiz to show the students level in a more formal way.
...because when a student sees a score, he/she associates it with an 'ending.' I saw it for years in my room: hand back a quiz with a score on it and the primary focus becomes the score rather than the written comments/feedback. That's why a score doesn't make sense on formative assessments - it takes away from the feedback, the "where to next?"

You're right...It makes no sense to me to have a kid take a formative assessment the way you describe it, ace it and then have to do it again just because the previous was "just practice."
See my comments above. On the flip side, it makes no sense to leave it up to the students to see through the score AND come in outside of class to act on the feedback given to them through the quiz.

I realize that in Karl's school this may be different, but for my school and presumably many others, if it's not done during class, then its optional.
Calc Dave brings up some good points about seeing the formative quiz as a data point for a grade, but only writing feedback. That seems to be more along my line of thinking.

Does any of this make sense? I'm getting a bit garbled between this thread, one on Karl's blog and one on my own. :)

Eric Townsley said...

I really have a hard time "grading" formative assessments. I view grades as a numeric (% in this case) representation of understanding.

Now with that being said, my unit tests I grade the Learning Targets on a 4 point scale. Students have the ability to re-take any Learning Target anytime later until our time together ends. My struggle is that if a student re-takes the test, spends time re-learning that target then isn't my test also a "formative" assessment?

More of a question than a response, but something I have to do to fit the grading system we all have in high schools.

Jennifer Borgioli Binis said...

Dave - you raise a very interesting point that parallels many of the conversations about grades. Should grades reflect the learning process or on-demand performance at a given time? Should they assess product or process? Do they even help or do we use because well... it's what we've always done?

I don't think anyone is saying you can't do or can do anything. That being said, as a profession we need to come to agreement about our lexicon and am grateful you brought up this topic so we can continue to explore the nuances of formative assessment.

I'd like to return to my question: who benefits from grading formative assessment?

I pulled a few of my resource books on assessment yout and when I opened the first one (Formative Assessment by Tuttle), I found this quote: If you give a student a grade on a piece of work and also include written comments for improvements, they will not look at the written feedback that you give them for improvement (Butler, 1988). The grade literally cancels out any comments. It is better to only include feedback and not include a grade.

Food for thought...

Jason Buell said...

Thanks David for the good convo. I love me some assessment talk.

Part of the problem, as pointed out by CalcDave is that, even on this thread, we're in disagreement about what grading means. Just from this thread I think we're at either 1. any numerical score 2. anything that goes in the gradebook but is subject to change 3. anything that goes in the gradebook and it can't be changed

I'm really just echoing multiple comments here. But the heart of the matter is that for something to be "formative" it matters more what happens next rather than the format or whether its graded or not. So the question is "Will putting a grade on this affect 1. Me as the teacher adjusting my teaching or 2. The student adjusting their learning tactics"

When are grades useful? I'm going to lump together numbers 1 and 2 from the definitions above and assume that most of us work from the assumption that grades aren't final until my principal takes my hands and forces me to hit the submit button.

I would argue that a numerical grade becomes more useful when our performance along the continuum becomes more and more abstracted. That is, when I can't directly see the results I would like a grade to know whether I'm improving. The creation of a product, like a paper or project, probably doesn't require a grade along the way because I have a few good exemplars to look at and I have my previous attempts to tell that I've been improving. Specific criterion-referenced feedback will get me there.

On the other hand, if my goal is greater conceptual knowledge it would help me to have some sort of continuum-based evaluation. It's harder for me to tell if I'm going in the right direction when I don't have an actual product in front of me to stare at. Certainly feedback is still crucial here, but there's really no easy way for me to tell if I'm going in the right direction. A numerical score helps let me know I'm improving.

Do grades get in the way of the feedback? They absolutely can. But there's nothing that says that grades and feedback have to be given at the exact same time. I also think this is largely an enculturation issue. Usually when students get grades and feedback, they have no opportunity to use their feedback so they have no reason to actually look at it. Looking at feedback is usually a waste of time. But if it's "this is how you score now, here's your feedback to get you higher, go use it" you're far more likely to get that feedback used.

@CalcDave- I'm going to definitely disagree with you on the "all are a little formative and a little summative." I'm 100% sure there are many of us that give tests, enter in scores, and move on. Same with the kids. Take a test, look at the score, move on. Nothing changes.

David Cox said...

I'll have to agree with JYB on this one. And I'll add: Is it possible that we are all trying to describe the same thing but from a different perspective?

For my skills tests, I assess one skill at a time. It is very targeted; very specific. As soon as my students finish their test and hit "submit," they see the correct answers and worked out solutions with verbal explanations. (I'm even learning to create the feedback on the dynamic questions I create myself) I can't imagine more feedback than that. Now what does the score mean? I try to include a few basic questions, a couple more difficult and a free response that will rule out the guessing factor. I kinda described this pretty thoroughly here. Students understand the rubric to mean something like this:
4=nailed it
3=approaching target
2=sees target
1=shooting the wrong target

I think I need to make something perfectly clear. In now way am I saying that all formative assessments need to be graded (by that I mean scored and put in the gradebook). I am saying that just because I put a score in the gradebook doesn't exclude that assessment from being formative (which is what I think Eric and Calculus Dave is saying).

Two things that I think we need to spend our time discussing (and it's not whether an assessment is formative or not):

1. What does a student do to bridge the achievement gap? And what does a proficient student do while we are working with the less than proficient students?

2. How can we take the stigma off THE GRADE!

If we truly believe that learning is a conversation, then that conversation takes place many different ways: written assessment, class activities, collaborative activities, etc.

I have found that if I express to my students that I don't really care for grades but I'm required to submit some sort of letter that is supposed to tell Mom and Dad how they're doing and explain to them exactly how that letter is derived, then they get it. I don't have nearly as much "test anxiety" as I used to have. In fact, I never discuss "grades" with students and I keep my gradebook scores uncalculated so the only thing the students, parents and I see in the gradebook are their proficiency levels for each skill (1-5). I calculate right before I hit submit at the end of a grading period adn un-calculate right after.

And Karl, glad you joined in here. This is definitely helping me think this through and I look forward to anything you may add.

Matt Townsley said...

I'd like to add one more thing to your list, Davidif you'll allow me. :)
What are we doing to help students before the assessment that goes into the grade book?

If it's not a whole lot, I've still got a beef with putting these quizzes into the grade book and assuming kids are going to come in outside of class to improve their scores. I know, details, details...

I think your last comment, Davidreally cleared up a few things in my mind (and it saved me from writing a giant post of my least for now)

Karl Fisch said...
This comment has been removed by the author.
Karl Fisch said...

Eh, comment got messed up. Let me try again.

Like most folks here (apparently), I’d just as soon we didn’t have grades at all. Like most folks here (assuming), I don’t have that choice. I've toyed with the idea of just giving feedback without the grade, but it just seems to fall apart with the restrictions we're under. In my school I not only have to report grades at the end of the semester, but my gradebook is online and expected to be reasonably update all the time. And we pull weekly eligibility directly from the gradebooks, so there has to be something reasonably representative of where the student is at in the gradebook all the time. So, for me, I have to move past the “should we have grades” issue for now, and focus on the assessment.

I’m with David here, I think we should talk with our students more about this. I think most of them are very capable of understanding the argument we’re making here about grades (although some won’t agree). Will all of them get it completely? No, but then again neither do we. Do I think most of them will get it enough to be able to focus on what we want them to focus on? Yes.

So, a question I have is how quickly and how thorough does the feedback need to be after these assessments? For those of us without laptops and a system like exam view, there’s going to be a little bit of a lag time there. My current plan (at least it was before you guys started messing with my head) is for students to work out the problems in front of the class immediately following the assessment. While they won’t have their assessment in front of them (due to the g-word), I still think that’s pretty decent immediate feedback. Those solutions will then be posted to the website and – combined with the info in our online gradebook which I’ll have updated by that night – they’ll have a pretty good idea of what they need to work on even before getting the assessment (with grades and comments) back.

One more practical question for David: When you say your only assess one skill at a time on those assessments, is that really just one skill per assessment? Or do you have multiple skills on the same assessment and then break them out in your gradebook?

I think it would help me a lot to come visit all of you and spend a day in your classrooms.

David Cox said...

Does something have to take place before an assessment? What if I gave a pre-test to see if a student has been taking my advice and actually watching my online examples and was ready to assess before the concept had actually been talked about in class? Should that student's proficiency level not be placed in the gradebook?

You've mentioned a lot about the fact that your students have to come in on their own time to reassess. What if you allowed what you are currently using as an ungraded FA to become the baseline score (where am I now?) and then let the time you use in class for what you're calling the SA be the reassessment? You'd actually be able to schedule reassessment time into your class. (you know I have to push you on this, right?)

Yes, I currently assess one skill at a time. To be honest, we have been doing a lot of experimenting with our assessment practices. Our district is in PI-4 but our school has the best scores in the county (go figure). Next year, my process may look a little more like that which you described.

I like your idea of having students work the problems right after the test. Do you plan on capturing a static solution and posting it or will you have your students do a mathcast of the solution?

I've had my students compare answers and then decide on a "group" answer which they then write on the whiteboard easels I have throughout my room. I have the ability to do more than that with the equipment I have in class but am still learning how to best utilize these tools.

As for the classroom visit, I'd love to have you. In fact, my master teacher moved out your way a few years ago.

Matt Townsley said...

What if you allowed what you are currently using as an ungraded FA to become the baseline score (where am I now?) and then let the time you use in class for what you're calling the SA be the reassessment?
David: Now we're talking about things that make sense to me! In my context which is different than Karl's as he described so eloquently over on my blog, it doesn't seem to make sense to give very little individual feedback to students, enter a score for their first written FA in the grade book and then expect them to come in outside of class to re-assess. It's not really a whole lot different than the "old system" other than the re-assessment piece (and in my opinion is an attempt at making summative assessment optionally formative rather than overhauling the entire culture of the classroom) What you're suggesting is assigning numbers to the written FA, which I did initially when I started this system a little over a year ago. I went away from it, because I felt students were more interested in the score than the changes they needed to make or the comments on their papers. <-- Helping students move past this mentality takes plenty of class discussions and time, agree? Karl, heads up, that's what you've got to look forward to. :)

Karl, you're welcome in my classroom here in Iowa anytime. While you're hear, it might be fun to visit Shawn C. next door, another standards-based grader who blogs at

Karl Fisch said...

David - My current plan is just to post a PDF of the solution as worked out by the students. My initial thought was to record it (mathcast) but, after talking that over with my wife (who teaches first grade right now, but used to teach middle school, including Algebra in 8th grade), I decided that was just a little bit too much too fast. I feel like the added complexity of putting a microphone on the kids, as well as the added level of self-consciousness on the part of the kids (not to mention remembering to start and stop the recording, and the rendering time) isn't worth the benefit I'd see by having the audio added. I may change my mind about that in year 2 (if I see a year 2).

So, I know between all the different blog posts each of you has done about this I should have it pretty clear in my mind what this looks like, but I still don't. I'm unclear on the exact sequence of events in David and Matt's classes in terms of instruction (live or recorded), pre-assessment (or FA or whatever you call it), the scope and format of that pre-assessment (paper, exam view, how many questions/concepts, even simply what it looks like format-wise), what the feedback to kids looks like on that (and whether you put anything in the gradebook), what the next step is (instruction, in-class assessments, out-of-class assessments, what gets put in the gradebook and when), and probably some more pieces in there somewhere.

Would it be worth putting something very detailed together somewhere (perhaps a wiki, because what I'm envisioning would be awfully long for a blog post)? I know you each have probably already done this in a blog post previously, but I sense that you both are modifying your ideas some and perhaps a new, this-is-what-I'm-thinking-for-next-year-right-now assessment post/wiki/whatever might be worth your time thinking through. Just a thought, no need to respond if that doesn't make sense to you.

David Cox said...

Matt Are you looking to change the culture of your classroom or are you just looking at becomming note efficient with your assessment, feedback, reteach and reassessment? (I guess maybe that would constitute culture change, wouldn't it?) I found that the discussion on what a grade actually means is worth the time. Plant the seed early.

Te export to PDF feature with Smart is great, isn't it? I'm interested in your wiki idea even if I'm not exactly sure what that entails. Following the blog trail gets tough sometimes. And one thing I know for sure: as soon as I start thinking I'm seeing something clearly, it's time to rethink how I'm looking at it.