Non-continuous

How to Grade Without Grading Anything

Mike asked and so I’ll share.

The underlying ideas here are, first, that when students see grades they think something is finished. They look at the grade and either smile or frown. Then they file the paper away – too often in the circular file. Secondly, even if I have provided feedback on the paper, the grade rules and the feedback is generally ignored. So, in the footsteps of one of my heros, Shawn Cornally, I got rid of the problem – the grades.

My thinking has shifted on assessment lately also. I used to think that if I was studying domain and range with my honors precal kids, then my assessments should be a few domain and range problems. Usually they are pretty low level Bloom’s stuff and kids that could memorize and repeat had an advantage. I hate admitting this about my assessments, but in general I think teachers test what is easy to test. The thing that changed my mind though was realizing that these same types of problems that I was testing on were the problems we were already looking at in class. What data was testing on them going to get me that I didn’t have already?

So, I decided my “assessments” would be more open ended or application type, and try to get at the big picture of whatever we are studying. Like this one on on functions or this one on on domain and range.

The students complete those in around 15 minutes each and then I put feedback on them that night. I try to stagger them, so I only have one class to do per night. They are handed back the next day(ish) and the students respond to my feedback. This feedback loop continues until I feel like I’ve gotten the most I can out of the majority of the students. I think 3 revisions is the most I’ve done. Both the original shot at it and the revisions are all done in class under test like conditions.

For the first four weeks of school the two problems above were the ones that I decided would make up a students grade so far. I decided on this format for helping the students reflect on their work. Below the dotted line is where it’s my turn to make comments.

Here is a student sample of the work including all feedback. And here is the completed grade summary that goes home for a parent signature and comments.

My comments on the grade summary were directed at advice to help students get better, a goal for the student, and/or a statement of agreement or disagreement with the student’s evaluation. Parents would have an idea of what their student’s grade was before progress reports came out and more importantly, some concrete information on why their grade is what it is.

Next thing to think about is how to have students summarize a grade for themselves for an entire quarter worth of work (and eventually a semester). They have 2 assessments on domain/range, 2 on functions, and 1 on transformations of functions. Maybe a summary of each idea which is then somehow combined into a single letter grade, or maybe a holistic approach that looks at their overall progress. I’m open for suggestions.

I haven’t graded ANYTHING yet.

That’s right! I have not put a grade on one piece of work so far this year.

Here are the pro’s:

• Students don’t ask what their grade is.
• Students don’t ask why their grade is what it is.
• Parents don’t e-mail me and complain ask about their student’s grade.
• My students are enjoying learning for the sake of learning.
• My students are revising their work and are showing gains in understanding.
• I can see students getting better and I actually feel like I’m developing talent in them.
• Students are evaluating their own work and justifying their evaluations – based on the work.
• I am communicating with parents about student work and their understanding of it.

CagleCartoons.com

Here are the con’s:

• I have more work to do than “usual”.
• My friend and colleague Dave has a lot more and it may make him explode (or implode).
• I have to provide 2 progress grades per quarter and 1 final semester grade per administrative rules.  It is becoming difficult to provide a “final” letter grade when nothing is graded.
• Very concrete minded kids feel that if their work is not judged in a sort of right/wrong/ABCDF way they aren’t anchored to anything.

All in all I am really very happy with the results.  Especially my Juniors – I have never enjoyed my Juniors in Honors Precalculus more than I do this year.  I thought about if it was just the kids or how I am rolling now with grades.  I distinctly remember liking previous classes until the grades started rolling out on assessments.  Then it quickly became nit-picky, negative, and sometimes confrontational.  In short – we were having conversations about grades rather than having conversations about math.  That sucked and I hated every minute of it.  By the end of last year a lot of my kids would roll their eyes and go “Oh boy, here it comes” anytime someone brought up their “grade”.  Grades do not equal learning and in many ways I think they prevent it.  If kids don’t need them to learn and we don’t need them to teach, then why do it?

I’ve left a lot out of this story and if anyone is interested, I’ll share more of what I am doing in place of grades.  My challenge now is to figure out how I’m going to have the kids justify their quarter grades…

Algorithm-o-rama

So, my son is in second grade but has math with the third graders. Right now their area of focus is “Regroup Ones and Tens.” This is a picture of what he is doing:

His complaint is that he doesn’t like the way they are doing it. In his mind #2 looks like this: 200 + 300 = 500, 80 + 60 = 140, and 4 + 7 = 11. So the answer is 651. He is disturbed by the idea that he has to work right to left. To him it is counter-intuitive (for obvious reasons, I think).

“Not liking something is not a reason for not doing it” would be my normal reply but in this case I’m not so sure. What is gnawing at me is something he said about #13. He sees the 6 + 5 as 11 (and has obviously been instructed to write that down in an attempt to explain why we leave the 1 in the “ones place” and move the ten to the “tens place”). I’m a little puzzled why they stop there and don’t write down 130 somewhere to be consistent, but anyway when he got to the end he added the 9 and the 1 and said it was 10. That bothers me. He doesn’t see it as 1000. I’m not sure if he sees it as 900 + 100 and hasn’t made the connection that 10 100′s is one thousand, or if he doesn’t even see it as that.

I’m pretty sure if he were doing it the way he wanted to do it (left to right), he would have no problem getting 900 + 120 + 11 = 1031. And he would understand the magnitude of the number. I’m afraid he is starting to just do stuff because the teacher says to. This is where kids start to dislike math. “I can do this stuff in a way that makes sense to me (and is mathematically sound) so why do I have to jump through hoops? That’s stupid.” I would agree.

So now I’m running through how I might broach this issue with his teacher. I want to do it in a way that doesn’t smack of “I know better than you.” Then, anticipating her response to “he needs to use the standard algorithm in order to do subtraction with ‘regrouping’” I’m again wondering why? He can come up with a method of working left to right with subtraction as well. One that reinforces place-value like what he does with addition.

Before I take this on, I need to know where I’m wrong. I’m thinking that I personally do not use any standard algorithms for addition or subtraction. Or multiplication or division for that matter. (In fact I’m convinced that partial products when multiplying both makes more sense and makes things easier in high school when we need to start multiplying polynomials.) I mean, does anyone other than third graders use standard addition and subtraction algorithms? Can we do without them?