Using rubrics - The letter grade on steroids

In my last post, I began discussing alternatives to the standard letter grade and mostly wrote about using narratives for evaluating work. Tonight, I'd like to discuss the use of criteria and grading rubrics.

Criterion-based grading, for me, is a large improvement on the standard math teacher grading system (i.e. add up points earned and divide by points possible to get a percentage that converts to a letter). I use criterion-based grading exclusively in my Senior Stats course. Here is an example of grading rubric I used this year.

Here is how I use my rubric. I read through the project as a whole, making notes and comments as I go. I then evaluate each criterion, one by one. Each criterion has various achievement levels. Some go from 0 to 2, others from 0 to 4. In order to reach a level 2, a project must satisfy all of levels 1 and 2. To reach level 3, a project must satisfy all the requirements of all 3 descriptions.

I attempt to write the descriptions as plainly as possible and in a logical progression so that attaining a higher level should show an improved understanding. For example, take my "Displays" criterion. To reach level 1, a student must only create one correct display that is relevant to the project topic. Level 2 is attained if a student makes multiple types of displays. So making 2 different histograms would be insufficient. Making a histogram and a boxplot would satisfy the description. In each case, the displays must be made "correctly," meaning, in part, that they should be accurate and be labeled sufficiently. To reach level 3, the displays must "communicate well" and have a "high level of accuracy." Essentially, this is a way for me to distinguish between the student that makes a few sloppy displays and the student who makes a few excellent displays. Finally, level 4 requires a certain degree of sophistication within the displays. This means that they are all effective and lead to insightful analysis. There is a level of complexity within the displays.

So, I evaluate the project against all of the criteria. I write narrative comments for each criterion to explain why a certain level was awarded. I note errors as well as strengths. This example will give you a taste of what I try to do each time (you can zoom in on the image to make it large enough to read).

In the end, however, by using achievement levels, what I've really done is assign a variety of grades to a project. In a sense, I've given a student a "letter" grade for their introduction, another for their data, one for their calculations, and so on. So, I feel like I'm not exactly moving away from the letter grade entirely. And, given where I teach, in the end, I do have to assign an actual letter grade to the project. So, I do my voodoo and do that. More on my voodoo in another post. I'm tired. Good night.

If not a letter grade... then what?

The basic theme of this blog is my disdain for the letter grade. As a professional educator, evaluation of students is a big part of my life. So, if I were to not use letter grades, then how would I evaluate my students?

The first idea that comes to mind is a narrative comment. Allow me to consider a hypothetical situation to better explain what I mean. I teach math, so students take many tests (and no, I do not like tests either, but that seems to be a discussion for a different blog... at the very best it's a tangent, and being a math teacher, I should know all about tangents, both the mathematical kind as well as those meandering ones such as when I start going off about tangents when I am supposed to be considering evaluation... )

Anyway, let us pretend that I give my ninth graders a test and the test includes problems on algebra, some on trigonometry, a few on matrices, some graphing, and some transformation problems. As this is math, I can create an answer key and I can correct a student's work against this answer key and I can quickly see a student's mistakes. I do not merely consider a student's answers; I also look at the supporting work, that is, the steps a student took to find, for example, the inverse of a matrix or to solve an equation. So, regardless of a student's answer, I can see the methodology and, really, the thinking a student utilized to arrive at their answer. Thus, I can evaluate not only the correctness of their answers but also the appropriateness of their method and their ability to communicate this method.

So, I go through and correct their test. I mark which answers are right, which are wrong, and I indicate where their method is appropriate and where it is not. Like most math teachers I know, I can award points for correct answers as well as for supporting work. So, then I add up all of these points and arrive a number. Now, many math teachers would know the possible number of points one might earn on a test, and at this point they would divide the number a student earned by the total possible to get a percentage which they would then convert magically into a letter. (See my last post to read some of my opinions on that.) But, the point of this post is to consider what to use in place of such a letter grade.

Back to the student's test... they have earned a number of points. Some of these points are for correct answers and some are for correct methods. Now, that number of points itself is feedback for a student and is thus a form of evaluation. Moreover, if I indicate clearly where they earned points and where they did not, then that is another level of evaluation. A student can see if they used the proper method and if their use of that method led to a correct answer. That, much more than a letter grade, tells a student if they have correctly learned how to find the inverse of a matrix or if their equation solving techniques are strong.

So, without any narrative comment (and without a silly letter), I have already provided a student with copious information regarding how they did. But, I have not really passed any sort of judgment yet as to my opinion on the quality of their work.

So, now the narrative comment becomes useful. I could convey to a student if I think they did well or not. I could judge their performance compared to earlier work. I could specifically state if they were strong on matrices, but weak on algebraic equations. I could clearly point out whether they chose the best methods or not and how accurate their answers were. I could also judge if they have been learning as much as I think they should have up to that point. Additionally, I could outline areas that they ought to focus on as they strive to improve.

Such a narrative could fill half a standard sheet of paper or more. Such a narrative could take 10-15 minutes to write. Such a narrative would provide far more useful feedback to a student than any letter grade could ever hope to.

But, what is the cost of such a narrative, filled as it would be entirely with my opinions? Does my opinion on the quality of the work really matter? Couldn't my corrections stand alone as all the evaluation I do and couldn't I then let a student make up their own opinions on the quality of their performance? That is a discussion for a future post.